Free CFA Level I 2027 Practice Exam Questions

This full-length practice set contains 180 three-choice, single-answer questions across the ten 2027 topics. Start at Question 1 , record your choices, then open the explanations to review your reasoning.

These are original Finance Prep practice questions. They are not official CFA Institute questions, copied live-exam content or exam dumps. Mastery Exam Prep / Finance Prep is independent from CFA Institute.

For exams beginning February 2027: use the official curriculum for your booked sitting. This set is not a 2026 curriculum mock.

Pacing your attempt

The official exam has two 90-question sessions of 135 minutes each. For a pacing exercise, allow up to 135 minutes for Questions 1–90, take a break, then allow another 135 minutes for Questions 91–180. This page mixes topics across both blocks and does not reproduce the official session topic arrangement, timer or testing interface. The total working-time reference is 270 minutes, excluding your break.

Questions 1-25

Question 1

Topic: Derivatives and Risk Management

A coffee roaster is considering a derivative covering a specified quantity of coffee. Cash settlement is linked to the difference between the market price of coffee and a price fixed at contract inception. The summary omits the settlement schedule and the parties’ payment obligations.

An analyst tentatively classifies the derivative as a forward contract. Which additional contractual provision would most likely make this classification defensible?

• A. One party may elect to receive a positive price difference on a specified future exercise date.
• B. Both parties must settle the price difference repeatedly, on specified quarterly payment dates.
• C. Both parties must settle the price difference once, on a specified future maturity date.

Best answer: C

Explanation: A forward contract obligates both counterparties to settle an agreed transaction on a specified future date. For a cash-settled commodity forward, the specified quantity multiplied by the difference between the market price at maturity and the contractual price determines the payment. The sign of that difference determines which counterparty pays; an unfavorable price movement does not permit either party to walk away.

A fixed reference price alone does not identify the derivative. Repeated obligatory fixed-versus-market price settlements are characteristic of a commodity swap. A holder’s right to exercise for a favorable payoff, rather than an obligation to settle either outcome, is characteristic of an option.

• A. A unilateral right to receive a favorable price difference describes an option rather than a forward’s obligation to settle.
• B. Repeated obligatory settlements of fixed-versus-market price differences characterize a commodity swap rather than a single-date forward.
• C. An obligatory, two-sided settlement on one future date supports classification as a forward rather than a periodic exchange or an exercise right.

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Question 2

Topic: Fixed Income

An analyst values an option-free, fixed-rate bond at settlement immediately after a coupon payment. The bond has the following terms:

• Par value: $1,000.
• Remaining maturity: five years.
• Annual coupon rate: 6%, paid semiannually.

The baseline value is $1,000 at a nominal annual yield of 6%, compounded semiannually. The analyst revises the required nominal annual yield to 4%, also compounded semiannually. The settlement date and promised payments remain unchanged.

Which revised valuation is most accurate?

• A. $1,089.83, representing a premium to par.
• B. $918.89, representing a discount to par.
• C. $1,047.13, representing a premium to par.

Best answer: A

Explanation: A bond’s value equals the present value of its remaining coupons and principal. The discount rate and number of periods must match the payment frequency. Here, each semiannual coupon is $30, five years contains ten payment periods, and the revised semiannual yield is 2%.

\[ P = 30\left(\frac{1-(1.02)^{-10}}{0.02}\right) + 1{,}000(1.02)^{-10} = 1{,}089.83 \]

The lower required yield raises the bond’s value from par to a premium of $89.83. Its 6% coupon rate exceeds the 4% required yield. Coupon income is not the total required return: buying above par introduces a loss between the purchase price and principal repayment at maturity, which offsets part of the coupon income.

• A. Discounting ten $30 semiannual coupons and the $1,000 principal at 2% per period gives $1,089.83; the coupon rate exceeds the required yield.
• B. This value results from treating the 4% nominal annual yield as a semiannual rate rather than dividing it by two.
• C. This value uses five discounting periods instead of ten, incorrectly treating five remaining years as five semiannual periods.

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Question 3

Topic: Alternative Investments

An analyst reviews an illiquid real estate partnership launched five years ago. The partnership uses no borrowing.

Performance evidence:

• Quarterly returns use appraised property values updated annually and held unchanged between updates. The annualized net Sharpe ratio is 1.30, compared with 0.65 for an index of leveraged listed property companies. Both ratios use quarterly returns and the same risk-free rate.
• Two properties were sold close to their latest appraised values. Investors made irregular contributions and received uneven distributions. The net since-inception IRR is 13%, versus the index’s 9% annualized time-weighted total return over the same period.
• A peer database includes only active funds, excludes liquidated funds with poor returns, and incorporates mostly strong pre-enrollment histories submitted by new entrants.

Which interpretation is least accurate when assessing the reliability and comparability of this performance evidence?

• A. Matching index investments to dated investor cash flows would improve timing comparability and leave leverage differences relevant to attributing performance to skill.
• B. Removing pre-enrollment return histories would address backfill bias and make the active-fund sample representative of the full fund population.
• C. Sales near the latest appraisals would corroborate those valuation levels and leave the effects of stale valuations on interim volatility unresolved.

Best answer: B

Explanation: Backfill bias and survivorship bias are distinct. Removing pre-enrollment histories addresses favorable retroactive reporting, but it does not restore excluded liquidated funds. The peer database can therefore overstate representative performance even after backfilled returns are removed.

Realized proceeds close to appraisals support valuation levels at sale, not the accuracy of quarterly economic returns between annual updates. Stale appraisals can suppress measured volatility and inflate the Sharpe ratio.

The partnership’s IRR is money-weighted, whereas the index return is time-weighted. Applying the same dated investor cash flows to hypothetical index investments improves timing comparability. Differences in leverage, liquidity, and other risks still matter. Neither a higher IRR nor a higher appraisal-based Sharpe ratio establishes superior manager skill.

• A. Cash-flow matching aligns the money-weighted comparison, but leveraged listed companies still have a different risk profile from the unleveraged partnership.
• B. Deleting backfilled histories does not restore excluded liquidated funds, so survivorship bias remains and the active-fund sample is still unrepresentative.
• C. Agreement at sale does not establish how economic values fluctuated between appraisal updates, so it does not validate reported volatility or the Sharpe ratio.

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Question 4

Topic: Ethical and Professional Standards

Anika Rao, CFA, owns and controls an investment company. Its East and West brokerage accounts each initially hold 60,000 shares of a thinly traded stock. Before arranging the trades below, Rao writes:

“Use these trades to lift reported activity and draw outside buyers for our planned sale.”

The trades execute at prevailing market prices. The exchange counts each execution once in reported trading volume.

Trades among unrelated investors total an additional 15,000 shares, bringing the day’s reported volume to 75,000 shares. Rao then posts publicly:

“Most of today’s 75,000-share trading volume represents buying by investors independent of our company.”

Under Standard II(B), Market Manipulation, which assessment of Rao’s conduct is most accurate?

• A. The conduct involves information-based manipulation only.
• B. The conduct involves transaction-based manipulation only.
• C. The conduct involves both transaction-based and information-based manipulation.

Best answer: C

Explanation: Standard II(B) prohibits practices intended to distort prices or artificially inflate trading volume to mislead market participants. Manipulation does not require execution at an artificial price.

Rao controls both sides of 60,000 shares of executions. The offsetting trades leave each account’s holdings unchanged and do not change the company’s economic exposure. They nevertheless account for 80% of the 75,000 shares reported as trading volume. Arranging these trades to attract outside buyers constitutes transaction-based manipulation.

The public statement introduces a separate misleading claim. Only 15,000 shares, or 20% of reported volume, involved unrelated investors. Although the total volume figure is accurate, attributing most activity to independent buyers is false and constitutes information-based manipulation.

• A. The arranged trades also artificially inflate activity to attract outside buyers; execution at prevailing market prices does not make them bona fide.
• B. Although the reported volume total is accurate, Rao falsely attributes most of it to independent buyers, so her statement also constitutes information-based manipulation.
• C. The controlled-account trades artificially inflate activity, and Rao’s statement misrepresents the source of 80% of the reported volume.

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Question 5

Topic: Financial Statement Analysis

An IFRS-reporting manufacturer reports an operating margin of 10% in 2025 and 14% in 2026.

2026 disclosures:

• Management extended the estimated useful lives of production equipment.
• The revision is described as a change in estimate and applied prospectively; the 2025 comparative is unchanged.
• Lower depreciation accounts for the entire margin increase.

An analyst developing an earnings forecast recommends that the company retrospectively restate 2025 earnings before comparing historical margins.

Which additional finding would make this recommendation most appropriate?

• A. The revised estimate will have a material effect on depreciation expense throughout the remaining service lives of the affected production equipment.
• B. The revised estimate incorporates operating information that first became available after the 2025 financial statements were authorized and materially reduces depreciation.
• C. The original estimate omitted reliable information reasonably obtainable before the 2025 financial statements were authorized, causing a material misstatement of depreciation.

Best answer: C

Explanation: Under IFRS, a useful-life revision resulting from new information is a change in accounting estimate. It affects depreciation prospectively in the current and future periods; previously reported earnings are not restated. A material prior-period error is different: overlooking reliable information reasonably available when earlier financial statements were authorized ordinarily requires retrospective correction.

Lower depreciation explains the entire increase from 10% to 14%, so the higher margin does not establish improved underlying operating performance. Formal restatement would be appropriate if the original estimate caused a material error, rather than simply being superseded by new information.

For forecasting, the analyst should separate the depreciation effect from operational trends. The revised depreciation estimate may support a higher future reported margin if it remains appropriate, but the four-percentage-point increase should not be extrapolated as recurring operational improvement.

• A. Materiality and persistence affect the importance of the revised estimate but do not convert a prospective estimate change into a prior-period error.
• B. Information first available after authorization supports a prospective estimate revision rather than demonstrating that the earlier financial statements contained an error.
• C. A material misstatement caused by overlooking reliable information reasonably available before authorization is a prior-period error that warrants retrospective correction.

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Question 6

Topic: Economics

An analyst compares relations between two countries with those of five years earlier.

• Government relations: A joint flood-control treaty remains in force, but the governments discontinue regular security talks and expand reciprocal restrictions on defense-related exports.
• Private business activity: Firms expand cross-border production partnerships, and annual bilateral trade and private foreign direct investment flows increase.

Based on these observations, which conclusion about geopolitical behavior and economic globalization is most appropriate?

• A. Cooperation between the governments has increased, and economic globalization has increased.
• B. Competition between the governments has increased, and economic globalization has decreased.
• C. Competition between the governments has increased, and economic globalization has increased.

Best answer: C

Explanation: Geopolitical cooperation and competition are dimensions of behavior, not fixed national labels or synonyms for globalization. Governments can compete over strategic interests while private firms deepen cross-border economic connections.

Here, ending security talks and expanding reciprocal export restrictions indicate increased competition between the governments. The continuing flood-control treaty shows that cooperation persists in another policy area. Meanwhile, growing production partnerships, trade, and private foreign direct investment indicate greater economic globalization. Integration driven by non-state actors does not establish that governments have become more cooperative, and greater strategic rivalry does not necessarily reverse cross-border economic integration.

• A. Expanding private business links indicate globalization rather than increased government cooperation; the governments have ended security talks and tightened reciprocal export restrictions.
• B. The observed expansion of production partnerships, bilateral trade, and private investment indicates greater economic integration despite the governments’ increasingly competitive behavior.
• C. Ending security talks and widening reciprocal export controls indicate greater government competition, while expanding production links, trade, and private investment indicate deeper economic integration.

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Question 7

Topic: Ethical and Professional Standards

An investment firm offers Maya Chen, CFA, responsibility for supervising a trading team. Her authority would cover work assignments and performance reviews.

Compliance findings:

• Personal-trading checks rely on annual employee certifications. Neither Chen nor compliance staff can access records needed to compare personal trades with client orders.
• Chen cannot require preclearance or enforce personal-trading restrictions without senior management’s approval.
• Chen reports the deficiencies and recommends access to transaction records and enforceable trading controls. Senior management rejects both changes.

Which response is most appropriate under the CFA Institute Standards of Professional Conduct?

• A. Accept the supervisory appointment after documenting the limitations and obtaining senior management’s written acknowledgment of the compliance risks.
• B. Accept the supervisory appointment after delegating personal-trading reviews to compliance and arranging regular reviews of its monitoring reports.
• C. Decline the supervisory appointment in writing until the firm adopts reasonable procedures for monitoring and enforcing personal-trading rules.

Best answer: C

Explanation: Standard IV(C), Responsibilities of Supervisors, requires reasonable efforts to prevent and detect violations by people subject to a member’s supervision or authority. When compliance procedures are inadequate, the member should notify senior management and recommend corrective action. If those deficiencies prevent effective supervision, the member should decline supervisory responsibility in writing until reasonable procedures are adopted.

Chen has already reported the gaps and recommended remedies. Her authority over assignments and performance reviews does not provide the records or enforcement powers needed to supervise personal trading. Senior management’s refusal leaves her unable to exercise effective supervision. Delegation may support an adequate supervisory system, but it does not remove the supervisor’s responsibility or repair the underlying deficiencies.

• A. Senior management’s acknowledgment documents the deficiencies but does not establish the monitoring and enforcement procedures needed for Chen to supervise effectively.
• B. Delegating reviews cannot overcome compliance staff’s lack of transaction records, and Chen would retain responsibility for reasonable supervisory efforts.
• C. Because Chen cannot establish or enforce adequate controls, she should decline the appointment in writing until reasonable supervisory procedures are adopted.

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Question 8

Topic: Corporate Finance

Harborwell’s CEO proposes acquiring a supplier owned by Harborwell’s controlling shareholder. The board has delegated acquisition negotiations to the CEO, who has no ownership interest in either company. The purchase would be financed with additional debt and substantially increase Harborwell’s revenue.

An analyst interprets the recommendation as reflecting a conflict between managers and shareholders. Which additional finding would make this interpretation most defensible?

• A. The acquisition would increase the expected value of Harborwell’s equity while reducing the expected value of its outstanding bonds.
• B. The acquisition would increase the CEO’s revenue-linked bonus while reducing the expected value of Harborwell’s equity.
• C. The acquisition would provide above-market sale proceeds to the controlling shareholder while reducing the expected wealth of minority shareholders.

Best answer: B

Explanation: Managers act as agents of shareholders, who delegate decision-making authority while seeking to maximize shareholder wealth. A manager-shareholder conflict arises when managerial incentives encourage decisions that benefit managers at shareholders’ expense.

Here, a revenue-linked bonus could reward company growth even when the acquisition destroys equity value. Because the CEO owns no shares, the CEO would receive the increased bonus without bearing the associated equity loss.

The parties benefiting and bearing the loss distinguish different agency conflicts. Above-market proceeds benefiting a controlling shareholder at minority shareholders’ expense indicate a conflict among shareholders. Increased equity value accompanied by reduced bond value indicates a conflict between shareholders and creditors.

• A. Higher equity value accompanied by lower bond value indicates a shareholder-creditor conflict because the wealth transfer occurs between capital providers.
• B. The revenue-linked bonus rewards the CEO for expanding the business even when the acquisition reduces shareholder wealth, demonstrating misaligned manager-shareholder incentives.
• C. Favorable sale terms at minority shareholders’ expense indicate a conflict among shareholders rather than establishing a personal incentive for the CEO.

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Question 9

Topic: Ethical and Professional Standards

A CFA charterholder refers a client to an outside investment manager and knows that the manager pays the charterholder’s firm a $600 referral fee.

• Local law expressly permits such referral payments without client disclosure or consent.
• The charterholder neither discloses the payment nor obtains the client’s consent before the management agreement is signed.
• The recommendation is suitable, the payment does not increase the client’s fees, and the client subsequently earns a positive net return.

Which assessment of the charterholder’s conduct is most accurate?

• A. The conduct complies with local law but violates professional standards because the charterholder failed to disclose the referral fee.
• B. The conduct complies with local law but violates professional standards because the client did not provide written consent to the arrangement.
• C. The conduct complies with local law and professional standards because the recommendation was suitable and did not increase the client’s fees.

Best answer: A

Explanation: Legal permission does not establish compliance with professional ethical standards. Under Standard VI(C), Referral Fees, a CFA charterholder must disclose compensation received by the charterholder or the employer for recommending products or services. Disclosure should communicate the nature and value of the benefit before the client enters an agreement for services.

Here, the firm’s $600 payment creates a disclosure obligation even though local law permits nondisclosure. A suitable recommendation, unchanged client fees, and favorable investment performance do not remove the potential conflict or replace disclosure. The applicable professional duty requires disclosure, not written client consent.

• A. Standard VI(C), Referral Fees, requires disclosure of referral compensation received by the member or the member’s employer, despite local legal permission.
• B. The applicable referral-fee obligation requires disclosure before the service agreement, not written client consent; the violation is the undisclosed payment.
• C. Suitability and unchanged client fees do not eliminate the professional obligation to disclose compensation received for recommending investment services.

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Question 10

Topic: Economics

An analyst obtains the following exchange-rate quotations, expressed in Swiss francs per US dollar:

Each forward point equals 0.0001 Swiss francs per US dollar. Use simple annualization with a 360-day year.

Which statement about the US dollar’s annualized forward premium or discount is most accurate?

• A. The US dollar trades at an annualized forward discount of 0.50%.
• B. The US dollar trades at an annualized forward discount of 2.00%.
• C. The US dollar trades at an annualized forward premium of 2.00%.

Best answer: B

Explanation: Signed forward points are added to the spot rate after conversion using the point size. The outright forward rate is \(0.9000 + (-45) \times 0.0001 = 0.8955\) Swiss francs per US dollar.

Because the quotation measures Swiss francs per dollar, the lower forward rate means the US dollar is at a forward discount. Its annualized percentage is:

\[ \left(\frac{0.8955 - 0.9000}{0.9000}\right) \times \frac{360}{90} = -2.00\%. \]

Thus, the US dollar trades at a 2.00% annualized forward discount, while the Swiss franc is correspondingly at a forward premium. This pricing relationship does not guarantee the direction of future spot-rate movements.

• A. The 0.50% discount applies to the 90-day term; multiplying by 360/90 gives an annualized discount of 2.00%.
• B. Subtracting 45 points gives 0.8955 Swiss francs per US dollar, a 0.50% term discount that annualizes to 2.00%.
• C. Negative forward points make each US dollar buy fewer Swiss francs forward, so the dollar trades at a discount rather than a premium.

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Question 11

Topic: Alternative Investments

An analyst compares three investments with similar underlying office properties. Each structure has debt equal to 40% of its underlying property value.

Ownership terms:

• Direct property: The investor controls leasing and maintenance. Selling the building typically takes six months.
• Private real-estate fund: A manager controls operations and financing. Units are valued quarterly using appraisals and cannot be redeemed during the seven-year fund term.
• Listed REIT: Managers appointed by the board control operations and financing. Shares trade daily on an exchange at market-determined prices.

Which assessment of the ownership exposures is least accurate?

• A. Listed REIT ownership provides liquid, market-priced shares; exchange trading replaces underlying property-market exposure with broader equity-market exposure.
• B. Direct ownership provides control over property operations; limited investment liquidity reflects the time required to sell the underlying building.
• C. Private fund ownership delegates property operations to the manager; financial leverage magnifies changes in investors’ equity values as property values change.

Best answer: A

Explanation: Direct real-estate ownership gives the investor control over the underlying asset. Private funds and listed REITs provide indirect ownership through vehicles whose managers oversee property operations. Their investor liquidity differs substantially: the private fund restricts redemptions, whereas REIT shares trade daily.

Exchange liquidity does not remove property-market exposure. REIT cash flows and values remain linked to rents, occupancy, and property values. Share prices can also respond to equity-market sentiment and differ from underlying net asset value. Daily trading makes short-term price fluctuations observable, while quarterly appraisals may smooth reported private-fund returns without reducing economic risk.

The 40% debt-to-property-value ratio creates financial leverage in each structure. Leverage magnifies changes in equity value regardless of whether the ownership claim is a building, a private fund unit, or a listed share.

• A. Exchange trading changes liquidity and pricing, but REIT values remain exposed to underlying property income and values.
• B. The investor controls leasing and maintenance but must sell the building to exit, combining operating control with limited liquidity.
• C. Manager control makes the exposure indirect, while borrowing magnifies the percentage sensitivity of investors’ equity to changes in property values.

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Question 12

Topic: Corporate Finance

An issuer wants assured funding for its seasonal inventory build at the lowest annual net financing cost. Routine operating cash needs are funded separately.

Current policy and assumptions:

• The issuer needs $4 million throughout the final three months of each year. Operating receipts release the full amount at year-end.
• It prefunds this need with a $4 million cash reserve financed by long-term debt. The reserve is idle for the first nine months.
• Annual rates are 6% for long-term debt, 2% for reserve cash, and 10% for a $4 million uncommitted revolver.
• Long-term debt can be repaid at par before each year begins. There are no borrowing fees. Interest is simple and prorated.

Bank update: The bank irrevocably commits the revolver for the coming year, with all drawing conditions satisfied. All other conditions remain unchanged.

Which funding policy is most appropriate for the coming year?

• A. Maintain a $2 million seasonal cash reserve financed with long-term debt and draw $2 million from the revolver during the inventory build.
• B. Maintain no seasonal cash reserve and draw $4 million from the revolver during the inventory build.
• C. Maintain a $4 million seasonal cash reserve financed with long-term debt and leave the revolver undrawn during the inventory build.

Best answer: B

Explanation: Temporary working-capital needs can be matched with short-term borrowing when repayment follows the release of operating cash and funding access is reliable. The bank’s commitment removes the availability risk that justified prefunding the seasonal reserve.

Although the revolver’s annual interest rate exceeds the long-term debt rate, borrowing is required for only three months. Its annual cost is \(4,000,000 \times 0.10 \times 3/12 = 100,000\) dollars. Maintaining the full reserve requires $240,000 of year-round debt interest and earns only $60,000 during the nine idle months, producing a net cost of $180,000.

Using the committed revolver therefore preserves assured seasonal funding while reducing annual net financing cost by $80,000. This conclusion depends on the facility’s reliable availability and the predictable release of cash at year-end.

• A. The equal funding mix assures liquidity, but costs $140,000 annually: $90,000 for the reserve and $50,000 for seasonal revolver borrowing.
• B. The committed revolver assures seasonal funding at an annual cost of $100,000, avoiding the greater cost of maintaining a prefunded reserve.
• C. The full reserve assures liquidity, but its annual net financing cost is $180,000: $240,000 of debt interest less $60,000 of cash interest.

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Question 13

Topic: Economics

An investment analyst evaluates a government’s proposal for $25 billion of temporary, debt-financed public works spending to reduce a recessionary output gap.

Current conditions:

• Public debt is $1.2 trillion and annual nominal GDP is $1.0 trillion.
• Unemployment is high, productive capacity is underused, and demand for private investment loans is weak.
• Long-term, fixed-rate, domestic-currency funding is available at low yields, and monetary policy is accommodative.

Which assessment of the proposal’s near-term effects is most accurate?

• A. The proposal is likely to leave aggregate demand unchanged because future tax obligations prompt fully offsetting private saving.
• B. The proposal is likely to support stabilization because unused resources and weak private borrowing reduce crowding-out pressure.
• C. The proposal is likely to weaken private investment because debt exceeding annual GDP indicates substantial crowding-out pressure.

Best answer: B

Explanation: Government debt should be assessed relative to GDP and alongside financing conditions and the state of the economy. The initial debt-to-GDP ratio is \(1.2/1.0 = 120\%\), but no universal ratio rules out effective fiscal stabilization.

Crowding out occurs when government borrowing raises interest rates and displaces private investment. Here, idle resources, weak private borrowing, accommodative monetary policy, and low yields support the case for temporary stimulus. Additional spending can increase activity rather than primarily displace private investment.

This near-term assessment does not establish long-term debt sustainability: future debt service, economic growth, and fiscal balances still matter. Anticipated future taxes may encourage private saving, but a complete offset is not an automatic consequence of borrowing.

• A. A full private-saving offset relies on restrictive Ricardian-equivalence assumptions; future tax obligations alone do not establish that households will neutralize the stimulus.
• B. Spending can mobilize idle resources when private demand is weak, while accommodative monetary policy and low borrowing costs limit near-term crowding out.
• C. A 120% debt-to-GDP ratio does not establish substantial crowding out; slack capacity, weak private borrowing, and low yields weaken that argument.

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Question 14

Topic: Derivatives and Risk Management

A manufacturer will borrow $15 million for six months, beginning three months from today. The loan’s interest rate will be set at origination as the prevailing six-month reference rate plus a borrower-specific credit spread. The credit spread is not fixed today.

An available forward rate agreement (FRA) uses the same reference rate and notional amount and covers the same borrowing period. An analyst writes:

“Enter a pay-fixed, receive-floating FRA. Matching the notional amount and borrowing period hedges changes in both the reference rate and the credit spread.”

Which correction to the analyst’s analysis is most accurate?

• A. Retain the pay-fixed, receive-floating FRA; it hedges reference-rate risk but leaves credit-spread risk.
• B. Use a receive-fixed, pay-floating FRA; it hedges reference-rate risk but leaves credit-spread risk.
• C. Retain the pay-fixed, receive-floating FRA; it hedges credit-spread risk but leaves reference-rate risk.

Best answer: A

Explanation: A future borrower is exposed to rising reference rates. A pay-fixed, receive-floating FRA generates a gain when its settlement reference rate exceeds the agreed fixed rate, offsetting the reference-rate component of higher borrowing costs. Matching the reference rate, notional amount, and borrowing period makes the FRA suitable for that exposure.

The borrower’s credit spread is a separate component of the loan rate and will be determined at origination. FRA settlement does not depend on that spread, so spread changes remain unhedged. This creates residual basis risk between the manufacturer’s actual borrowing rate and the rate underlying the derivative. Matching the notional amount and period does not eliminate this risk.

• A. The FRA offsets the reference-rate component, but the borrower’s credit spread is outside its settlement rate and remains exposed to change.
• B. A receive-fixed, pay-floating FRA loses when the reference rate rises, reinforcing rather than offsetting the manufacturer’s higher borrowing cost.
• C. FRA settlement depends on the reference rate rather than the borrower’s credit spread, so the stated hedge coverage is reversed.

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Question 15

Topic: Economics

An analyst reviews three changes at a packaging manufacturer. In each comparison, production costs per unit other than the component described remain unchanged.

• Larger plant: The firm increases normal annual output by moving to a larger plant. Bulk-purchasing discounts lower material cost per unit.
• Seasonal production: The firm temporarily increases output at its existing plant. Annual rent is unchanged, so rent per unit falls.
• Further expansion: The firm adds production capacity and increases normal annual output. Additional management layers raise coordination cost per unit.

Which interpretation is least accurate?

• A. The further expansion represents diseconomies of scale through higher coordination costs per unit.
• B. The seasonal increase represents economies of scale through lower rent per unit.
• C. The larger plant represents economies of scale through lower material costs per unit.

Best answer: B

Explanation: Economies of scale occur when increasing production scale reduces long-run average cost, with all inputs adjustable. Bulk-purchasing savings at the larger plant support this interpretation because material cost per unit falls while other unit costs remain unchanged. Diseconomies of scale occur when expansion increases long-run average cost, as additional management and coordination costs do here.

The seasonal increase changes utilization of the existing plant rather than plant scale. Its unchanged rent is spread over more units, reducing average fixed cost and, under the stated assumptions, short-run average total cost. This temporary reduction does not establish economies of scale, which concern average cost at different scales of production when all inputs can be varied.

• A. Higher coordination cost per unit after a permanent increase in scale raises long-run average cost when other unit costs are unchanged.
• B. Lower rent per unit spreads an unchanged fixed cost over more output at the existing plant; it does not establish lower long-run average cost.
• C. A permanent increase in production scale that reduces material cost per unit, with other unit costs unchanged, lowers long-run average cost.

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Question 16

Topic: Fixed Income

A bank has transferred credit-card receivables in a true sale to a bankruptcy-remote issuer. The asset-backed securities are currently in their revolving period, and the bank provides no repayment guarantee.

Cash-flow terms:

• During the revolving period, principal collections purchase new receivables. During early amortization, available principal collections repay senior notes before subordinated notes.
• At each quarter-end, early amortization is triggered for the following month if the arithmetic average of the quarter’s three monthly principal payment rates is below 10%.
• Each monthly principal payment rate equals principal collections divided by beginning receivables.

Quarter ended 30 June 2027: Beginning receivables were $100 million in each month.

Additional evidence:

• Throughout the quarter, 90% of receivables related to accounts open for at least 24 months.
• Receivables delinquent by at least 60 days increased from 2% to 4% of the pool.
• The sponsoring bank’s corporate credit rating was upgraded in June.

Which conclusion about the senior notes beginning on 1 July 2027 is most accurate?

• A. Early amortization begins; pool collections repay senior principal, and borrower payment behavior remains the main repayment risk.
• B. Revolving purchases continue; pool collections acquire receivables, and borrower payment behavior remains the main repayment risk.
• C. Early amortization begins; bank cash flows repay senior principal, and sponsor creditworthiness becomes the main repayment risk.

Best answer: A

Explanation: A credit-card ABS payment-rate trigger uses the contractual measurement period, not just the latest monthly observation. With beginning receivables of $100 million each month, the monthly principal payment rates are 8%, 7%, and 12%. Their arithmetic average is \( (8\% + 7\% + 12\%)/3 = 9\% \), below the 10% threshold.

Early amortization therefore begins on 1 July. Principal collections stop funding new receivables and instead repay senior notes before subordinated notes. This protection redirects available cash but does not guarantee immediate or complete repayment.

Borrower performance remains central: delinquencies have doubled despite stable seasoning. The bank’s rating upgrade does not improve cardholders’ payment capacity or provide a repayment guarantee. Slower collections and credit losses can still impair the timing and amount of senior repayments.

• A. The 9% quarterly average triggers early amortization, while repayment continues to depend on collections from cardholders rather than the sponsoring bank.
• B. June’s 12% payment rate exceeds the threshold, but the quarterly average is 9%, which triggers early amortization and ends revolving purchases.
• C. Early amortization redirects pool principal collections; it does not create a bank repayment obligation, and the bank provides no guarantee.

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Question 17

Topic: Ethical and Professional Standards

An adviser reviews a proposed investment for a client whose investment policy statement calls for long-term capital growth over a 15-year horizon with moderate overall risk. The client’s stable employment income exceeds routine expenses, and the client has no debt. A $120,000 portfolio withdrawal is planned in nine months.

The proposed private equity fund is fully funded at purchase, requires no additional capital contributions, has a seven-year lockup, and has estimated annual return volatility of 35%. The current portfolio meets the client’s risk mandate.

Assume the portfolio volatility estimates appropriately reflect the fund’s economic return variability and correlations with the other holdings.

Which conclusion about the proposed allocation is most accurate under the CFA Institute Standards of Professional Conduct?

• A. The allocation is unsuitable given the fund’s seven-year lockup and the client’s withdrawal scheduled in nine months.
• B. The allocation is suitable given the portfolio’s overall risk and the cash available for the planned withdrawal.
• C. The allocation is unsuitable given the fund’s standalone volatility and the client’s moderate overall risk tolerance.

Best answer: B

Explanation: Under Standard III(C), Suitability, recommendations must fit the client’s objectives, constraints, and risk tolerance in the context of the total portfolio. A high-volatility or illiquid asset is not automatically unsuitable when its allocation and role are compatible with that portfolio.

The adviser reallocates $100,000 of the $2,000,000 portfolio from diversified equities to the fund, creating a 5% position. Estimated portfolio volatility remains 9.0%, consistent with the client’s accepted risk mandate. The unchanged $250,000 cash balance covers the $120,000 withdrawal and leaves $130,000. Stable income covers routine spending, and the seven-year lockup fits within the 15-year horizon. These facts support suitability despite the fund’s higher standalone volatility.

• A. Existing cash can fund the planned withdrawal, so the fund’s lockup does not create a near-term liquidity shortfall.
• B. The 5% allocation preserves the portfolio’s estimated risk, and the $250,000 cash balance covers the $120,000 withdrawal.
• C. Moderate risk tolerance applies to the total portfolio, whose estimated volatility is unchanged, rather than to each holding in isolation.

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Question 18

Topic: Economics

An emerging-market economy has experienced large short-term foreign capital inflows, rapid domestic credit growth, and currency appreciation. The government wants to reduce exposure to volatile funding and ease exchange-rate pressure.

It requires resident borrowers to place 20% of the proceeds of each new foreign loan with a maturity of one year or less in a central-bank deposit. The deposit earns no interest and is returned after one year.

Which assessment of the restriction’s effects is least accurate?

• A. It can ease upward pressure on the exchange rate by discouraging short-term foreign capital inflows.
• B. It can raise the effective cost of foreign financing by tying up part of each loan’s proceeds.
• C. It can protect domestic producers from import competition by imposing an additional customs charge on foreign goods.

Best answer: C

Explanation: Capital restrictions target cross-border financial transactions rather than trade in goods. Here, the non-interest-bearing deposit makes short-term foreign borrowing less attractive: borrowers cannot immediately use all the proceeds while remaining liable for the full loan. This can discourage inflows, moderate currency appreciation, and reduce exposure to abrupt reversals of foreign funding.

The trade-off is reduced access to foreign financing and potentially higher effective funding costs for domestic firms. A customs tariff, by contrast, taxes imported goods. The deposit requirement does not impose such a tax, although its effects on capital flows and the exchange rate may indirectly influence import and export competitiveness.

• A. Making short-term inflows less attractive can moderate their contribution to the currency appreciation described.
• B. Borrowers cannot use 20% of the loan proceeds for one year, and the required deposit earns no interest.
• C. The deposit applies to cross-border borrowing, not merchandise imports, so it does not impose a customs charge on foreign goods.

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Question 19

Topic: Fixed Income

A fixed-income analyst compares five-year, fixed-rate, option-free sovereign and corporate bonds denominated in the same currency and subject to the same tax treatment.

The analyst proposes the following conclusion:

The sovereign bond should have a lower required yield than the corporate bond.

Assume that yield premiums above a common default-risk-free benchmark consist only of compensation for credit risk and liquidity risk. Which additional estimate would make the conclusion most defensible?

• A. The sovereign’s credit-risk premium exceeds the corporate issuer’s by 35 basis points.
• B. The sovereign’s credit-risk premium exceeds the corporate issuer’s by 15 basis points.
• C. The sovereign’s credit-risk premium exceeds the corporate issuer’s by 25 basis points.

Best answer: B

Explanation: Required yields compensate investors for the risks specified in the comparison, so a liquidity advantage must be weighed against any credit-risk disadvantage. The sovereign’s estimated liquidity premium is 25 basis points below the corporation’s. A sovereign credit-risk premium 15 basis points higher therefore produces a net yield difference of \(15 + 10 - 35 = -10\) basis points, supporting a lower sovereign required yield.

Regular benchmark auctions, a large outstanding issue, and broad investor participation can support secondary liquidity. Bank syndication facilitates corporate issuance but does not itself ensure active subsequent trading. Neither funding method establishes creditworthiness: the sovereign can face greater credit risk despite having the lower required yield.

• A. A 35-basis-point credit disadvantage exceeds the sovereign’s 25-basis-point liquidity advantage, making its required yield 10 basis points higher.
• B. The sovereign’s 25-basis-point liquidity advantage exceeds its 15-basis-point credit disadvantage, making its required yield 10 basis points lower.
• C. A 25-basis-point credit disadvantage exactly offsets the sovereign’s liquidity advantage, implying equal required yields rather than a lower sovereign yield.

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Question 20

Topic: Financial Statement Analysis

An analyst initially accepts a manufacturer’s year-end receivables transfer as an outright sale qualifying for derecognition under IFRS. The manufacturer reports the following amounts, in millions of dollars:

Transfer details:

• On the final day of the current year, the manufacturer received $12 million for receivables with a carrying amount of $12 million.
• It removed these receivables and included the proceeds in operating cash flow.
• Use a 360-day year and the arithmetic mean of opening and closing receivables. Ignore fees, interest, and tax effects.

New information: A contract review establishes that the manufacturer retains substantially all risks and rewards of the transferred receivables. All other transactions remain unchanged.

Which revised current-year receivables collection period and operating cash flow are most accurate?

• A. A collection period of 48 days and operating cash flow of $30 million.
• B. A collection period of 48 days and operating cash flow of $18 million.
• C. A collection period of 30 days and operating cash flow of $18 million.

Best answer: B

Explanation: Under IFRS, retaining substantially all risks and rewards prevents derecognition of transferred receivables. The cash received is accounted for as borrowing, not an operating cash inflow.

Closing receivables therefore become $22 million. Average receivables are \( (10 + 22)/2 = 16 \) million, giving a collection period of \( 16/120 \times 360 = 48 \) days. Operating cash flow becomes $18 million after removing the $12 million financing proceeds.

The prior-year collection period was \( 12.5/100 \times 360 = 45 \) days. Thus, collections have slowed and operating cash flow has declined from $20 million despite higher credit sales. The apparent improvement arose from derecognition and cash-flow classification rather than stronger underlying cash collection. This indicates a reporting-quality problem, but it does not by itself establish that revenue was overstated.

• A. Restoring the receivables gives a 48-day collection period, but the proceeds represent borrowing and must be excluded from operating cash flow.
• B. Continued receivables recognition produces average receivables of $16 million, while financing classification removes the $12 million proceeds from operating cash flow.
• C. Removing the financing proceeds gives $18 million of operating cash flow, but continued recognition of the receivables increases the collection period to 48 days.

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Question 21

Topic: Economics

A price-taking manufacturer sells its product for $24 per unit, a price expected to remain unchanged. If it operates next quarter, its profit-maximizing output is 10,000 units.

Next-quarter forecasts:

Fixed costs are unavoidable during the quarter, while variable costs are avoided if production stops. All figures include economic costs.

Long-run outlook: All costs become avoidable. Economies of scale would reduce average total cost from $27 per unit at the current plant scale to $25 at a larger scale. No feasible scale offers average total cost below $25.

Which plan is most appropriate for maximizing economic profit in the short run and the long run?

• A. Continue production next quarter and exit the industry in the long run.
• B. Continue production next quarter and expand the plant in the long run.
• C. Shut down production next quarter and exit the industry in the long run.

Best answer: A

Explanation: The short-run operating decision depends on covering avoidable variable costs, not on covering all costs. Unavoidable fixed costs remain payable whether production continues or stops. Here, revenue exceeds variable costs by $60,000. Operating therefore produces a $30,000 economic loss, compared with a $90,000 loss from shutting down.

At 10,000 units, average variable cost is $18 and average total cost is $27. The $24 price covers variable cost but falls below break-even at this output.

In the long run, all costs are avoidable, and continued operation must cover total economic costs. Economies of scale lower average total cost to $25, but that minimum still exceeds the expected $24 price. Lower average cost reduces losses without eliminating them, so expansion is unwarranted and long-run exit is appropriate.

• A. Production contributes $60,000 toward unavoidable fixed costs next quarter, but the expected price remains below the lowest attainable long-run average total cost.
• B. Although production is preferable next quarter, the larger plant’s $25 average total cost still exceeds the expected $24 price.
• C. Shutting down next quarter creates a $90,000 loss, whereas producing limits the loss to $30,000 because revenue exceeds variable costs.

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Question 22

Topic: Economics

An analyst reviews the following indicators for an economy over three consecutive quarters. Credit data cover the same borrower group throughout.

Leverage equals outstanding loans divided by collateral market value. Leverage and collateral values are measured at quarter-end. Loan growth is the quarter-on-quarter percentage change in outstanding loans, with no write-offs or other adjustments.

Which interpretation of the credit cycle is most accurate?

• A. Net new borrowing is accelerating; tighter lending standards can moderate the debt accumulation reflected in the rising leverage ratio.
• B. The loan stock is decreasing; falling collateral values can raise leverage even while borrowers repay more debt than they incur.
• C. The loan stock is increasing; falling collateral values and tighter lending standards can reinforce the contraction in economic activity.

Best answer: C

Explanation: Outstanding loans are a stock, whereas net new borrowing is a flow. Positive loan growth means the stock is still increasing. With the Q1 loan balance indexed to 100, it rises to 104 in Q2 and 105.04 in Q3. Net new borrowing thus falls from 4 to 1.04, but debt continues accumulating while output declines. The stock of credit need not peak at the same time as economic activity.

Leverage rises because loan balances increase while collateral values fall; the ratio alone does not show borrowing acceleration. Falling collateral values and tighter lending standards can reduce borrowing capacity, financing, and spending, reinforcing the downturn. Existing debts can persist even when new borrowing slows, illustrating delayed adjustment in the credit cycle.

• A. With the Q1 loan balance indexed to 100, net borrowing falls from 4 in Q2 to 1.04 in Q3, despite rising leverage.
• B. Positive loan growth in all three quarters means the loan stock is rising, even though its rate of growth declines.
• C. Positive loan growth persists as GDP falls, while weaker collateral and tighter lending standards can reduce financing and amplify the downturn.

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Question 23

Topic: Financial Statement Analysis

A manufacturer applying IFRS and the cost model reviews a machine for impairment at 31 December 2027. The machine generates cash flows independently of other assets.

Asset data:

• Carrying amount after 2027 depreciation: $960,000.
• Fair value less costs of disposal: $720,000.
• Remaining useful life: six years.
• Depreciation method: straight-line, with zero residual value.

An analyst proposes recognizing a $240,000 impairment loss for 2027 and reducing 2028 depreciation expense by $40,000 relative to the amount without impairment. Assume no subsequent impairment reversal or change in depreciation estimates.

Which estimate of value in use would make both proposals most appropriate?

• A. A value in use of $840,000.
• B. A value in use of $1,080,000.
• C. A value in use of $600,000.

Best answer: C

Explanation: Under IFRS, recoverable amount is the higher of value in use and fair value less costs of disposal. An impairment loss arises when carrying amount exceeds recoverable amount. With value in use of $600,000, recoverable amount is therefore $720,000.

Under the cost model, the $240,000 write-down reduces both profit and the asset’s carrying amount. Annual straight-line depreciation over the six remaining years falls from $160,000 to $120,000, a $40,000 decrease. Lower depreciation increases subsequent earnings relative to the amount without impairment, all else equal.

The impairment charge itself is noncash. It reduces current earnings and reported assets but does not create a cash outflow.

• A. Recoverable amount would be $840,000, producing a $120,000 impairment loss and a $20,000 reduction in annual depreciation.
• B. Recoverable amount would exceed the $960,000 carrying amount, so no impairment loss or related depreciation reduction would be recognized.
• C. Recoverable amount would be $720,000, producing a $240,000 impairment loss and a $40,000 reduction in annual depreciation.

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Question 24

Topic: Corporate Finance

An analyst evaluates a manufacturing firm’s 2026 performance. Invested capital is defined as operating assets minus non-interest-bearing operating liabilities, and ROIC uses the average of beginning and ending invested capital. Interest is fully tax-deductible, and there are no other non-operating items.

The analyst writes:

“ROIC is net income of $13.5 million divided by average invested capital of $180 million, or 7.5%. This shortfall relative to WACC suggests economic value destruction in 2026.”

Which correction to the analyst’s ROIC and conclusion is most accurate?

• A. ROIC is 13.3%, above WACC, suggesting the firm created economic value in 2026.
• B. ROIC is 10.0%, above WACC, suggesting the firm created economic value in 2026.
• C. ROIC is 9.0%, equal to WACC, suggesting the firm earned only its required return in 2026.

Best answer: B

Explanation: ROIC measures the return earned on capital supplied by both debt and equity investors. Its numerator is net operating profit after tax (NOPAT), not net income after interest expense.

NOPAT is $24 million multiplied by 75%, or $18 million. Average invested capital is $180 million, so ROIC is 10.0%. The 1 percentage-point excess over the 9.0% WACC implies estimated economic profit of $1.8 million for 2026.

This positive spread suggests economic value creation during the measured period, but it does not establish that a particular project has positive NPV. ROIC reflects accounting profits and recorded capital, which are influenced by depreciation and investment timing. NPV instead depends on expected incremental cash flows and their timing.

• A. The 13.3% result uses pre-tax operating profit of $24 million, overstating ROIC by failing to deduct taxes.
• B. After-tax operating profit is $18 million; dividing by average invested capital of $180 million gives 10.0%, exceeding the 9.0% WACC.
• C. The 9.0% result divides after-tax operating profit by ending invested capital of $200 million rather than average invested capital of $180 million.

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Question 25

Topic: Quantitative Methods

An analyst is estimating a nominal discount rate for the promised payment on a four-year corporate zero-coupon bond.

Market data and estimates:

Both government yields are nominal annual effective rates in the corporate bond’s currency. Government securities are default-free and highly liquid. The corporate and four-year government bonds have equal maturity-risk premiums. Use an additive premium approximation.

Which required nominal annual return is most appropriate?

• A. 6.4%
• B. 8.4%
• C. 5.6%

Best answer: A

Explanation: A required return represents compensation investors demand for committing funds and bearing risk. It serves as an opportunity cost and therefore as a discount rate for valuation.

The four-year government yield provides the maturity-matched nominal benchmark. It already includes compensation for expected inflation and the maturity risk assumed common to both four-year bonds. Only the additional corporate default and liquidity premiums need to be added:

\[ r = 4.8\% + 1.2\% + 0.4\% = 6.4\% \]

This required rate is not a guaranteed achieved return. For example, issuer default could reduce the payment received and cause the realized return to fall below the rate used for valuation.

• A. Adding the corporate default and liquidity premiums to the maturity-matched nominal government yield gives \(4.8\% + 1.2\% + 0.4\% = 6.4\%\).
• B. The 8.4% calculation adds expected inflation again, although inflation is already reflected in the nominal government yield.
• C. The 5.6% calculation uses the one-year government yield rather than the maturity-matched four-year benchmark.

Questions 26-50

Question 26

Topic: Portfolio Construction

An analyst is establishing investment objectives for two pension plans sponsored by the same employer. Their governing documents contain the following provisions:

Which conclusion about the arrangements and the allocation of investment and longevity-related funding risk is most accurate?

• A. Alder is defined benefit, with the employer bearing investment and longevity-related funding risk; Birch is defined contribution, with participants bearing both risks.
• B. Alder is defined contribution, with participants bearing investment and longevity-related funding risk; Birch is defined benefit, with the employer bearing both risks.
• C. Alder is defined benefit, with the employer bearing investment risk and participants bearing longevity-related funding risk; Birch is defined contribution, with participants bearing both risks.

Best answer: A

Explanation: A defined benefit plan specifies retirement benefits. Alder promises $24,000 annually for each retiree’s lifetime, so the employer must fund those payments even when investment returns disappoint or retirees live longer than expected. Its investment objectives therefore center on supporting promised pension payments and managing funding risk.

A defined contribution plan specifies contributions rather than benefits. Birch’s employer commits 6% of salary to individual accounts, with no guaranteed lifetime income or additional funding after investment shortfalls. Investment objectives consequently reflect participants’ retirement needs and risk tolerances. Participants bear investment risk and the possibility of exhausting their balances during retirement.

• A. Alder’s employer must maintain lifetime payments despite funding shortfalls; Birch participants rely on accumulated account assets and bear the risk of depletion.
• B. Alder guarantees retirement payments, whereas Birch guarantees contributions; fixed dollar benefits and percentage contributions do not reverse these classifications.
• C. Alder’s lifetime pension commitment requires the employer to finance additional payments when retirees live longer, placing longevity-related funding risk on the employer.

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Question 27

Topic: Fixed Income

An analyst reprices a six-year zero-coupon bond at yields 100 basis points above and below its current yield of 5.00%. All yields are annually compounded, and the bond’s cash flow is held fixed.

The analytical modified duration at the current yield is 5.7143 years. Ignoring rounding error, which statement about the numerical duration estimate and the effect of reducing the symmetric yield shock is most accurate?

• A. 5.7191 years; reducing the symmetric yield shock should bring the estimate closer to the analytical value.
• B. 5.4468 years; reducing the symmetric yield shock should bring the estimate closer to the analytical value.
• C. 5.7191 years; reducing the symmetric yield shock should leave the difference from the analytical value unchanged.

Best answer: A

Explanation: Modified duration measures the local percentage price sensitivity to a change in yield. Holding cash flows fixed, the symmetric repricing estimate is:

\[ D_{\text{mod}} \approx \frac{P_- - P_+}{2P_0\Delta y} \]

Here, \(P_-\) is the price at the lower yield, \(P_+\) is the price at the higher yield, and \(P_0\) is the current price. A 100-basis-point shock means \(\Delta y = 0.01\), giving:

\[ D_{\text{mod}} \approx \frac{79.0315-70.4961}{2(74.6215)(0.01)} = 5.7191\text{ years}. \]

For this zero-coupon bond, analytical modified duration is \(6/1.05 = 5.7143\) years. The small difference arises because the numerical estimate uses a finite interval rather than the derivative at the current yield. Smaller symmetric shocks bring the estimate closer to the analytical value, ignoring rounding error. No additional compounding adjustment is needed.

• A. The estimate is \(8.5354/1.49243 = 5.7191\) years, and smaller shocks reduce the finite-difference error relative to the analytical derivative.
• B. The symmetric repricing formula already estimates modified duration; dividing its 5.7191-year result by 1.05 again produces the understated 5.4468-year figure.
• C. The symmetric repricing formula approximates the local derivative, so its finite-shock error decreases as the yield interval shrinks.

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Question 28

Topic: Quantitative Methods

Before reviewing a model signal, an analyst assigns a 30% probability that a fund will outperform its benchmark over the next year. For comparable fund-year observations, the model’s favorable-signal frequencies are:

The analyst assumes these conditional frequencies apply to the fund. The model produces a favorable signal, and the analyst reports:

“The probability of outperformance after a favorable signal is \(0.80/(0.80 + 0.20) = 80\%\).”

The most accurate corrected probability of outperformance, conditional on the favorable signal, is closest to:

• A. 63.2%
• B. 38.0%
• C. 54.5%

Best answer: A

Explanation: Bayes’ formula requires conditional signal frequencies to be weighted by the prior probabilities of their respective outcomes. The analyst adds unweighted likelihoods, effectively treating outperformance and non-outperformance as equally likely despite the 30% prior.

Let \(O\) denote outperformance and \(F\) a favorable signal. The total probability of a favorable signal is:

\[ P(F) = 0.30(0.80) + 0.70(0.20) = 0.38. \]

The updated probability is:

\[ P(O\mid F) = \frac{0.30(0.80)}{0.38} = 0.6316. \]

The favorable signal raises the estimated probability of outperformance from 30% to approximately 63.2%. The 80% frequency describes favorable signals among outperformers; the posterior describes outperformers among favorable-signal observations. These probabilities condition on different populations.

• A. Outperformance and a favorable signal jointly have probability 24%, while favorable signals have total probability 38%; their ratio gives the posterior.
• B. This is the unconditional probability of a favorable signal, not the probability of outperformance conditional on receiving that signal.
• C. This result weights the outperforming cases by their prior probability but leaves the 20% signal frequency among non-outperforming cases unweighted.

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Question 29

Topic: Derivatives and Risk Management

An analyst compares the values of a European call and a European put before and after a stock’s annualized volatility estimate increases from 20% to 30%. The non-dividend-paying stock’s price remains $100. Both options have a $100 strike and six months to expiration in both valuations. The risk-free rate is unchanged.

The analyst writes:

Greater volatility does not by itself imply a higher expected stock return, so neither option’s value should increase.

Which conclusion most accurately corrects the analysis?

• A. The call value increases and the put value decreases; the stock’s expected return need not increase.
• B. The call and put values both increase; the stock’s expected return need not increase.
• C. The call and put values both increase; the stock’s expected return also increases.

Best answer: B

Explanation: Standard call and put options have convex payoffs. Large upward stock-price moves benefit a call holder, while large downward moves benefit a put holder. Unfavorable outcomes produce zero expiration payoff rather than an increasingly negative payoff. With spot price, strike, remaining maturity, interest rates, and dividend assumptions unchanged, higher volatility increases the value of both options.

Volatility measures dispersion of possible returns, not their expected direction or average. Higher option values therefore do not require a higher expected stock return. The analyst correctly separates volatility from expected return but incorrectly concludes that the absence of a higher expected return prevents option values from increasing.

• A. Higher volatility also increases the put’s value by increasing the potential benefit from large stock-price declines, rather than causing its value to fall.
• B. Both options have positive sensitivity to volatility because of their convex payoffs; their values can increase without a higher expected stock return.
• C. Greater volatility increases return dispersion but does not establish a higher expected stock return; increasing option values does not support that inference.

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Question 30

Topic: Ethical and Professional Standards

Amira Chen, CFA, reviews a fund’s marketing exhibit as of 31 December 2026. The fund began operating with a momentum strategy on 1 January 2024 and switched to a value strategy on 1 January 2025.

The draft exhibit links the value strategy’s 2024 backtest with its subsequent live performance. The supporting annual total returns are all gross of fees:

Which statement most appropriately describes the value strategy’s actual track record for marketing purposes?

• A. The value strategy earned an actual cumulative return of 15.50% from 1 January 2025 through 31 December 2026.
• B. The value strategy earned an actual cumulative return of 3.95% from 1 January 2024 through 31 December 2026.
• C. The value strategy earned an actual cumulative return of 38.60% from 1 January 2024 through 31 December 2026.

Best answer: A

Explanation: Standard III(D), Performance Presentation, requires performance information to be fair, accurate, and complete. Backtested returns may accompany actual results when their hypothetical nature and relevant periods are clearly identified; linking them does not create an actual track record.

The value strategy’s live performance begins on 1 January 2025. Its cumulative actual return is \(1.10 \times 1.05 - 1 = 0.155\), or 15.50%. The 2024 model result can be included in an appropriately labeled illustration, but cannot be described as realized performance. The fund’s full actual history can also be reported with disclosure of the change from momentum to value, rather than attributed wholly to the value strategy.

• A. Only the 2025 and 2026 returns were earned under the value strategy, and geometrically linking them produces a 15.50% cumulative return.
• B. This result links all actual fund returns, but the 2024 loss arose under the momentum strategy and cannot be attributed to the value strategy.
• C. This result links the 2024 backtest to live returns, so labeling the entire period as actual misrepresents the hypothetical portion of the history.

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Question 31

Topic: Ethical and Professional Standards

A CFA candidate moderates a study group’s shared folder. Members submit links to public learning materials, original practice problems, and study notes. Some notes contain recollections of actual CFA examination questions, and she rejects those passages.

A submitted concept checklist contains no question wording, numerical details, or exam-session identifiers. The candidate concludes that it may be shared in the members-only folder because every term appears in the published curriculum.

Which additional fact would most likely make sharing the checklist consistent with the CFA Institute Standards of Professional Conduct?

• A. The checklist will be shared after the examination window has closed and all candidates have completed that administration.
• B. The checklist was compiled from public learning materials independently of any member’s recollections of actual examination content.
• C. The checklist will be shared only with registered CFA candidates who agree to keep the group’s discussions confidential.

Best answer: B

Explanation: Standard VII(A), Conduct as Participants in CFA Institute Programs, protects the confidentiality of actual examination content. This protection extends beyond verbatim questions: reporting which concepts were tested can disclose confidential information even when question wording, numerical details, and examination identifiers are removed. A concept’s appearance in the published curriculum does not make a report of its appearance on an actual examination permissible.

A checklist developed independently from public learning materials supports legitimate preparation. The moderator should distinguish public resources and independently created practice materials from recalled questions and summaries revealing what was tested. The decisive consideration is the checklist’s source and what it communicates, not whether access is restricted or the examination window has ended.

• A. Examination confidentiality continues after the examination window closes, so completion of the administration does not permit disclosure of recalled content.
• B. Independent preparation from public materials permits discussion of curriculum concepts without communicating what appeared on an actual CFA examination.
• C. Registered candidates are not authorized recipients of confidential examination content, and a private confidentiality agreement does not authorize its disclosure.

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Question 32

Topic: Quantitative Methods

An analyst is selecting a fully invested portfolio of two assets. Short selling is prohibited. The annual forecasts are:

The covariance of annual returns is 0.0150. Variances and covariance are calculated using returns expressed as decimals.

Which allocation and expected annual return most accurately describe the minimum-variance portfolio permitted by the mandate?

• A. 80% in Asset A and 20% in Asset B, with an expected annual return of 5.8%.
• B. 100% in Asset A and 0% in Asset B, with an expected annual return of 5.0%.
• C. 125% in Asset A and -25% in Asset B, with an expected annual return of 4.0%.

Best answer: B

Explanation: Minimum-variance weights depend on both asset variances and their covariance. The unrestricted weight in Asset A equals Asset B’s variance minus the covariance, divided by the sum of both variances minus twice the covariance:

\[ w_A^* = \frac{0.0400 - 0.0150}{0.0100 + 0.0400 - 2(0.0150)} = 1.25 \]

This gives weights of 125% in Asset A and -25% in Asset B. With short selling prohibited, the feasible weight in Asset A ranges from 0% to 100%. Because portfolio variance is a convex function of the weight and the unrestricted minimum lies above this range, the feasible minimum occurs at 100% in Asset A.

The permitted portfolio therefore has expected annual return of 5.0% and variance of 0.0100. Minimizing variance is a risk objective, not expected-return maximization. Investing entirely in Asset B would offer a higher expected return of 9.0%, but also a higher variance of 0.0400.

• A. Ignoring covariance gives an 80% weight in Asset A; including covariance produces portfolio variance of 0.0128, exceeding Asset A’s variance of 0.0100.
• B. The unrestricted optimum requires shorting Asset B, so the long-only minimum occurs entirely in Asset A, whose expected return is 5.0%.
• C. These weights minimize variance without short-sale restrictions, but the negative weight in Asset B violates the mandate.

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Question 33

Topic: Equities

A research analyst estimates a company’s total equity value at $1,000 million using a constant-growth free cash flow to equity (FCFE) model. The current assumptions are 4% perpetual FCFE growth and a 10% required equity return.

The company proposes a debt-financed expansion. The analyst updates perpetual FCFE growth to 6% and the required equity return to 12%, with these forecasts for the first year after expansion:

The first-year FCFE occurs one year from today and grows at 6% annually thereafter.

After incorporating the expansion, the estimated total equity value is closest to:

• A. $833 million.
• B. $1,250 million.
• C. $500 million.

Best answer: A

Explanation: FCFE measures cash available to common shareholders after reinvestment and net debt financing. Capital expenditures less depreciation and increases in non-cash working capital reduce FCFE, while net borrowing increases it.

With amounts in millions, first-year FCFE is \(100 - 50 - 20 + 20 = 50\). The constant-growth valuation gives:

\[ \text{Equity value} = \frac{50}{0.12 - 0.06} = 833.3 \]

Equity value therefore falls from $1,000 million to approximately $833 million. Higher growth does not increase value here because the required equity return also rises, leaving the required-return-minus-growth spread unchanged at 6%. The original valuation implies first-year FCFE of $60 million, so the expansion reduces expected shareholder cash flow despite the additional borrowing. Growth, reinvestment needs, and financing risk must be evaluated together.

• A. First-year FCFE is $50 million; dividing by the updated required-return-minus-growth spread of 6% gives an equity value of approximately $833 million.
• B. This estimate combines the updated 6% growth rate with the old 10% required return, omitting the increased equity risk associated with greater leverage.
• C. This estimate omits net borrowing, producing first-year FCFE of $30 million rather than $50 million and understating cash available to shareholders.

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Question 34

Topic: Alternative Investments

An investor wants to fund a $261,000 cash obligation on 31 December 2027 using a redemption from just one of two hedge fund holdings.

Account facts:

• Each holding was worth $1,000,000 at the beginning of 2027 and $1,070,000 at year-end before fees. There were no interim investor cash flows.
• Both initial lockups have expired. Full-redemption notices were submitted 100 days before 31 December.

Contractual terms:

All fees are calculated and deducted at year-end. No hurdles, high-water marks, or other fees apply. Gates cap the cash paid on the redemption date; remaining balances stay invested. Both funds settle permitted redemptions on 31 December.

Which conclusion is most accurate?

• A. Only Fund B can meet the cash obligation, and its incentive fee is lower than Fund A’s.
• B. Both funds can meet the cash obligation, and Fund A’s incentive fee is lower than Fund B’s.
• C. Only Fund B can meet the cash obligation, and its incentive fee is higher than Fund A’s.

Best answer: C

Explanation: Fee rates must be applied to their contractual bases before determining redemption proceeds.

• Fund A’s management fee is $20,000. Its incentive fee is \(0.20 \times (70,000 - 20,000) = 10,000\) dollars. After-fee NAV is $1,040,000, so the 25% gate permits $260,000.
• Fund B’s management fee is \(0.01 \times 1,070,000 = 10,700\) dollars. Its incentive fee is \(0.15 \times 70,000 = 10,500\) dollars. After-fee NAV is $1,048,800, so the gate permits $262,200.

Only Fund B meets the $261,000 obligation. Its lower incentive-fee rate nevertheless produces a larger incentive payment because it applies to gross gains. Expired lockups and timely notices establish redemption eligibility but do not remove the gates.

• A. Fund B can provide sufficient cash, but its incentive fee is $10,500, exceeding Fund A’s $10,000 despite its lower stated rate.
• B. Fund A’s incentive fee is lower, but applying the gate to its after-fee NAV permits only $260,000, below the $261,000 obligation.
• C. Fund B permits a $262,200 redemption and charges a $10,500 incentive fee, while Fund A permits $260,000 and charges $10,000.

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Question 35

Topic: Derivatives and Risk Management

An analyst considers a European call and put on the same stock. Both have a strike price of $100 and expire in six months. Assume an arbitrage-free market.

Observed data:

• The put price is $4.20 per share.
• An existing forward contract on the stock settles on the option expiration date and has a fixed delivery price of $106 per share.
• The risk-free discount factor to that date is 0.98.

The analyst estimates the call value at $10.08 per share using the existing contract’s delivery price in put-call forward parity. Which additional fact is sufficient to justify this estimate?

• A. The stock has a spot price of $106 at the valuation date.
• B. The existing forward has zero market value at the valuation date.
• C. The existing forward had zero market value when it was initiated.

Best answer: B

Explanation: Put-call forward parity uses the current delivery price for a newly initiated, zero-value forward, rather than necessarily the delivery price fixed in an existing contract. For European options with the same underlying, strike and maturity, \(C-P=D(F-K)\), where \(C\) and \(P\) are current option values, \(D\) is the discount factor, \(F\) is the current forward price, and \(K\) is the option strike.

An existing long forward with delivery price \(K_f\) has current value \(v=D(F-K_f)\). If its current value is zero, then \(F=K_f=106\). Therefore, \(C=4.20+0.98(106-100)=10.08\), or $10.08 per share. Zero value at inception does not establish today’s forward price, and spot price alone does not account for financing and dividends.

• A. A $106 spot price does not establish a $106 forward price because financing costs and stock dividends affect the forward price.
• B. Zero current market value makes the existing $106 delivery price equal the current forward price required by put-call forward parity.
• C. Zero value at inception establishes the forward price when the contract was entered into, not at the current valuation date.

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Question 36

Topic: Financial Statement Analysis

A manufacturing company reporting under IFRS grants equity-settled employee stock options on 1 January 2027.

Award and reporting facts:

• The options vest after three years of service, and the company expects all awards to vest.
• For 2027, the company recognizes $600,000 of compensation expense and an equal credit to equity.
• Its indirect cash flow statement starts from operating profit and adds back the $600,000 noncash charge.
• No options are exercised in 2027. Future exercises require employees to pay cash in exchange for newly issued shares.

Ignoring income tax effects, which conclusion about the award is least accurate?

• A. Future exercises generate financing cash inflows because employees pay cash in exchange for shares newly issued by the company.
• B. The award has no economic cost to existing shareholders because its expense is added back in operating cash flow.
• C. The charge reduces net income while leaving total equity unchanged because the expense is matched by an equity credit.

Best answer: B

Explanation: Equity-settled employee options generally recognize compensation expense over the vesting period using grant-date fair value. Expense recognition does not require the options to have vested or been exercised.

Here, the $600,000 charge reduces net income and retained earnings. The equal credit to another equity component leaves total equity unchanged, ignoring taxes. Adding the noncash charge back to operating profit prevents it from reducing operating cash flow; the addback does not itself create cash.

Noncash compensation is not economically free. Employees receive valuable rights, and issuing shares upon exercise creates potential dilution for existing shareholders. Any cash exercise proceeds arise when employees exercise their options and are classified as financing cash inflows, separate from the earlier compensation expense.

• A. Cash received from issuing shares is a financing inflow, and those proceeds arise upon exercise rather than during expense recognition or vesting.
• B. The addback removes a noncash charge from the cash flow reconciliation; employees still receive valuable option rights that impose an economic cost on shareholders.
• C. The expense lowers retained earnings by $600,000, while the matching credit to another equity component offsets that reduction in total equity.

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Question 37

Topic: Portfolio Construction

A U.S. retail investor is selecting a vehicle for a diversified U.S. equity portfolio held in a taxable account. The investor wants to manage realized gains and losses on individual stocks and meets the minimum investment requirements for these alternatives:

• A conventional U.S.-domiciled open-end mutual fund.
• A U.S.-domiciled ETF using in-kind creations and redemptions.
• A separately managed equity account whose manager accepts investor-specific tax instructions.

The investor would trade fund shares through ordinary retail brokerage transactions and is not an ETF authorized participant.

Which assessment of tax-control rights and vehicle mechanics is least accurate?

• A. The mutual fund can distribute taxable capital gains from portfolio transactions to the investor even when the investor retains all fund shares.
• B. The separately managed account can realize losses on selected stocks in response to the investor’s individual tax circumstances and instructions.
• C. The ETF can provide individual-stock tax-loss harvesting control comparable to the separately managed account through its in-kind creation and redemption mechanism.

Best answer: C

Explanation: Pooled funds and separately managed accounts differ in the level at which investors can control realized gains and losses. Mutual fund and ETF investors own fund shares rather than the underlying portfolio securities directly. They can realize gains or losses by selling their fund shares, while the fund manager controls underlying security transactions.

ETF in-kind creations and redemptions generally involve authorized participants and can reduce fund-level capital-gain realization and distributions. This tax efficiency does not give retail shareholders personalized tax-loss harvesting rights over individual stocks inside the ETF. A conventional mutual fund may distribute taxable capital gains even to shareholders who retain their shares. In the separately managed account, direct stock ownership allows the manager to implement security-level tax-loss harvesting under the investor’s instructions.

• A. Portfolio-level gains can be distributed to a U.S. mutual fund shareholder independently of whether that shareholder redeems any shares.
• B. Direct ownership and the manager’s acceptance of tax instructions allow selected stock losses to be realized in the investor’s own account.
• C. In-kind redemptions can improve ETF tax efficiency, but retail shareholders do not direct tax-loss sales of the fund’s underlying stocks.

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Question 38

Topic: Quantitative Methods

An analyst compares a full-market-capitalization-weighted index with a float-adjusted market-capitalization-weighted index. Both contain only the firms below at the same prices. Alder and Briar are technology companies; Cedar is a utility. Freely available shares exclude all restricted ownership. Share counts are in millions.

Relative to full-capitalization weighting, which conclusion about technology-sector exposure under float-adjusted weighting is most accurate?

• A. It decreases by approximately 12.3 percentage points.
• B. It decreases by approximately 38.0 percentage points.
• C. It decreases by approximately 32.6 percentage points.

Best answer: A

Explanation: Float-adjusted capitalization equals share price multiplied by shares freely available to investors. Each weight uses total float-adjusted capitalization as its denominator, so the weights continue to sum to 100%.

Before adjustment, Alder, Briar, and Cedar have capitalizations of $4.0 billion, $4.0 billion, and $2.0 billion, respectively. Technology exposure is therefore \( (4.0 + 4.0)/10.0 = 80.0\% \).

After adjustment, their investable capitalizations are $1.2 billion, $3.0 billion, and $2.0 billion. Technology exposure becomes \( (1.2 + 3.0)/6.2 \approx 67.7\% \), a decrease of approximately 12.3 percentage points. Excluding restricted technology holdings shifts relative exposure toward the fully available utility. Float adjustment measures available ownership at market value, not share counts or trading volume.

• A. Technology’s full-capitalization weight is 80.0%; its float-adjusted weight is $4.2 billion divided by $6.2 billion, or 67.7%.
• B. Using the original $10.0 billion index capitalization as the denominator produces 42.0% technology exposure; the denominator must also exclude restricted ownership.
• C. Technology represents 47.4% of freely available shares by count, but float-adjusted weights must incorporate each company’s share price.

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Question 39

Topic: Equities

An analyst compares a float-adjusted market-capitalization-weighted index and an equal-weighted index containing the same 50 stocks. There are no dividends, corporate actions, or rebalancing during the month. Ardent’s share price increases 10%, while all other constituent prices remain unchanged.

Trading observations:

• Only 15% of Ardent’s outstanding shares are freely tradable.
• Ardent has a relatively wide quoted bid-ask spread and little displayed quantity at the best ask.
• A large market buy exhausts the best-ask quantity, with the remaining shares purchased at higher ask prices.

Which conclusion is least appropriate based solely on this evidence?

• A. Ardent’s large weight in the float-adjusted index reflects a high intrinsic equity value relative to the other constituents.
• B. The float-adjusted index’s higher return reflects its greater exposure to Ardent’s share-price increase.
• C. The purchase’s execution above the initial best ask reflects limited market depth in Ardent’s shares.

Best answer: A

Explanation: Float-adjusted capitalization weighting uses the market value of publicly tradable shares, not estimated intrinsic value. A company can have a substantial index weight despite a low free-float percentage if its total market capitalization is sufficiently large.

With all other constituent prices unchanged, Ardent accounts for the entire index return: \(0.20 \times 10\% = 2.0\%\) for the float-adjusted index and \(0.02 \times 10\% = 0.2\%\) for the equal-weighted index. The return difference therefore reflects weighting concentration.

Market depth describes the quantity available at quoted prices. The purchase consumes the best-ask quantity and reaches higher asks, supporting the liquidity interpretation. Neither index weights nor execution records establish intrinsic value, which requires analysis of expected cash flows and their risk.

• A. Float-adjusted weights depend on market prices, shares outstanding, and free-float percentages; they do not establish relative intrinsic equity values.
• B. Ardent’s 10% gain contributes 2.0% at a 20% initial weight, versus 0.2% at a 2% initial weight.
• C. Exhausting the best-ask quantity and purchasing additional shares at higher asks demonstrates insufficient depth at the initial quote for the order size.

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Question 40

Topic: Quantitative Methods

An analyst uses Monte Carlo simulation to estimate the probability that a $100,000 investment will be worth less than $125,000 after five years, with no external cash flows.

Simulation model:

• Annual log returns are independent and normally distributed, with a historical estimated mean of 6% and standard deviation of 15%. These parameters remain fixed across both runs.
• Investment value evolves according to \(W_t = W_{t-1}e^{r_t}\), where \(r_t\) is the simulated annual log return.

Each run uses independent simulated paths:

The analyst concludes:

The smaller sampling error confirms that our return assumptions are appropriate for forecasting real-world shortfall risk.

Which correction to the analyst’s interpretation is most accurate?

• A. More paths reduce uncertainty in the mean and volatility inputs; they do not establish that the assumed return process is economically appropriate.
• B. More paths reduce bias caused by the normal-return assumption; they do not establish that the assumed return process is economically appropriate.
• C. More paths reduce simulation sampling error; they do not establish that the assumed return process is economically appropriate.

Best answer: C

Explanation: Monte Carlo probabilities are conditional on the assumed return distribution, its parameters, and the investment-value relationship. The 40.9% result estimates shortfall probability under the specified model, rather than establishing the actual probability independently of that model.

For independent paths, the sampling standard error of an estimated event probability is approximately \(\sqrt{\hat{p}(1-\hat{p})/N}\), where \(\hat{p}\) is the simulated probability and \(N\) is the number of paths. Increasing the path count by a factor of 100 therefore reduces standard error by approximately a factor of 10.

This improvement concerns numerical precision. It neither improves the historical estimates of mean and volatility nor validates normality and independence. Separate empirical and economic assessment is needed to evaluate whether those assumptions adequately represent investment risk.

• A. The mean and volatility inputs remain fixed; additional simulated paths provide no new historical evidence to reduce uncertainty in those estimates.
• B. Additional paths reproduce the same assumed normal distribution more precisely; they cannot correct any bias arising from an inappropriate distributional assumption.
• C. The hundredfold increase in paths reduces sampling standard error approximately tenfold, but provides no evidence validating the fixed return assumptions.

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Question 41

Topic: Corporate Finance

A manufacturer incurred recurring losses from purchases at inflated prices from a director-owned supplier. It now requires independent approval of related-party contracts and makes the chief financial officer accountable for compliance. Its bank subsequently offers a lower loan spread.

To isolate the risk effect, an analyst holds forecasts of positive future cash flows to equity constant and lowers the required equity return. The analyst concludes:

“Lower governance risk guarantees a higher realized stock return for investors buying after the reforms are fully reflected in the share price.”

Which correction is most accurate?

• A. The lower required return decreases estimated share value, while subsequent realized stock returns remain uncertain.
• B. The lower required return increases estimated share value, while subsequent realized stock returns remain uncertain.
• C. The lower required return leaves estimated share value unchanged, while subsequent realized stock returns remain uncertain.

Best answer: B

Explanation: Effective governance can reduce agency costs by limiting self-dealing and holding decision makers accountable. Independent approval of supplier contracts reduces opportunities for overpayments, supporting more reliable operating cash flows. The bank’s narrower loan spread is consistent with improved creditor confidence and lower perceived credit risk.

Equity value is the present value of expected cash flows to shareholders. Holding positive cash-flow forecasts constant, a lower required equity return reduces the discount rate and raises estimated value. This valuation effect differs from a guaranteed subsequent investment return. Once the market price reflects the expected benefits of reform, investors buying at that price have no assurance of superior realized performance. Actual returns depend on subsequent cash flows, risk assessments, distributions, and the eventual selling price.

• A. With positive forecast cash flows unchanged, reducing the discount rate increases their present value rather than decreasing it.
• B. A lower governance risk premium raises the present value of unchanged cash flows, but does not guarantee higher returns after the benefits are priced in.
• C. Unchanged cash-flow forecasts do not imply unchanged value when the required return used to discount those cash flows has fallen.

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Question 42

Topic: Economics

An analyst observes the following market quotes. Exchange rates are stated in US dollars per euro.

Both interest rates use simple interest, and the six-month period is 0.5 years. Borrowing and lending rates are identical within each currency. Ignore transaction costs, bid-ask spreads, taxes, and default risk.

For initial borrowing of $1,000,000 or its euro equivalent at spot, which fully covered strategy and approximate maturity profit are most accurate?

• A. Borrow euros, invest in US dollars, and buy euros forward; the profit is approximately $8,455.
• B. Borrow US dollars, invest in euros, and sell euros forward; the profit is approximately $8,455.
• C. Borrow US dollars, invest in euros, and sell euros forward; the profit is approximately $18,182.

Best answer: B

Explanation: Covered interest rate parity equates domestic investment returns with foreign investment returns converted at a contracted forward rate. The no-arbitrage six-month forward rate is \(1.1000 \times 1.025 / 1.015 = 1.11084\) US dollars per euro.

The quoted rate of 1.1200 makes euros overpriced forward. Borrowing $1,000,000 and converting at spot provides €909,090.91. Investing for six months produces €922,727.27, which can be sold forward for $1,033,454.55. The dollar loan repayment is $1,025,000, leaving a profit of approximately $8,455.

The forward contract fixes the conversion rate and locks in the profit. An expected future spot rate would not provide the same protection.

• A. Buying euros forward to repay the euro loan costs $1,033,454.55, exceeding the dollar investment proceeds of $1,025,000 and creating a loss.
• B. Selling the €922,727.27 investment proceeds forward produces $1,033,454.55, exceeding the dollar loan repayment of $1,025,000 by $8,454.55.
• C. The $18,182 amount reflects the spot-to-forward currency gain on principal alone, omitting interest earned on euros and interest owed on dollars.

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Question 43

Topic: Ethical and Professional Standards

Elena Ward, CFA, is selecting an investment for a client’s short-term reserve. The client’s mandate requires daily liquidity and short-duration, investment-grade bond exposure.

Documented comparison: Both funds meet the mandate and hold the same securities in the same proportions. Ward’s analysis finds equivalent expected pre-fee returns, risks, service quality, and transaction costs.

Firm incentives: Ward’s employer permits either fund but has established a proprietary-fund sales target linked to her bonus. The client received full and fair disclosure of this compensation conflict and acknowledged it.

A colleague proposes:

“Both funds meet the mandate, and the conflict has been disclosed, so recommend the proprietary fund to support our sales target.”

Which recommendation is most appropriate when applying Ward’s duties of loyalty to the client and employer under the CFA Institute Code and Standards?

• A. Recommend investing half the allocation in each of the two funds.
• B. Recommend investing the entire allocation in the independently managed fund.
• C. Recommend investing the entire allocation in the firm’s proprietary fund.

Best answer: B

Explanation: Standard III(A), Loyalty, Prudence, and Care, requires placing client interests ahead of the employer’s or member’s interests. Sales targets are permissible business goals, but they cannot justify a recommendation that sacrifices the client’s financial interests.

Both funds satisfy the mandate. Their equivalent portfolios and services mean that the proprietary fund’s higher expenses provide no offsetting client benefit. The independently managed fund therefore offers the better expected after-fee outcome.

Full and fair disclosure addresses the compensation conflict, but the client’s acknowledgment does not replace Ward’s duty of loyalty or objective analysis. Loyalty to her employer does not require favoring its product at the client’s expense. Proprietary funds remain permissible when their characteristics and costs are justified by the client’s needs.

• A. Splitting the allocation increases expenses relative to using the external fund and adds no diversification benefit because both funds hold the same portfolio.
• B. With equivalent investment and service benefits, the external fund’s lower expenses better serve the client’s financial interests; the sales target does not override that duty.
• C. Suitability and conflict disclosure do not justify choosing a higher-cost equivalent fund primarily to meet the employer’s sales target.

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Question 44

Topic: Alternative Investments

A relative-value hedge fund expects a corporate bond’s spread over its Treasury benchmark to narrow. It begins a one-month period with $10 million of investor equity and the following positions. Borrowing funds the remaining net investment.

During the month, the corporate bond’s yield rises by 40 basis points and the Treasury yield rises by 10 basis points. Net financing and short-borrowing costs total $100,000. There are no investor contributions or withdrawals.

Using first-order duration estimates and ignoring convexity and coupon income, the fund’s approximate return on beginning investor equity and the main driver of its loss are most likely:

• A. A 13.0% loss, primarily from widening corporate credit spreads.
• B. A 13.0% loss, primarily from rising benchmark interest rates.
• C. A 1.3% loss, primarily from widening corporate credit spreads.

Best answer: A

Explanation: A duration-matched relative-value trade hedges parallel yield changes but retains exposure to changes in the spread between its positions. Here, the exposures match because \(100 \times 4 = 80 \times 5\). The corporate spread widens by 30 basis points, moving against the fund’s convergence thesis.

The long bond loses approximately \(100 \times 4 \times 0.004 = 1.6\) million dollars. The Treasury short gains approximately \(80 \times 5 \times 0.001 = 0.4\) million dollars. After financing costs, the net loss is $1.3 million, giving an equity return of \(-1.3/10 = -13.0\%\).

Leverage magnifies the loss relative to investor equity. Neutrality to parallel interest-rate movements does not eliminate spread risk or financing costs.

• A. Spread widening causes a $1.2 million trading loss; financing costs raise the loss to $1.3 million, or 13.0% of investor equity.
• B. The positions have equal dollar-duration exposure, so losses from the common increase in benchmark yields are approximately offset by gains on the Treasury short.
• C. The $1.3 million net loss must be divided by $10 million of investor equity, not the $100 million long position.

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Question 45

Topic: Financial Statement Analysis

Larkspur Manufacturing reports under IFRS and expanded direct-to-consumer sales through its website in 2026. Sales increased from $100 million in 2025 to $120 million in 2026.

Production costs are included in cost of sales. Marketing and outbound delivery costs are included in selling and distribution expense. These classifications are unchanged, and there are no other income or expense items.

Income statement data, as percentages of sales:

Based on the common-size analysis, which conclusion about the change in profitability is least accurate?

• A. The decline in operating margin reflects a higher selling and distribution burden outweighing the improvement in gross margin.
• B. The increase in operating profit in dollars reflects improved operating cost efficiency relative to sales.
• C. The increase in net profit margin reflects lower interest and tax burdens outweighing the decline in operating margin.

Best answer: B

Explanation: Common-size analysis measures income statement items relative to sales, so higher dollar profit does not necessarily indicate improved profitability per dollar of sales.

Gross margin rose from 40% to 45%. Selling and distribution expense, however, rose from 15% to 22% of sales, while administrative expense remained at 10%. Operating margin therefore declined from 15% to 13%. The direct-to-consumer channel shift is consistent with higher gross margins and greater marketing and delivery costs; unchanged accounting classifications support comparison across years.

Operating profit nevertheless increased from $15 million to $15.6 million. Its 4% growth was slower than the 20% sales growth, indicating that the dollar increase came from a larger sales base rather than improved operating cost efficiency.

The combined interest and tax burden declined from 7.3% to 4.2% of sales. Consequently, net profit margin increased from 7.7% to 8.8%, despite weaker operating profitability.

• A. Gross margin increased by 5 percentage points, while selling and distribution expense increased by 7 percentage points of sales, reducing operating margin.
• B. Operating profit rose from $15 million to $15.6 million as sales expanded, while operating costs increased from 85% to 87% of sales.
• C. Interest and tax burdens fell by a combined 3.1 percentage points, exceeding the 2-percentage-point operating margin decline and raising net profit margin.

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Question 46

Topic: Equities

At the start of a year, an investor buys 100 shares of a stock at $40 per share. The following events occur:

• Midyear: The stock pays its only dividend of $2 per share and trades at $40 immediately after payment.
• After the dividend: A 2-for-1 stock split occurs.
• Year-end: The stock trades at $22 per post-split share.

The baseline assumes the dividend is held as cash earning no return. The investor instead reinvests the entire dividend immediately at the midyear price. All prices and corporate actions remain unchanged. Ignore taxes and transaction costs.

Under the revised assumption, the stock’s price return and the investor’s total return over the year, respectively, are closest to:

• A. 10.5% and 15.5%.
• B. 10.0% and 15.5%.
• C. 10.0% and 15.0%.

Best answer: B

Explanation: Price return measures price appreciation on a comparable share basis. The 2-for-1 split makes the $22 ending price equivalent to $44 per original share. Thus, price return is \(44/40 - 1 = 10.0\%\).

The initial investment is $4,000. The investor receives a $200 dividend, which purchases five additional shares at $40 each. The split doubles the resulting 105 shares to 210 shares. Ending wealth is therefore $4,620, and total return is \(4{,}620/4{,}000 - 1 = 15.5\%\).

Under the cash-retention baseline, ending wealth would be $4,400 in stock plus $200 in cash, producing a 15.0% total return. Reinvestment adds $20 to ending wealth and raises total return by 0.5 percentage points. It does not change the stock’s price return.

• A. The 10.5% figure includes gains on shares purchased with dividend income; the stock’s price return uses only comparable starting and ending prices.
• B. The split-adjusted ending price is $44, and reinvestment produces ending wealth of $4,620 from the initial $4,000 investment.
• C. The 15.0% total return assumes the dividend remains in cash and omits the $20 gain earned by reinvesting it.

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Question 47

Topic: Quantitative Methods

An analyst uses the following baseline joint probability distribution for the one-year returns of two portfolios. The outcomes are mutually exclusive and exhaustive, and the baseline correlation is 1.00.

The analyst revises only Portfolio B’s return in the outcome with probability 0.50, from 5% to 15%. All probabilities and other returns remain unchanged.

The revised correlation between the portfolios’ returns is closest to:

• A. 0.707
• B. 1.000
• C. 0.816

Best answer: C

Explanation: Correlation equals covariance divided by the product of the return standard deviations. Expressing returns as decimals, the revised probability-weighted means are \(E(R_A)=0.05\) and \(E(R_B)=0.10\).

For each joint outcome, subtract the revised means from the paired returns, multiply the deviations, and weight by the outcome’s probability. The covariance contributions are 0.005625, 0, and 0.001875, totaling 0.0075.

Probability-weighting the squared deviations gives variances of 0.01125 for Portfolio A and 0.00750 for Portfolio B. Therefore:

\[ \rho_{A,B}=\frac{0.0075}{\sqrt{0.01125\times0.00750}}\approx0.816. \]

Covariance is unchanged because Portfolio A’s return in the revised outcome equals its expected return. Portfolio B’s variance increases, however, reducing correlation from its baseline value of 1.00.

• A. Retaining Portfolio B’s baseline mean of 5% when calculating its revised variance produces this value; its revised mean is actually 10%.
• B. Covariance remains unchanged, but Portfolio B’s variance increases from 0.0050 to 0.0075, so perfect positive correlation no longer holds.
• C. Using decimal returns, the covariance is 0.0075 and the revised variances are 0.01125 and 0.0075, giving a correlation of approximately 0.816.

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Question 48

Topic: Portfolio Construction

An investor seeks the highest expected annual return with annual portfolio volatility no greater than 10%. The investor may select only one risky portfolio and place any remaining capital in a risk-free asset yielding 2% annually. Borrowing and short selling are prohibited.

All three risky portfolios hold diversified baskets of securities. Their volatility estimates incorporate correlations among their holdings.

An analyst concludes:

Portfolio C is dominated by B. B exceeds the volatility limit, so investing entirely in A is the optimal allocation.

Which allocation most accurately corrects the analyst’s conclusion?

• A. Hold four-ninths in B and five-ninths in the risk-free asset, for an expected return of 6%.
• B. Hold all capital in A and none in the risk-free asset, for an expected return of 7%.
• C. Hold two-thirds in B and one-third in the risk-free asset, for an expected return of 8%.

Best answer: C

Explanation: The volatility limit applies to the investor’s final allocation, not to the risky holding alone. Portfolio C is correctly eliminated because B offers a higher expected return at the same volatility.

For a risky portfolio combined with a risk-free asset, the Sharpe ratio measures the expected excess return available per unit of volatility. B’s ratio is \((11 - 2)/15 = 0.60\), compared with \((7 - 2)/10 = 0.50\) for A.

Because the risk-free asset has zero volatility, a weight \(w\) in B produces final volatility of \(w\sigma_B\). The maximum permitted weight is therefore \(w = 10/15 = 2/3\). Expected return is:

\[ 2\% + \frac{2}{3}(11\% - 2\%) = 8\%. \]

B is the preferred risky component, while the investor’s final allocation includes one-third in the risk-free asset to satisfy the volatility constraint.

• A. This allocation has only 6.67% volatility; increasing the weight in B to two-thirds raises expected return while remaining within the 10% limit.
• B. Although this allocation satisfies the volatility limit, combining B with the risk-free asset produces an 8% expected return at the same 10% volatility.
• C. The allocation has volatility of two-thirds times 15%, or 10%, and expected return of two-thirds times 11% plus one-third times 2%, or 8%.

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Question 49

Topic: Portfolio Construction

An adviser is reviewing the investment policy statement of an investor with a $400,000 portfolio. The investor states:

“I could tolerate a 35% portfolio decline and would remain invested.”

Financial profile:

• Consulting income is variable and leaves little surplus after living expenses and mortgage payments.
• A $120,000 tuition payment is due in 12 months and will be funded from the portfolio.
• Cash savings outside the portfolio cover one month of living expenses.
• The remaining portfolio assets are intended for retirement in 25 years.

Which approach to setting the portfolio’s current risk tolerance is most appropriate?

• A. Use financial capacity as the binding limit on portfolio risk.
• B. Use the midpoint of willingness and financial capacity to set portfolio risk.
• C. Use stated willingness as the binding limit on portfolio risk.

Best answer: A

Explanation: Willingness to take risk reflects psychological comfort with losses; ability to take risk depends on financial resources and constraints. When they differ, the lower of willingness and ability generally limits appropriate risk tolerance.

Comfort with a 35% decline indicates high willingness. Financial capacity is more limited because income is variable, cash reserves are small, and $120,000 must be available in 12 months. The 25-year retirement horizon applies to the remaining assets, not to the tuition payment. The policy should therefore constrain risk to current financial capacity and provide for near-term liquidity. This does not require eliminating growth investments, and risk tolerance can be reassessed if financial circumstances improve.

• A. Variable income, limited reserves, and the near-term tuition payment constrain the ability to bear losses below the investor’s stated willingness.
• B. A midpoint would exceed the lower financial-capacity limit; willingness and ability are distinct considerations rather than ratings to be averaged.
• C. Willingness and a long retirement horizon do not override the limited loss-bearing capacity created by near-term obligations, small reserves, and variable income.

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Question 50

Topic: Economics

Two firms selling differentiated products choose prices independently and simultaneously for a single selling period. Each can charge either $50 or $40, has constant unit variable costs of $20, and incurs no fixed costs. Quantities sold depend on both firms’ prices:

Which pricing outcome and combined profit are most likely in Nash equilibrium?

• A. One firm charges $40 and the other $50, generating combined profit of $4,200.
• B. Both firms charge $50, generating combined profit of $4,800.
• C. Both firms charge $40, generating combined profit of $4,400.

Best answer: C

Explanation: A Nash equilibrium occurs when neither firm can improve its profit by changing its own action while the rival’s action remains unchanged. Profit equals price minus unit variable cost, multiplied by quantity sold.

• If the rival charges $50, charging $50 earns $2,400, while charging $40 earns $3,000.
• If the rival charges $40, charging $50 earns $1,200, while charging $40 earns $2,200.

Thus, $40 is a dominant strategy for each firm. Both charge $40 in equilibrium, earning combined profit of $4,400. Charging $50 together would produce higher combined profit of $4,800, but each firm has an individual incentive to undercut that price. Joint profit maximization and independent profit maximization therefore lead to different outcomes.

• A. The firm charging $50 earns $1,200 and can increase its profit to $2,200 by matching $40, so unequal prices are unstable.
• B. With its rival charging $50, either firm can increase its profit from $2,400 to $3,000 by charging $40, so this outcome is unstable.
• C. Charging $40 is each firm’s best response to either rival price, and each earns $2,200 when both charge $40.

Questions 51-75

Question 51

Topic: Alternative Investments

An investor has just paid the initial capital calls for two private-equity funds. Both have three-year investment periods beginning at subscription, and their capital commitments are binding. Years below are measured from subscription.

The portfolio companies have comparable business risk. Their debt is nonrecourse to fund investors. Neither fund plans interim distributions. Fund A plans to sell its shares and distribute proceeds when its 12-month post-IPO lockup ends. Fund B plans to distribute proceeds at trade-sale closing. Neither exit is guaranteed.

Which comparison of the remaining funding obligation and the earliest planned cash distribution is most accurate?

• A. Fund A has a smaller remaining funding obligation and a longer planned wait for cash distributions than Fund B.
• B. Fund A has a smaller remaining funding obligation and a shorter planned wait for cash distributions than Fund B.
• C. Fund A has a larger remaining funding obligation and a longer planned wait for cash distributions than Fund B.

Best answer: A

Explanation: A capital commitment is an obligation to provide funds when called, not an amount necessarily invested immediately. After the initial payments, Fund A’s remaining obligation is $12 million minus $9 million, or $3 million. Fund B’s is $8 million minus $2 million, or $6 million.

An IPO also does not necessarily provide immediate cash to existing investors. Fund A’s planned Year 4 listing is followed by a 12-month lockup, so its earliest planned cash distribution is at the end of Year 5. Fund B plans a cash distribution at its Year 4 trade-sale closing. These dates remain forecasts because either exit could be delayed or fail.

Fund A’s higher portfolio-company leverage amplifies equity downside exposure; it does not reduce the investor’s binding commitment. Its higher target gross multiple is neither a realized return nor an annualized return. Realized investor returns depend on actual capital calls, net distributions, and their timing.

• A. Fund A requires another $3 million versus Fund B’s $6 million, while its lockup delays planned cash distributions until Year 5 rather than Year 4.
• B. The IPO does not immediately produce distributable cash for Fund A; its shares remain locked up until Year 5, after Fund B’s planned cash exit.
• C. Fund A’s larger total commitment does not imply more remaining funding: its uncalled commitment is $3 million, compared with Fund B’s $6 million.

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Question 52

Topic: Equities

An analyst evaluates a full market-capitalization-weighted price-return index containing only the following stocks. Its initial divisor is 100,000.

During the measurement period:

• Stock A completes a 2-for-1 split and closes at $22.
• Stock B closes at $27 ex-dividend and pays an ordinary cash dividend of $1 per share at the end of the period.
• Stock C closes at $21.

There are no other corporate actions or constituent changes. The index’s price return for the period is closest to:

• A. An increase of 0.83%.
• B. A decrease of 19.17%.
• C. A decrease of 0.83%.

Best answer: C

Explanation: A market-capitalization-weighted price index uses current shares outstanding and excludes cash dividends from its return. A 2-for-1 split doubles A’s shares to 2,000,000 while mechanically halving its price. The split alone leaves market capitalization unchanged, so no divisor adjustment is needed.

Initial aggregate market capitalization is $40,000,000 + $60,000,000 + $20,000,000 = $120,000,000. Ending capitalization is $44,000,000 + $54,000,000 + $21,000,000 = $119,000,000.

With the unchanged divisor of 100,000, the index falls from 1,200 to 1,190. Its price return is \(1,190/1,200 - 1 \approx -0.83\%\).

B’s $2,000,000 dividend would be included in a total-return calculation, producing a positive 0.83% return, but it is excluded from the price return.

• A. Including B’s $2,000,000 cash dividend produces a total return of 0.83%, rather than the requested price return.
• B. This result leaves A’s share count at 1,000,000 after the split, incorrectly treating its mechanically lower per-share price as lost market capitalization.
• C. Using A’s post-split share count, aggregate market capitalization decreases from $120,000,000 to $119,000,000, producing a price return of approximately -0.83%.

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Question 53

Topic: Equities

An analyst estimates the following market model from historical annual total returns, rather than excess returns:

\[ R_{i,t} = 0.02 + 1.20R_{m,t} + \varepsilon_t \]

Here, \(R_{i,t}\) is the stock return, \(R_{m,t}\) is the market return, and \(\varepsilon_t\) is the regression residual. Returns are expressed as decimals.

For the coming year, the annual risk-free rate is 3.0% and the expected annual market return is 8.0%. The analyst uses CAPM to estimate an equilibrium required return and assumes the estimated beta remains appropriate.

Which interpretation is least accurate?

• A. The stock’s equilibrium required annual return is 11.6%, using the estimated intercept and beta with the expected annual market return.
• B. A one-percentage-point higher market return is associated with a 1.20-percentage-point higher fitted stock return in the historical sample.
• C. The stock’s equilibrium required annual return is 9.0%, using the estimated beta with the risk-free rate and the expected market risk premium.

Best answer: A

Explanation: The market model describes historical return co-movement; CAPM relates an equilibrium required return to systematic risk. The estimated slope of 1.20 can inform CAPM when it remains an appropriate estimate of beta.

The required annual return is:

\[ r_i = r_f + \beta_i\bigl(E[R_m] - r_f\bigr) = 3.0\% + 1.20(8.0\% - 3.0\%) = 9.0\% \]

The market-model intercept of 2.0% is the fitted stock return when the market return equals zero. Substituting an 8.0% market return into that historical relationship produces 11.6%, but does not establish an equilibrium required return. The intercept, residual variation, and historical goodness of fit do not independently establish the future return investors require.

• A. The calculation \(2.0\% + 1.20 \times 8.0\% = 11.6\%\) applies the historical regression relationship, not the CAPM equilibrium required-return relationship.
• B. The estimated beta is the regression slope, measuring the change in fitted stock return associated with a change in market return.
• C. CAPM gives \(3.0\% + 1.20(8.0\% - 3.0\%) = 9.0\%\), applying beta to the expected market risk premium.

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Question 54

Topic: Ethical and Professional Standards

Mara Ellis, CFA, has distributed a buy report to 12 institutional clients stating that a biotechnology issuer’s lead drug has received regulatory approval.

Subsequent findings:

• The regulator’s public website confirms that the application remains pending and approval has not been granted.
• During a private call, the issuer’s CFO inadvertently reveals that a recently completed clinical trial failed. The result is material, confidential, and has not been publicly released.

As part of the firm’s immediate effort to prevent misuse and correct the research, which action is least appropriate under the CFA Institute Standards of Professional Conduct?

• A. Inform compliance of the trial failure and request that the issuer be placed on the firm’s restricted list.
• B. Withdraw the report and send recipients a correction of the approval claim using the regulator’s public information.
• C. Withdraw the report and send recipients a correction that identifies the failed clinical trial as the reason.

Best answer: C

Explanation: Standard II(A), Material Nonpublic Information, prohibits acting or causing others to act on material information that is not public. Sending the trial result to all 12 client recipients would not make it public and could prompt investment decisions based on that information. Disclosure to designated compliance personnel instead supports controls against misuse.

The misleading approval claim also requires prompt correction under Standard I(C), Misrepresentation. Ellis can withdraw the report and correct that claim using the regulator’s public record without revealing the trial failure. Correcting the public error need not wait for the issuer’s announcement. Ellis should encourage the issuer to disseminate the trial result through an appropriate public channel.

• A. Sharing the result with compliance supports trading controls and limits sensitive information to personnel responsible for preventing misuse.
• B. The public regulatory record supports correcting the approval claim, allowing prompt remediation without disclosing the material nonpublic trial result.
• C. A notice to the firm’s clients is not public dissemination, and disclosing the failed trial could cause trading on material nonpublic information.

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Question 55

Topic: Financial Statement Analysis

An analyst is converting an IFRS retailer’s 2026 operating cash flows from the indirect method to the direct method. Consolidated cost of sales was $120 million, consisting entirely of the carrying amount of merchandise sold.

The analyst gathers the following balances, in millions of dollars:

Additional information:

• A business acquisition during 2026 added $5 million of inventory and $2 million of trade payables to the consolidated balances at the acquisition date.
• Trade payables relate solely to merchandise purchases.
• Apart from the acquisition, there were no noncash or foreign-currency movements affecting these accounts.

Cash paid to merchandise suppliers during 2026 was most likely:

• A. $117 million.
• B. $122 million.
• C. $119 million.

Best answer: C

Explanation: Cash payments to suppliers are reconstructed by first calculating merchandise purchases, then adjusting purchases for changes in trade payables. Acquisition-date balances must be excluded from reported working-capital changes because their initial recognition does not represent operating purchases or payments.

All amounts below are in millions of dollars:

• Operating inventory increase: \(32 - 24 - 5 = 3\).
• Merchandise purchases: \(120 + 3 = 123\).
• Operating trade payable increase: \(21 - 15 - 2 = 4\).
• Cash paid to suppliers: \(123 - 4 = 119\).

An inventory increase raises purchases relative to cost of sales. A payable increase reduces cash payments relative to purchases.

• A. This amount excludes acquired inventory but uses the full $6 million payable increase, incorrectly treating acquired payables as an operating increase.
• B. Using the unadjusted inventory increase of $8 million and payable increase of $6 million incorrectly includes the acquisition-related balances in operating movements.
• C. Excluding acquired balances gives an inventory increase of $3 million and a payable increase of $4 million, yielding payments of $119 million.

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Question 56

Topic: Derivatives and Risk Management

A non-dividend-paying stock currently trades at $80. A derivative pays cash only at the end of one year. In a one-period binomial model, the only possible terminal outcomes are:

The effective annual risk-free rate is 5%. Assume frictionless markets, unrestricted short selling, and borrowing and lending at the risk-free rate.

Which valuation conclusion is most appropriate for determining the derivative’s current no-arbitrage value?

• A. Value the derivative at $10.58 using risk-neutral probabilities and the risk-free discount rate.
• B. Value the derivative at $12.38 using forecast probabilities and the risk-free discount rate.
• C. Value the derivative at $11.90 using forecast probabilities and the stock’s forecast return as the discount rate.

Best answer: A

Explanation: No-arbitrage valuation uses risk-neutral probabilities that make the stock’s expected growth equal to the risk-free growth rate. The risk-free-grown current stock price is $84, which lies strictly between the terminal prices of $64 and $100. Therefore, valid risk-neutral probabilities exist.

The up-state risk-neutral probability is:

\[ p = \frac{80(1.05)-64}{100-64} = \frac{5}{9}. \]

The derivative’s current value, in dollars, is:

\[ V_0 = \frac{(5/9)(20)+(4/9)(0)}{1.05} = 10.58. \]

Equivalently, a replicating portfolio holds \(5/9\) shares and borrows approximately $33.86. Its terminal net value is $20 in the up state and $0 in the down state. Its initial cost is approximately $44.44 minus $33.86, or $10.58. The analyst’s forecast probabilities affect expected returns, not this replication cost.

• A. The stock’s risk-free-grown price is $84, implying an up-state risk-neutral probability of \(5/9\) and a discounted expected payoff of $10.58.
• B. This discounts the analyst’s forecast payoff of $13 at 5%, but forecast probabilities do not determine the cost of replicating the payoff.
• C. The stock’s forecast return is 9.25%, but discounting the derivative’s forecast payoff at that rate incorrectly assigns it the stock’s risk exposure.

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Question 57

Topic: Ethical and Professional Standards

Lila Chen, CFA, a portfolio manager, receives two unsolicited offers:

• Client: After the completed year’s portfolio returns are finalized, an existing client offers Chen a $4,000 resort voucher in recognition of her service. The gift has no future-performance or preferential-treatment conditions.
• Issuer: A company Chen is evaluating offers a $2,000 weekend package covering resort lodging and golf for Chen and her partner. The weekend includes a one-hour product briefing that is also available by public webcast.

Before accepting either offer, Chen fully discloses its source, value, and terms to her employer. Her employer gives written permission to accept both.

Which assessment is most accurate under the CFA Institute Standards of Professional Conduct?

• A. Accepting the issuer’s package would comply because written employer approval satisfies the disclosure requirement for benefits received from third parties.
• B. Accepting the issuer’s package would breach the Standards because its leisure benefits could reasonably be expected to impair independent investment judgment.
• C. Accepting the client’s gift would breach the Standards because its substantial value makes recognition for completed investment services an improper benefit.

Best answer: B

Explanation: Independence and Objectivity requires assessing a benefit’s source, purpose, timing, and likely influence, rather than relying solely on its value or disclosure. The issuer’s recreational package is unnecessary to obtain the publicly webcast briefing and could influence Chen’s evaluation of the company. Employer permission does not eliminate that threat.

The client’s gift recognizes completed service and is not contingent on future results or preferential treatment. Such client gifts may be accepted with employer disclosure, allowing the employer to monitor possible favoritism in client service or investment allocation. Chen has disclosed the gift before acceptance. By contrast, a client incentive agreed in advance for future performance requires prior written consent under Additional Compensation Arrangements. Reasonable research-related hospitality is not automatically prohibited.

• A. Employer approval addresses the employer’s interests but does not make potentially influential issuer hospitality acceptable under Independence and Objectivity.
• B. Resort lodging and golf for Chen and her partner extend beyond reasonable research hospitality, particularly when the briefing is available by webcast.
• C. A disclosed, unconditional reward for completed service may be accepted; substantial value alone does not make a client’s gift prohibited.

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Question 58

Topic: Financial Statement Analysis

On 1 January 2027, an IFRS-reporting company purchases a zero-coupon bond for $100,000 and classifies it as fair value through other comprehensive income (FVOCI).

• The bond pays $121,000 at maturity on 31 December 2028.
• Its effective annual interest rate at purchase is 10%.
• Its fair value on 31 December 2027 is $106,000, and the company continues to hold it.

Assume no income taxes, impairment, foreign exchange effects, or dividends.

For 2027, which statement most accurately describes the bond’s effects on retained earnings and accumulated other comprehensive income (OCI)?

• A. Retained earnings are unchanged, and accumulated OCI increases by $6,000.
• B. Retained earnings increase by $10,000, and accumulated OCI decreases by $4,000.
• C. Retained earnings increase by $6,000, and accumulated OCI is unchanged.

Best answer: B

Explanation: For a debt instrument measured at FVOCI, effective-interest income enters profit or loss even when no cash interest is received. With no taxes or dividends, that income increases retained earnings.

The bond earns interest of \(100{,}000 \times 10\% = 10{,}000\), increasing its amortized cost to $110,000. Its year-end fair value is $106,000, so the fair value adjustment recognized in OCI is \(106{,}000 - 110{,}000 = -4{,}000\).

Retained earnings therefore increase by $10,000, while accumulated OCI decreases by $4,000. Total shareholders’ equity increases by $6,000. Comparing fair value only with the purchase price gives the total equity change but does not correctly separate earnings from OCI.

• A. A zero-coupon bond still accrues effective-interest income; treating the entire fair value increase as OCI omits $10,000 of earnings.
• B. Effective-interest income is $10,000, while the $106,000 fair value is $4,000 below the $110,000 year-end amortized cost.
• C. Recognizing the full $6,000 fair value increase in earnings applies fair-value-through-profit-or-loss measurement rather than the stated FVOCI treatment.

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Question 59

Topic: Corporate Finance

An analyst reviews an investor’s purchase of 70% of Marlow Corporation’s voting shares from its founder. The shares are fully paid and freely transferable. The investor elects a new board, which appoints a new chief executive.

Marlow’s bank loan is secured by its operating assets. No shareholder has guaranteed the loan, and the loan contains no change-of-control clause.

Which interpretation of the transaction is most accurate?

• A. Voting control passes to the investor; Marlow remains the borrower and retains ownership of its operating assets.
• B. Voting control passes to the investor; Marlow remains the borrower and the investor directly owns 70% of its operating assets.
• C. Voting control passes to the investor; the investor assumes 70% of the loan and Marlow retains ownership of its operating assets.

Best answer: A

Explanation: A corporation has a legal identity separate from its shareholders. Ownership of 70% of voting shares gives the investor control over board elections, not direct title to corporate property. The board delegates day-to-day management to executives, so replacing management does not replace the legal entity.

Marlow therefore continues to own its operating assets and remains liable for the entire bank loan. With fully paid shares and no shareholder guarantee, ownership alone does not make the investor personally responsible for that loan. Freely transferable shares allow ownership and control to change while the corporation and its obligations continue.

• A. The share transfer changes control, while Marlow’s separate legal identity preserves its asset ownership and responsibility for the existing loan.
• B. The investor owns shares in Marlow, not fractional title to its operating assets; those assets remain the corporation’s property.
• C. Purchasing shares does not transfer a proportional share of corporate debt to the investor; Marlow remains liable for the entire loan.

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Question 60

Topic: Fixed Income

An analyst uses an external long-term issuer credit rating of BBB, with a stable outlook, as one input when assessing a company’s senior unsecured bond.

Baseline liquidation scenario: The bank loan and bond rank equally as unsecured claims. There are no other creditor claims or liquidation costs.

Changed condition: The existing bank loan becomes secured by assets expected to generate $40 million of the $80 million in liquidation proceeds. The bond remains unsecured. Claim amounts, total liquidation proceeds, and the issuer’s operating outlook are unchanged. The rating agency has not revised the issuer rating or outlook.

Relative to the baseline, the analyst’s estimate of the bond’s loss given default should most likely:

• A. Remain at 20.0%.
• B. Increase to 33.3%.
• C. Increase to 66.7%.

Best answer: B

Explanation: An issuer credit rating is an opinion about issuer creditworthiness, not a guarantee of an individual bond’s recovery. It remains useful in credit analysis, but issue-specific security and payment priority require separate assessment. An unchanged rating or stable outlook does not establish unchanged loss severity.

Initially, $80 million of proceeds covers $100 million of equally ranking claims, implying 80% recovery and 20% loss given default. After the amendment, the secured lender receives $40 million from its collateral. The remaining $40 million is available against the unsecured bond’s $60 million claim.

The bond’s revised loss given default is \(1 - 40/60 = 33.3\%\). Its loss severity therefore increases despite the unchanged issuer rating.

• A. The unchanged issuer rating does not preserve the bond’s prior loss severity after the bank lender obtains collateral priority.
• B. The secured loan receives $40 million, leaving bondholders $40 million against $60 million of claims, producing a 33.3% loss.
• C. The revised 66.7% figure is the bond’s recovery rate, whereas loss given default is the unrecovered proportion of its claim.

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Question 61

Topic: Fixed Income

An analyst discounts a bond’s remaining coupons and principal to the settlement date using its quoted nominal annual yield with semiannual compounding. The resulting present value is 101.10. The analyst proposes using 101.10 as the dealer’s quotation without further adjustment. All prices are stated per $100 of par value.

Bond and settlement facts:

• Annual coupon rate: 6%, paid semiannually.
• Previous coupon date: 1 July 2027.
• Next coupon date: 1 January 2028.
• Settlement date: 1 October 2027.
• Accrued-interest convention: Actual/Actual, using 92 elapsed days in a 184-day coupon period.
• Transaction fees: None.

Which interpretation would make the analyst’s proposed quotation most defensible?

• A. A full-price quotation corresponding to a clean price of 99.60.
• B. A clean-price quotation corresponding to a full price of 102.60.
• C. A full-price quotation corresponding to a clean price of 98.10.

Best answer: A

Explanation: The settlement-date present value of remaining bond payments is the full, or dirty, price. The clean price excludes interest accrued since the previous coupon payment.

Each semiannual coupon is $3.00 per $100 of par value. Under the stated Actual/Actual convention, accrued interest is \(3.00 \times \frac{92}{184} = 1.50\). Therefore, the clean price is \(101.10 - 1.50 = 99.60\).

The proposed quotation of 101.10 is defensible as a full-price quotation. The buyer pays $101.10 per $100 of par value, with no additional accrued-interest adjustment. The $1.50 difference between full and clean prices represents accrued coupon interest, not a trading gain. The quoted yield determines discounting; the coupon rate determines accrued interest.

• A. Discounting the remaining payments to settlement produces the full price; subtracting accrued interest of 1.50 gives a clean price of 99.60.
• B. The settlement-date present value already includes accrued interest; treating 101.10 as a clean price would add 1.50 a second time.
• C. Subtracting 3.00 incorrectly accrues the annual coupon over the semiannual period; accrued interest is 1.50, not 3.00.

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Question 62

Topic: Financial Statement Analysis

An analyst reviews an appliance manufacturer’s IFRS financial statements for the year ended 31 December 2026.

Reporting facts:

• Management lowered expected future warranty claims and released $4 million of its warranty provision.
• Reported EBIT, including the release, is $31 million; interest expense is $10 million.
• A debt covenant requires interest coverage of at least 3.0 times, defined as reported EBIT divided by interest expense without adjustments.

Oversight record:

Which conclusion about the reporting oversight is most accurate?

• A. The lender’s covenant increases the incentive to reduce the provision, while favorable analyst reports mainly reflect management’s forecast.
• B. The lender’s review independently corroborates the provision estimate, while favorable analyst reports mainly reflect management’s forecast.
• C. The lender’s covenant increases the incentive to reduce the provision, while favorable analyst reports independently corroborate management’s forecast.

Best answer: A

Explanation: Contractual monitoring disciplines reporting through financial thresholds, but it can also create incentives for earnings-enhancing estimates. Without the $4 million release, EBIT would be $27 million and interest coverage would be \(27/10 = 2.7\), below the required 3.0 times. Reported coverage is \(31/10 = 3.1\), so compliance depends on the provision reduction. The lender’s arithmetic check does not independently validate expected warranty claims.

An unmodified audit opinion provides reasonable assurance that financial statements are free of material misstatement, not certainty about estimation outcomes or the absence of reporting incentives. Regulatory filing acceptance without substantive review does not establish the estimate’s reliability. Analysts repeating management’s forecast contribute no independently verified information about claims. The evidence identifies a reporting incentive and limits on corroboration; it does not establish that the provision was misstated.

• A. The release moves coverage from 2.7 to 3.1 times, achieving compliance, while analysts reuse the forecast that supports the release.
• B. The lender verifies arithmetic using reported figures, so covenant compliance supplies no independent evidence about the reasonableness of the warranty provision.
• C. The analyst reports contain no independent verification, so agreement with management supplies no separate corroboration of the claims forecast.

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Question 63

Topic: Alternative Investments

An analyst evaluates a hedge fund’s annual fees. No subscriptions, redemptions, or distributions occur during the year.

Fund data:

• Beginning-year NAV: $100 million.
• Investment gain before fees: $20 million.
• Prior peak NAV after all fees, used as the high-water mark: $103 million.

Fee terms:

• Management fee: 2% of beginning-year NAV, deducted first.
• Incentive fee: 20%, subject to a 5% annual hard hurdle based on beginning-year NAV and the high-water mark.
• Both incentive-fee protections are evaluated using NAV after the management fee but before the incentive fee. The hurdle has no carryforward.

The incentive-fee-bearing gain and the investors’ net return for the year are most likely:

• A. A fee-bearing gain of $13 million and a net return of 15.4%.
• B. A fee-bearing gain of $10 million and a net return of 16.0%.
• C. A fee-bearing gain of $15 million and a net return of 15.0%.

Best answer: A

Explanation: A hard hurdle excludes the specified current-period return from incentive fees. A high-water mark prevents incentive fees on recovery up to a previously achieved peak NAV after fees. Both can apply together, but their NAV thresholds are compared rather than added.

The management fee is $2 million, leaving NAV of $118 million before the incentive fee. The hard hurdle establishes a threshold of $105 million, which exceeds the $103 million high-water mark. Thus, the fee-bearing gain is $13 million, and the 20% incentive fee is $2.6 million.

Ending NAV after all fees is $115.4 million. Relative to beginning NAV of $100 million, the investors’ net return is \(115.4/100 - 1 = 15.4\%\).

• A. The $105 million hard-hurdle level is binding, so the $13 million fee base produces a $2.6 million incentive fee and a 15.4% net return.
• B. This subtracts the $5 million hurdle return from gains above the $103 million high-water mark, incorrectly adding the two protections.
• C. This charges fees on all gains above the $103 million high-water mark, treating the hard hurdle as a soft trigger rather than excluding the hurdle return.

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Question 64

Topic: Fixed Income

A manufacturer with established commercial paper market access needs $20 million today for 120 days, when seasonal receivables will be collected. Each of these alternative funding packages can provide the full amount now:

• Commercial paper: 30-day maturities, supported by a committed bank backstop available through day 180 solely to repay maturing paper. Backstop borrowings mature on day 180, and all draw conditions remain satisfied during a funding-market disruption.
• Uncommitted bank line: The facility expires on day 180. Each advance matures in 30 days, and every renewal requires bank approval.
• Secured bank loan: Principal matures on day 120. The manufacturer has sufficient eligible receivables to provide the required collateral.

The treasurer prioritizes continuity of funding during short-term market disruptions over modest differences in borrowing costs. Which approach is least appropriate?

• A. Use 30-day advances under the uncommitted bank line, renewing them until the receivables are collected.
• B. Use the 120-day secured bank loan, repaying principal when the seasonal receivables are collected.
• C. Use 30-day commercial paper, drawing the committed backstop if issuance is disrupted before the receivables are collected.

Best answer: A

Explanation: Rollover risk arises when borrowing matures before cash becomes available for repayment. A credit facility’s expiration date is distinct from the maturity of each advance. Although the uncommitted line expires on day 180, its advances mature every 30 days, and the bank is not obligated to renew them. It therefore provides the weakest protection against a funding-market disruption.

Commercial paper also requires frequent refinancing, but the committed backstop can repay maturing paper and maintain financing beyond day 120 under the stated conditions. The secured loan directly spans the full funding period, with repayment aligned to receivable collection. Established market access supports borrowing today; it does not guarantee future refinancing.

• A. The facility’s 180-day expiry does not extend each advance’s 30-day maturity; discretionary renewals leave the manufacturer exposed to a funding shortfall.
• B. The loan aligns principal repayment with receivable collection, and adequate eligible collateral supports borrowing without an interim refinancing requirement.
• C. The committed backstop can repay maturing paper throughout the 120-day funding need, so interrupted commercial paper issuance need not interrupt funding.

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Question 65

Topic: Corporate Finance

A retailer’s finance director proposes extending supplier payment terms and concludes that cash will be tied up for fewer days even though the operating cycle will lengthen.

Estimates for the coming year:

• Annual credit sales under either policy: $73 million.
• Annual cost of sales and credit purchases under either policy: $36.5 million each.
• Use a 365-day year. Balances below are annual averages in millions of dollars.

If suppliers approve the extension, all payments remain within agreed terms, and the estimates are achieved, which conclusion is most accurate?

• A. The cash conversion cycle falls by 25 days to -20 days, with customer collections preceding supplier payments on average.
• B. The cash conversion cycle falls by 7.5 days to 5 days, with supplier payments preceding customer collections on average.
• C. The cash conversion cycle falls by 20 days to -5 days, with customer collections preceding supplier payments on average.

Best answer: C

Explanation: The cash conversion cycle equals the inventory period plus the receivable period minus the payable period. Inventory uses cost of sales, receivables use credit sales, and payables use credit purchases.

Daily credit sales are $200,000, while daily cost of sales and credit purchases are each $100,000. Dividing the average balances by these daily amounts gives:

• Existing policy: inventory 30 days, receivables 10 days, and payables 25 days. The cash conversion cycle is \(30 + 10 - 25 = 15\) days.
• Proposed policy: inventory 35 days, receivables 15 days, and payables 55 days. The cash conversion cycle is \(35 + 15 - 55 = -5\) days.

The operating cycle lengthens from 40 to 50 days, but supplier financing increases by 30 days. Consequently, the cash conversion cycle falls by 20 days. A negative cycle is possible: customer cash is collected before suppliers are paid on average. The agreed payment extension distinguishes this liquidity benefit from overdue supplier obligations.

• A. These results omit the receivable period, which rises from 10 to 15 days and must be included in the cash conversion cycle.
• B. These results incorrectly use sales to calculate inventory and payable periods; those periods require the cost of sales and credit purchases denominators.
• C. The proposed cycle is \(35 + 15 - 55 = -5\) days, compared with 15 days under the existing policy.

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Question 66

Topic: Corporate Finance

A distributor is assessing a proposal to extend customer credit and negotiate later payments to suppliers.

Forecast assumptions:

• All sales and purchases are on credit; daily sales remain $120,000 and daily purchases remain $70,000.
• Working-capital balances other than receivables and payables remain unchanged.
• Suppliers approve the later payments, but current early-payment discounts are lost.

Excluding the cost of lost discounts, which conclusion about the cash conversion cycle and the cash invested in working capital is most accurate?

• A. The cash conversion cycle lengthens by 5 days, and $150,000 of cash is absorbed.
• B. The cash conversion cycle shortens by 5 days, and $150,000 of cash is absorbed.
• C. The cash conversion cycle shortens by 5 days, and $350,000 of cash is released.

Best answer: B

Explanation: The cash conversion cycle equals receivable days plus inventory days minus payable days. It declines from \(30 + 40 - 20 = 50\) days to \(40 + 40 - 35 = 45\) days.

The dollar effect must be calculated separately for each balance:

• Receivables increase by \(10 \times 120{,}000 = 1{,}200{,}000\) dollars, absorbing cash.
• Payables increase by \(15 \times 70{,}000 = 1{,}050{,}000\) dollars, releasing cash.

With all other balances unchanged, cash invested in operating working capital increases by $150,000. A shorter cycle does not necessarily release cash when collection and payment days both change: receivables are based on sales, while payables are based on purchases. Here, the higher dollar base for receivables outweighs the greater extension of payable days. Losing early-payment discounts adds a separate economic cost not included in the working-capital calculation.

• A. Payable days increase by 15, exceeding the 10-day increase in receivable days; because payable days are subtracted, the cycle shortens.
• B. Additional receivables absorb $1.2 million and additional payables release $1.05 million, leaving $150,000 absorbed as the cycle declines from 50 to 45 days.
• C. Multiplying the five-day cycle reduction by daily purchases ignores that additional receivables absorb cash at the higher daily sales amount.

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Question 67

Topic: Corporate Finance

A company’s founder owns 20% of its equity but holds 65% of its voting rights through a dual-class share structure. The founder proposes selling a subsidiary to a private company that the founder wholly owns. An independent committee will provide a valuation and a non-binding recommendation before approval.

Governance provisions:

• Full-board approval requires a simple majority. Most directors are affiliated with the founder and are eligible to vote on the sale.
• Ordinary shareholder approval requires a simple majority of voting rights.
• The board may make completion conditional on binding approval by a majority of disinterested shareholders, excluding the founder and affiliated holders.

Which approval requirement would most effectively limit the founder’s ability to complete the sale on terms unfavorable to minority shareholders?

• A. Require approval by disinterested shareholders.
• B. Require approval by the full board.
• C. Require approval by all voting shareholders.

Best answer: A

Explanation: Controlling-shareholder and minority-shareholder interests can diverge in related-party transactions. If the subsidiary is sold below fair value, the founder bears only 20% of the seller’s resulting loss through equity ownership but captures the buyer’s benefit through full ownership of the private company. Dual-class shares strengthen the founder’s ability to pursue that transfer despite limited economic exposure.

Independent valuation helps assess transaction terms, but a non-binding recommendation cannot block approval by an affiliated board or a controller-dominated shareholder vote. Under the stated governance provisions, binding approval by disinterested shareholders gives investors who lack the buyer’s private benefit the power to reject unfavorable terms. That decision authority provides the strongest protection among the available approval requirements.

• A. Binding approval excluding the founder and affiliated holders gives shareholders who do not benefit from the buyer authority to reject the transaction.
• B. Founder-affiliated directors can carry the board vote, and the independent committee’s advisory recommendation does not prevent them from approving unfavorable terms.
• C. The founder’s 65% voting rights can carry an ordinary shareholder resolution despite the founder owning only 20% of the company’s equity.

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Question 68

Topic: Derivatives and Risk Management

An analyst observes the following for a dividend-paying stock:

• Current spot price: $50 per share.
• Guaranteed dividend: $1 per share in three months, with no other dividends before maturity.
• Six-month forward delivery price: $51.50 per share.
• Borrowing and lending rate: 2% per three-month period, compounded quarterly.
• Analyst’s forecast of the spot price in six months: $54 per share.

The forward requires no initial payment and is physically settled. The stock can be purchased or sold short, short-sale proceeds can be invested, and short sellers must compensate the share lender for dividends. All interim receipts are reinvested and payments financed at the stated rate. Assume no transaction costs, taxes, or default risk.

Which strategy is most appropriate for locking in an arbitrage profit?

• A. Short one share, invest the $50 proceeds, and buy a six-month forward at $51.50.
• B. Borrow $50, buy one share, and sell a six-month forward at $51.50.
• C. Buy a six-month forward at $51.50 and sell the delivered share at the prevailing spot price.

Best answer: B

Explanation: The no-arbitrage forward price equals the financed spot price minus the maturity value of known asset income. Borrowing $50 for two quarters creates a $52.02 repayment. The $1 dividend received after one quarter grows to $1.02 by maturity. Therefore, the fair six-month forward price is $51.00, calculated as \(50(1.02)^2 - 1(1.02)\).

The quoted delivery price of $51.50 exceeds this level. Buying the stock with borrowed funds and selling the forward locks in $51.50 from delivery plus $1.02 from dividend reinvestment, against a $52.02 liability. The resulting $0.50 profit does not depend on the terminal stock price. In contrast, a forward purchase followed by a spot sale remains a directional position because its selling price is uncertain.

• A. The invested proceeds net of the financed dividend payment equal $51.00 at maturity, so obtaining the replacement share for $51.50 locks in a $0.50 loss.
• B. The $51.50 forward proceeds plus the $1.02 reinvested dividend exceed the $52.02 loan repayment, locking in a $0.50 profit.
• C. The profit equals the future spot price minus $51.50; the $54 forecast suggests a gain but does not guarantee the sale price.

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Question 69

Topic: Ethical and Professional Standards

Maya Chen, CFA, manages a discretionary portfolio. The client’s current written mandate requires redemption proceeds to be available within five business days. Her supervisor asks her to select the employer’s private-credit fund because it generates more management-fee revenue than the employer’s bond fund.

Fund details:

• Private-credit fund: A 12-month lockup prevents redemption during that period.
• Bond fund: Redemption proceeds are available within three business days; the fund is otherwise suitable for the client.

All fees, the employer’s financial interests, and both funds’ liquidity terms have been fully and fairly disclosed. The client has not authorized a change to the mandate.

Which statement about Chen’s duties is most accurate?

• A. Chen may select the private-credit fund once its liquidity terms and the employer’s management fees have been fully disclosed.
• B. Chen must select an unaffiliated liquid fund to prevent employer management-fee income from conflicting with her duty to the client.
• C. Chen may select the employer’s bond fund and allow the firm to receive its fully disclosed management fees.

Best answer: C

Explanation: Client interests take priority when an employer’s commercial instruction conflicts with a client obligation. Standard III(A), Loyalty, Prudence, and Care, establishes that priority, while Standard III(C), Suitability, requires discretionary investments to remain consistent with the portfolio’s mandate. The private-credit fund’s lockup violates the client’s liquidity requirement. Disclosure informs the client but does not authorize changing that requirement.

Standard IV(A), Loyalty, still requires loyalty to the employer, but it does not justify breaching client duties. Nor does client loyalty require eliminating every commercial benefit to the employer. Chen may select the suitable bond fund and allow the firm to earn its fully disclosed management fees.

• A. Disclosure does not amend the client’s mandate; the private-credit fund’s 12-month lockup conflicts with the five-business-day liquidity requirement.
• B. Employer affiliation and fee income do not automatically prohibit a suitable investment when the financial interests and fees are fully and fairly disclosed.
• C. The bond fund meets the mandate, and client-first duties do not prohibit fully disclosed employer fees on a suitable investment.

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Question 70

Topic: Alternative Investments

An allocator reviews three-year results through 31 December 2026 for a corporate-credit hedge fund and a broad hedge-fund database composite.

• Fees: Fund returns are net of a 1.5% annual management fee and 20% performance fee. Composite returns are net of varying fee schedules.
• Database: Histories of funds that closed or stopped reporting are removed from all historical composite results.
• Fund exposure: Secured borrowing finances assets equal to four times NAV. Credit spreads narrowed during the period.
• Liquidity: Monthly redemptions require 30 days’ notice. Many holdings trade infrequently and use estimated month-end valuations.

Which due-diligence approach is most appropriate for evaluating manager skill and the fund’s ability to meet stressed redemptions?

• A. Use a fee-comparable credit-strategy benchmark of current reporters, and test redemption funding using stressed sale proceeds and margin requirements.
• B. Use a fee-comparable credit-strategy benchmark including former reporters, and test redemption funding using stressed sale proceeds and margin requirements.
• C. Use a fee-comparable credit-strategy benchmark including former reporters, and test redemption funding using reported volatility and maximum drawdown.

Best answer: B

Explanation: Evaluating hedge fund skill requires comparable fee treatment and strategy exposure, together with an unbiased performance history. The fund’s higher net return coincided with narrowing credit spreads and substantial leverage, so it may reflect systematic credit exposure rather than manager skill. Retaining closed and nonreporting funds avoids survivorship and reporting-selection biases that can inflate historical benchmark performance. A corrected return gap still requires adjustment for strategy exposure before attribution to skill.

Low reported volatility and shallow drawdowns do not establish liquidity. Infrequent trading and estimated valuations can smooth reported returns without improving the ability to sell assets. Secured borrowing can also create additional margin demands during stress. Redemption analysis should therefore compare available cash and stressed asset-sale proceeds, after financing obligations, with the amount and timing of redemption requests.

• A. Restricting the benchmark to current reporters retains the database’s survivorship and reporting-selection biases despite matching fees and credit exposure.
• B. Including former reporters addresses survivorship bias, while stressed liquidation proceeds and financing demands directly assess cash available for the redemption schedule.
• C. Volatility and drawdown measure reported NAV fluctuations, not cash availability; estimated valuations and leveraged financing further weaken their usefulness as redemption-capacity measures.

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Question 71

Topic: Economics

A Canadian portfolio analyst reviews the following spot exchange rates, quoted as Canadian dollars (CAD) per US dollar (USD):

Over this period, the Canadian dollar’s change in value relative to the US dollar is closest to:

• A. An appreciation of 12.0%.
• B. A depreciation of 12.0%.
• C. A depreciation of 10.7%.

Best answer: C

Explanation: A currency’s percentage change must be calculated from its value in units of the comparison currency. The CAD per USD quote measures the US dollar’s value, so the observations must be inverted to measure the Canadian dollar’s value.

The reciprocal rates are \(1/1.2500 = 0.8000\) USD per CAD initially and \(1/1.4000 \approx 0.714286\) USD per CAD finally. Thus:

\[ \left(\frac{1.2500}{1.4000}-1\right)\times100 \approx -10.7\% \]

The Canadian dollar depreciated by approximately 10.7%, while the US dollar appreciated by 12.0%. Percentage changes in reciprocal quotations are not equal and opposite because each change is measured against its own beginning value.

• A. The higher CAD per USD rate means each US dollar buys more Canadian dollars, so the 12.0% appreciation belongs to the US dollar.
• B. Reversing the sign of the 12.0% quote increase ignores the reciprocal relationship; 12.0% measures the US dollar’s appreciation.
• C. Taking reciprocals gives USD per CAD values of 0.8000 and approximately 0.714286, a decline of about 10.7% from the beginning value.

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Question 72

Topic: Fixed Income

On 1 March 2027, immediately after a coupon payment, an analyst values a default-free, annual-pay bond with a $1,000 face value. Its remaining payments and the corresponding annual-effective spot rates are:

The two-year annual-pay par rate for the same curve is quoted as 5.9412%. Using that rate, the analyst calculates the bond’s value in dollars as:

\[ V = \frac{80}{1.059412} + \frac{1{,}080}{(1.059412)^2} = 1{,}037.78. \]

The corrected value of the bond is closest to:

• A. $1,038.12
• B. $1,041.21
• C. $1,036.67

Best answer: A

Explanation: Each fixed cash flow must be discounted using the spot rate corresponding to its maturity. Because the rates are annual effective, the two-year payment requires two years of compounding:

\[ V = \frac{80}{1.04} + \frac{1{,}080}{1.06^2} = 76.9231 + 961.1962 = 1{,}038.12. \]

A par rate is the coupon rate that makes a comparable bond worth its face value under the term structure. It is not a single discount rate that correctly values every coupon schedule. The analyst incorrectly treats the quoted par rate as this bond’s yield to maturity. This bond’s 8% coupon exceeds the 5.9412% par rate, so its correctly calculated value is above par.

• A. Discounting $80 at 4% for one year and $1,080 at 6% for two years gives $1,038.12.
• B. This value uses the simple-interest denominator \(1 + 2(0.06)\) for the final payment; annual-effective compounding requires \(1.06^2\).
• C. Discounting both payments at the two-year spot rate gives this value; the first payment instead requires the one-year spot rate.

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Question 73

Topic: Corporate Finance

An analyst evaluates a proposed recapitalization that increases a company’s financial leverage without changing its operating risk. The analyst estimates the following financing weights and costs:

The marginal corporate tax rate is 25%, and the company can fully use all interest deductions.

Which statement about the proposal’s effect on WACC is most accurate?

• A. WACC remains unchanged, because unchanged operating risk makes the overall required return independent of the financing mix.
• B. WACC decreases, because replacing equity with tax-deductible debt outweighs the increase in required returns.
• C. WACC increases, because higher required returns outweigh the benefit of replacing equity with tax-deductible debt.

Best answer: C

Explanation: WACC weights the after-tax cost of debt and the cost of equity using market-value financing shares. Interest deductibility reduces debt’s effective cost, but greater leverage can increase default risk for lenders and financial risk for shareholders, raising both required returns.

Here, the after-tax debt cost increases from \(5\% \times (1 - 0.25) = 3.75\%\) to \(8\% \times (1 - 0.25) = 6.00\%\). Therefore:

\[ \begin{aligned} \text{Current WACC} &= 0.20(3.75\%) + 0.80(10\%) = 8.75\% \\ \text{Proposed WACC} &= 0.60(6.00\%) + 0.40(14\%) = 9.20\% \end{aligned} \]

The 0.45 percentage-point increase indicates that higher component costs more than offset the benefit of greater reliance on relatively inexpensive, tax-deductible debt. Greater leverage does not automatically lower WACC.

• A. Unchanged operating risk does not establish a constant WACC when taxes and changing financial risk affect financing costs; the calculated WACC rises by 0.45 percentage points.
• B. Debt remains cheaper than equity after tax, but the proposal’s higher component costs produce a 9.20% WACC, compared with the current 8.75%.
• C. Using after-tax debt costs, WACC increases from 8.75% to 9.20%, so higher required returns more than offset the benefit of greater debt financing.

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Question 74

Topic: Financial Statement Analysis

A company reporting under IFRS recognized a $3.0 million deferred tax asset at 31 December 2026 for a $12.0 million deductible temporary difference, using a 25% tax rate.

31 December 2027 tax-note evidence:

• The deductible temporary difference and the related tax base remain unchanged.
• A newly enacted 30% tax rate will apply when the difference reverses.
• Revised forecasts support $8.0 million of probable taxable profit, before using this deduction, during the reversal period.
• No other sources of taxable profit support recognition.

All changes in this deferred tax asset are recognized in profit or loss.

Which interpretation of the combined year-end deferred tax adjustments is most accurate?

• A. Tax expense increases and equity decreases by $1.0 million; the lower deferred tax asset reflects reduced expectations for future taxable profit.
• B. Tax expense decreases and equity increases by $0.6 million; the higher deferred tax asset reflects remeasurement at the increased tax rate.
• C. Tax expense increases and equity decreases by $0.6 million; the lower deferred tax asset reflects reduced expectations for future taxable profit.

Best answer: C

Explanation: IFRS recognizes a deferred tax asset only to the extent that probable taxable profit will be available to utilize the deductible temporary difference. Measurement uses the enacted or substantively enacted tax rate expected when the difference reverses.

Only $8.0 million of the $12.0 million deduction now meets the recognition criterion. In millions of dollars, the revised asset is \(8.0 \times 0.30 = 2.4\), compared with the opening $3.0 million. The $0.6 million reduction is recognized as deferred tax expense, reducing net income and retained earnings by the same amount.

The deduction and tax base have not changed. Reduced recognition reflects weaker expectations for taxable profit, not a smaller underlying temporary difference. The higher enacted tax rate partly offsets the effect of reduced recoverability.

• A. The $1.0 million reduction uses the former 25% rate; measurement must use the enacted 30% rate applicable when the difference reverses.
• B. Applying 30% to the full $12.0 million produces $3.6 million, but only $8.0 million of probable taxable profit supports recognition.
• C. The recognized asset falls from $3.0 million to $2.4 million, increasing deferred tax expense and reducing retained earnings by $0.6 million.

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Question 75

Topic: Equities

An unlisted company has 10 million common shares outstanding. It is considering two transactions, each priced at $20 per share. Shares purchased may be newly issued shares or existing shares sold by current shareholders.

Both routes conclude with the company’s common shares listed on the same stock exchange. Ignore transaction costs and assume there are no other changes in shares outstanding.

Which statement about company financing and subsequent investor-to-investor exchange trades is most accurate?

• A. The private transaction raises $40 million more for the company, and subsequent exchange trades provide both investor liquidity and additional company capital.
• B. The private transaction raises $40 million more for the company, and subsequent exchange trades provide investor liquidity rather than additional company capital.
• C. Both transactions raise $60 million for the company, and subsequent exchange trades provide investor liquidity rather than additional company capital.

Best answer: B

Explanation: Newly issued shares provide capital to the company; sales of existing shares provide proceeds to their owners. Public versus private describes how a transaction is conducted, not necessarily who receives the money.

The public offering increases shares outstanding by 1 million, raising $20 million for the company. Its remaining 2 million shares are existing shares, generating $40 million for selling shareholders. The private transaction increases shares outstanding by 3 million, so all $60 million goes to the company. It therefore raises $40 million more.

After listing, investor-to-investor exchange trades are secondary-market transactions. They provide shareholder liquidity but do not raise additional company capital.

• A. The financing comparison is accurate, but investor-to-investor exchange trades send cash to selling shareholders rather than to the company.
• B. The public offering raises $20 million and the private transaction raises $60 million; subsequent investor-to-investor trades transfer proceeds to selling shareholders.
• C. The public offering’s $60 million transaction value includes sales by existing shareholders; only its 1 million newly issued shares raise company capital.

Questions 76-100

Question 76

Topic: Fixed Income

A professional investor is comparing three one-year euro-denominated bonds issued by a German company. The investor is eligible for all three offerings. Each repays €1,000 at maturity, with any coupon also paid then. Assume all payments occur as contracted and there are no transaction costs.

Issue terms:

• Offered only in Germany’s domestic market: German law, €1,000 purchase price, 5.0% coupon.
• Offered only in France’s domestic market: French law, €950 purchase price, zero coupon.
• Offered only in the UK and Singapore: English law, €1,000 purchase price, 4.5% coupon.

Tax assumptions for this investor:

• All interest payments, including additional interest paid under a gross-up clause, face 20% unrecoverable withholding.
• The zero-coupon bond’s redemption discount is taxed at 25% at maturity.
• There are no other taxes.

Only the English-law bond contains the following clause, which is enforceable under its governing law:

The issuer shall increase interest payments so that the holder receives the stated coupon amount after withholding.

The bond offering the highest after-tax holding-period return is most accurately described as:

• A. A Eurobond governed by English law.
• B. A foreign bond governed by French law.
• C. A domestic bond governed by German law.

Best answer: A

Explanation: After-tax holding-period return measures net coupon income and redemption gains relative to the purchase price. An enforceable tax gross-up shifts the withholding burden to the issuer; it does not make the interest tax-exempt.

The English-law bond promises a €45 coupon after withholding. The issuer therefore pays €56.25 before withholding, calculated as \( 45 / (1 - 0.20) \). The investor receives €45 and earns 4.5% on the €1,000 purchase price.

The German-market bond nets €40 from its €50 coupon, yielding 4.0%. The French-market bond’s €50 discount incurs €12.50 tax, leaving a €37.50 gain and a return of \( 37.50 / 950 \approx 3.95\% \).

The euro-denominated issue offered outside the euro area in the UK and Singapore is a Eurobond. Issuance category and governing law are distinct characteristics; the enforceable contract and investor-specific taxes determine the net cash flows.

• A. The enforceable gross-up preserves the €45 net coupon, producing a 4.5% return, the highest after-tax return among the eligible issues.
• B. Tax reduces the €50 redemption discount to a €37.50 gain, producing a 3.95% after-tax return on the €950 purchase price.
• C. The domestic bond nets €40 after withholding on its €50 coupon, producing a 4.0% return despite its higher stated coupon.

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Question 77

Topic: Fixed Income

An analyst evaluates a CDO backed by $100 million of corporate loans. Firms in one cyclical industry account for 60% of collateral principal, and their defaults are highly positively correlated.

Principal distributions are paid senior first, then mezzanine, then equity. Principal losses are allocated in reverse order. There are no reserves or external guarantees.

In a stress scenario, $10 million of loan principal defaults, with immediate recovery of 40% of par. No other losses occur in the scenario. Ignore interest, expenses, and discounting.

Which assessment of principal losses and remaining credit risk is least accurate?

• A. Senior investors remain exposed to future principal losses because correlated defaults can exhaust the subordinated tranches.
• B. Equity investors incur a larger percentage principal loss than the collateral pool because their tranche absorbs losses first.
• C. Mezzanine investors incur no principal loss because the equity tranche covers the net collateral loss in this scenario.

Best answer: C

Explanation: A CDO waterfall gives senior investors payment priority while allocating collateral losses to equity first, then mezzanine, and finally senior investors. Subordination redistributes credit risk rather than eliminating it.

The net collateral loss is \(10 \times (1 - 0.40) = 6\) million dollars. The equity tranche absorbs $5 million and is exhausted. The remaining $1 million loss reaches the mezzanine tranche, representing approximately 6.67% of its initial principal. Senior investors incur no principal loss in this scenario.

The equity tranche’s 100% loss compared with the collateral pool’s 6% loss illustrates structural leverage. Senior protection remains finite: concentrated industry exposure and positively correlated defaults increase the risk that multiple borrowers default together and exhaust subordinated protection.

• A. Senior investors avoid losses in this scenario, but correlated defaults in the concentrated collateral pool can generate losses exceeding junior protection.
• B. Equity investors lose their entire $5 million, a 100% loss, while the collateral pool loses $6 million, or 6%.
• C. Net collateral losses of $6 million exceed the $5 million equity tranche, allocating $1 million of loss to mezzanine investors.

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Question 78

Topic: Financial Statement Analysis

An analyst reviews a manufacturer’s 10.2% nominal revenue growth for the year ended 31 December 2026. The manufacturer and its competitor sell only the same product category in the same domestic market; neither changed its business scope.

Initial review: All external figures below cover that market and year. The analyst initially favors the industry index as corroborating evidence.

The matching industry price deflator rose 6.0%.

Clarification: The statistical agency confirms that its industry index measures sales at constant prices rather than nominal sales. All growth figures and other facts remain unchanged.

Following this clarification, which external source is most appropriate for corroborating the magnitude of the manufacturer’s reported revenue growth?

• A. The competitor’s revenue disclosure.
• B. The industry’s sales index.
• C. The customers’ purchase survey.

Best answer: A

Explanation: Corroborating revenue growth requires external evidence with comparable measurement, market coverage, and timing. The competitor’s nominal revenue growth is the strongest available match to the manufacturer’s reported nominal growth.

The clarification changes how the industry figure should be interpreted. Constant-price sales growth excludes price changes. Using the matching deflator, implied nominal industry growth is \(1.098 \times 1.06 - 1 = 0.16388\), or approximately 16.4%. Customer unit purchases likewise measure quantities rather than sales value.

The competitor’s disclosure supports the plausibility of the manufacturer’s growth, but it does not independently verify correct revenue recognition. The difference from nominal industry growth could warrant investigating pricing, product mix, or market share; it does not by itself establish an accounting misstatement.

• A. The competitor’s 9.5% growth uses the same nominal revenue basis, product market, and period, providing the closest comparable support for the manufacturer’s 10.2% growth.
• B. The clarified index measures real sales growth; incorporating the 6.0% deflator increase implies nominal industry growth of approximately 16.4%, rather than 9.8%.
• C. The survey measures quantities rather than revenue, so its 10.0% growth omits selling-price changes despite its numerical proximity to the manufacturer’s reported growth.

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Question 79

Topic: Economics

A manufacturer imports a critical component from Country R, which may impose an export restriction during the next year. If imposed, the restriction would interrupt production, with different disruption durations and cash-flow losses possible.

Valuation assumptions:

• Equity value if no restriction is imposed: $240 million.
• Probability that the restriction is imposed: 20%.
• All loss estimates are present-value reductions in cash flows available to shareholders, discounted using the same unchanged required return.

The analyst uses a $60 million loss estimate to propose a revised equity value of $228 million. Which interpretation of the loss estimate is most appropriate for the analyst’s calculation?

• A. The probability-weighted present-value loss across policy outcomes, including imposition and non-imposition of the restriction.
• B. The probability-weighted present-value loss across disruption scenarios conditional on the restriction being imposed.
• C. The present-value loss associated with the most severe disruption outcome conditional on the restriction being imposed.

Best answer: B

Explanation: An export restriction transmits geopolitical risk through supply availability: fewer imported components can interrupt production and reduce cash flows to shareholders. Valuation separates the probability of the restriction from the expected severity of the loss if it occurs.

Because the required return is unchanged, the analyst reduces the no-restriction equity value by the probability-weighted present value of the cash-flow loss. A conditional expected loss of $60 million produces an unconditional expected loss of \(0.20 \times 60 = 12\) million dollars. The revised equity value is therefore $240 million minus $12 million, or $228 million. The conditional loss estimate must account for the possible disruption durations and their probabilities after imposition.

• A. An estimate already averaged across both policy outcomes includes the 20% occurrence probability; applying that probability again understates the expected loss.
• B. Weighting the conditional expected loss by the 20% occurrence probability gives a $12 million expected loss and a $228 million equity value.
• C. The most severe disruption measures worst-case severity, not the average loss conditional on imposition, so it does not support the proposed expected valuation.

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Question 80

Topic: Fixed Income

An analyst evaluates an option-free corporate bond using 52 weekly observations from 2026. Price changes are adjusted for coupon-payment and passage-of-time effects, and government yield-curve movements are approximately parallel.

Estimates and observations:

• Analytical duration: approximately 6.0 years throughout the sample, calculated by shifting the government yield curve while holding the credit spread constant.
• Empirical duration: 4.5 years, estimated by regressing percentage price changes on changes in the matched-maturity government yield.
• Credit spreads generally narrowed when government yields rose and widened when government yields fell.

When reconciling the two estimates, which interpretation is least accurate?

• A. The empirical estimate incorporates spread-rate co-movement that reduced the observed price response to changes in government yields.
• B. The empirical estimate isolates government-rate sensitivity by separating the price effects of credit-spread changes from those of government-yield changes.
• C. The analytical estimate measures sensitivity to small parallel government-yield changes under the assumption that the credit spread remains unchanged.

Best answer: B

Explanation: Analytical duration measures price sensitivity under specified pricing assumptions. Here, the 6.0-year estimate holds the credit spread constant while shifting the government curve. Empirical duration summarizes the price response associated with government-yield movements in the historical sample.

When government yields rose, narrowing spreads partly offset the resulting price decline. When government yields fell, widening spreads partly offset the price increase. This can produce an empirical duration below the analytical estimate. Using government-yield changes as the sole regression variable does not remove correlated credit-spread effects.

Neither estimate is an unconditional forecast. Analytical duration depends on its fixed-spread assumption, while empirical duration depends on historical sample conditions that may change.

• A. Spread narrowing offsets price losses when government yields rise, so opposite spread-rate movements can reduce the magnitude of the historical price response.
• B. A regression on government-yield changes alone includes correlated spread effects; it does not measure the price response with spreads held constant.
• C. Holding the credit spread constant is precisely the assumption used to calculate the analytical sensitivity to parallel government-curve shifts.

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Question 81

Topic: Alternative Investments

An analyst reviews the following fund record. Position exposures are measured relative to net asset value (NAV).

Which classification of the fund is most accurate?

• A. A hedge fund investment because its mandate combines long and short public-equity positions with leverage.
• B. A traditional equity investment because its portfolio contains exchange-listed shares valued at daily market prices.
• C. A private equity investment because its investors own privately placed interests in a limited partnership.

Best answer: A

Explanation: Alternative investments can be distinguished by their strategies and access structures, not only by the assets they hold. This fund implements a leveraged long-short equity strategy using traditional public equities. Its gross exposure is 200% of NAV, while its net long exposure is 100%; the net figure does not eliminate position or financing risk.

The limited partnership is the ownership vehicle. Privately issued fund interests do not establish private equity exposure when the underlying holdings are listed shares. Similarly, daily market-price valuation does not imply daily investor liquidity: quarterly redemptions and a 60-day notice requirement restrict access to capital. Neither alternative classification nor short selling guarantees lower risk or positive returns.

• A. The long-short mandate, exposure above NAV, and margin financing identify a hedge fund strategy despite the traditional assets underlying it.
• B. The holdings are traditional assets, but the leveraged long-short mandate makes the fund an alternative investment rather than a traditional equity strategy.
• C. Privately placed partnership interests describe the access vehicle; the underlying investments are publicly traded shares rather than ownership of private companies.

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Question 82

Topic: Portfolio Construction

An endowment retains control of its asset-allocation policy and hires Rowan Asset Management to run a passive, index-tracking equity portfolio in a separately managed account. Rowan charges an annual management fee of 0.20% of average assets under management (AUM), with no performance fee.

The increase in AUM results solely from market appreciation, with no contributions or withdrawals. Which interpretation of the mandate’s revenue and investment gains is most accurate?

• A. Management-fee revenue rises by 20%, and the market gains belong to the endowment.
• B. Management-fee revenue rises by 20%, and the market gains belong to Rowan.
• C. Management-fee revenue is unchanged, and the market gains belong to the endowment.

Best answer: A

Explanation: The endowment is the asset owner: it determines its allocation policy and receives the portfolio’s investment gains or losses. Rowan is an external asset manager providing passive implementation through a separately managed account. Reporting client assets as AUM does not make those assets Rowan’s property.

Rowan earns service revenue through its management fee. Applying 0.20% to average AUM produces fees of $200,000 in Year 1 and $240,000 in Year 2, a 20% increase. An unchanged fee rate does not imply unchanged dollar revenue. Market appreciation can therefore increase an asset manager’s fee revenue even without new client contributions or performance-based compensation.

• A. Average AUM increases by 20%, raising the proportional management fee by 20%; the endowment remains the owner of the invested assets.
• B. AUM measures assets managed for clients, not Rowan’s proprietary investment capital, so the account’s market gains belong to the endowment.
• C. The unchanged percentage fee applies to a larger asset base, increasing annual management-fee revenue from $200,000 to $240,000.

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Question 83

Topic: Financial Statement Analysis

An analyst reviews a manufacturer reporting under IFRS. Management’s 2026 profit target for bonuses is unattainable even before warranty expense. Its 2027 bonuses will depend on 2027 pretax profit.

Warranty information:

• Warranty expense and the closing provision for 2026 sales are both $9 million.
• The analyst’s unbiased estimate of the year-end warranty obligation is $6 million.
• Assume all claims are settled for $6 million in 2027 and all remaining warranty coverage expires that year.
• There are no other warranty obligations. Assume no restatement of 2026 results and ignore taxes.

The analyst concludes:

The excess $3 million provision lowers 2026 profit and is a warning sign of earnings management, not proof of fraud. Claim payments reduce the provision, so these warranties have no effect on 2027 profit.

Which correction to the analyst’s conclusion about 2027 pretax profit is most accurate?

• A. These warranties will decrease 2027 pretax profit by $6 million.
• B. These warranties will increase 2027 pretax profit by $3 million.
• C. These warranties will increase 2027 pretax profit by $9 million.

Best answer: B

Explanation: Warranty expense is recognized when a provision is established; subsequent claim payments reduce that liability. Relative to the unbiased estimate, recording $9 million rather than $6 million reduces 2026 pretax profit by an additional $3 million.

In 2027, the $6 million settlement leaves a $3 million provision. Once the remaining warranty coverage expires, that unused amount is reversed through income, increasing 2027 pretax profit by $3 million. The excess provision therefore shifts profit between periods rather than changing cumulative profit across both years.

An unattainable current-year bonus target and a profit-based future bonus create an incentive to defer earnings through an inflated estimate. Conservative-looking accounting does not necessarily improve reporting quality. The estimate and compensation structure warrant scrutiny, but they do not independently establish fraudulent intent.

• A. The $6 million of claim payments reduces the previously recognized liability rather than creating a new warranty expense in 2027.
• B. Claim payments reduce the provision to $3 million, which is reversed to income when the remaining warranty coverage expires.
• C. Settling $6 million of claims consumes part of the provision, leaving only $3 million available for reversal to income.

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Question 84

Topic: Quantitative Methods

An analyst compares two one-year simulations for a non-dividend-paying stock currently priced at $50:

• Model S assumes the simple return is normally distributed.
• Model C assumes the continuously compounded return is normally distributed.

Both assumed return distributions have nonzero variance. Historical continuously compounded returns appear approximately normal in the analyst’s sample.

Which conclusion is least accurate given these assumptions and evidence?

• A. Model C produces lognormally distributed terminal prices and assigns probability only to prices strictly above zero.
• B. Model S produces normally distributed terminal prices and assigns a nonzero probability to prices below zero.
• C. The historical sample establishes that future terminal prices follow the lognormal distribution produced by Model C.

Best answer: C

Explanation: Normal and lognormal distributions differ in their implications for prices. For a stock without dividends, the simple return is \(R=P_1/P_0-1\). If \(R\) is normal with nonzero variance, then \(P_1=P_0(1+R)\) is also normal. Returns below -100% have nonzero probability and imply negative prices, an economically incompatible outcome.

If the continuously compounded return \(r=\ln(P_1/P_0)\) is normal, then \(P_1=P_0e^r\) is lognormal and strictly positive. The corresponding simple return, \(e^r-1\), is bounded below by -100% and is not normally distributed.

Approximately normal historical log returns can support using a lognormal price model. They do not guarantee that future log returns will be normal or that future prices will follow the assumed lognormal distribution.

• A. Exponentiating a normally distributed continuously compounded return gives a lognormal terminal price, which remains strictly positive.
• B. A normal simple return is unbounded below, so returns below -100% produce negative terminal prices.
• C. An approximately normal historical sample supports a modeling assumption but cannot establish the distribution of future returns or prices.

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Question 85

Topic: Equities

An analyst values Aster and a peer using a constant-growth dividend discount model. Both companies finance growth solely through retained earnings and distribute all remaining earnings as dividends. Their return on equity (ROE), earnings growth, and required equity return are assumed constant indefinitely.

The analyst writes:

The peer’s implied payout ratio is 75%. Using this payout ratio for Aster gives a justified forward P/E of \(0.75/(0.10-0.06)=18.75\).

After correcting the analysis, Aster’s justified forward P/E is closest to:

• A. 17.5 times
• B. 7.5 times
• C. 18.6 times

Best answer: A

Explanation: When growth is financed entirely through retained earnings, sustainable growth equals ROE multiplied by the retention ratio. Aster must retain \(6\%/20\%=30\%\) of earnings, leaving a 70% dividend payout ratio.

Under the constant-growth dividend discount model, justified forward P/E equals the payout ratio divided by the difference between the required equity return and earnings growth. Aster’s justified forward P/E is therefore \(0.70/(0.10-0.06)=17.5\).

The peer retains 25%, pays out 75%, and has a justified forward P/E of \(0.75/(0.10-0.04)=12.5\). Aster supports a higher multiple under the stated profitability, growth, and required-return assumptions. However, its forecasts require greater earnings retention, so applying the peer’s payout ratio overstates its value. A growth premium must reflect both future growth and the cash available for distributions after reinvestment.

• A. Aster’s 30% retention implies a 70% payout, giving a forward P/E of \(0.70/(0.10-0.06)=17.5\).
• B. Using Aster’s 30% retention ratio in the numerator produces 7.5, but the dividend model requires its 70% payout ratio.
• C. Multiplying 17.5 by the earnings growth factor of 1.06 gives approximately 18.6, which is a justified trailing P/E rather than forward P/E.

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Question 86

Topic: Quantitative Methods

A client requires an expected one-year return of at least 9%. An analyst must construct a fully invested portfolio using only the following two assets. Short sales are prohibited.

The estimated correlation between the assets’ one-year returns is -1.

Under these estimates, what is the minimum portfolio standard deviation that meets the client’s expected return requirement?

• A. 15%
• B. 5%
• C. 0%

Best answer: B

Explanation: Perfect negative correlation eliminates portfolio volatility only when the assets’ weighted volatility contributions are equal. Let \(w_B\) be the weight in Asset B; the weight in Asset A is \(1-w_B\).

The expected return requirement implies:

\[ E(R_p)=6\%(1-w_B)+12\%w_B\ge9\%,\qquad w_B\ge0.50. \]

With correlation equal to -1, portfolio standard deviation is:

\[ \sigma_p=|10\%(1-w_B)-20\%w_B|=|10\%-30\%w_B|. \]

Zero volatility occurs at \(w_B=1/3\), but that allocation earns an expected return of only 8%. For feasible weights from 0.50 to 1, volatility increases as the weight in Asset B increases. Thus, the minimum-risk qualifying allocation invests 50% in each asset and has a standard deviation of 5%.

Equal capital weights do not eliminate risk when asset volatilities differ. With perfect positive correlation, long-only volatility contributions add rather than offset.

• A. Adding the equal-weight volatility contributions gives 15%, which corresponds to perfect positive correlation rather than the specified perfect negative correlation.
• B. The return requirement forces at least 50% into Asset B; at 50%, the opposing weighted volatility contributions are 5% and 10%, leaving 5%.
• C. Zero volatility requires two-thirds in Asset A and one-third in Asset B, producing an expected return of 8%, below the client’s requirement.

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Question 87

Topic: Portfolio Construction

An adviser reviews a draft investment policy statement (IPS) for an individual with a $3,000,000 taxable portfolio. The client has agreed to the spending and capital-preservation goals below. Assume annual inflation of 2%.

Draft IPS:

• Return objective: Target a 4% annual after-tax nominal total return. Fund a $120,000 withdrawal at the end of the first year, increase subsequent withdrawals with inflation, and preserve the portfolio’s purchasing power after withdrawals.
• Risk objective: Moderate portfolio risk, reflecting the client’s financial capacity and willingness to accept temporary declines.
• Liquidity: Reserve the amounts needed for the next two scheduled annual withdrawals in cash or short-term government securities.
• Time horizon: 25 years.
• Taxes: Evaluate investment results after taxes applicable to the client’s taxable account.
• Legal constraints: No special legal or regulatory restrictions apply.
• Unique constraints: Exclude tobacco producers.
• Responsibilities: The adviser implements the allocation, the client reports material changes, and both review the IPS annually.

When evaluating the draft’s internal consistency and purpose, which conclusion is least accurate?

• A. The return target serves as a planning benchmark because the IPS records agreed objectives rather than assuring future investment results.
• B. The liquidity policy supports near-term spending because the reserve is sized to cover two years of planned withdrawals.
• C. The return objective supports capital preservation because the after-tax nominal target matches the portfolio’s initial annual withdrawal rate.

Best answer: C

Explanation: Return objectives must be consistent with spending, inflation, taxes, and risk tolerance. The first-year withdrawal is 4% of the $3,000,000 portfolio. At a 4% after-tax nominal return, the portfolio earns $120,000, which is entirely withdrawn. Ending nominal capital remains $3,000,000, so purchasing power falls when inflation is 2%.

Preserving purchasing power after the first withdrawal requires ending capital of $3,060,000. The required first-year after-tax nominal return is therefore 6%: 4% for spending plus 2% for capital growth. The adviser and client should reconcile the return objective with spending needs and risk tolerance; simply raising the target does not establish its feasibility. The liquidity reserve addresses cash availability, not the long-term return shortfall. An IPS documents an agreed investment framework and review process, not guaranteed outcomes.

• A. An IPS specifies agreed objectives and monitoring standards; it does not assure that a targeted return will be realized.
• B. Reserving the amounts needed for the next two planned withdrawals aligns liquid assets with the client’s near-term cash-flow needs.
• C. A 4% return funds the $120,000 withdrawal but leaves nominal capital unchanged, so 2% inflation erodes the portfolio’s purchasing power.

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Question 88

Topic: Equities

An analyst uses a constant-growth dividend discount model to estimate a company’s justified forward P/E. Growth is financed entirely through retained earnings, and earnings and dividends grow at the sustainable growth rate.

Baseline inputs:

The analyst lowers the forecast ROE to 10%. The payout ratio, required return, and observed peer multiple remain unchanged.

Which conclusion following the revision is most accurate?

• A. The justified forward P/E remains 14.3 and matches the observed peer multiple.
• B. The justified forward P/E declines to 10.0 and is below the observed peer multiple.
• C. The justified forward P/E declines to 10.6 and is below the observed peer multiple.

Best answer: B

Explanation: A justified forward P/E depends on forecast fundamentals rather than an observed trading ratio. Under the constant-growth dividend discount model, it equals the dividend payout ratio divided by the difference between the required return and growth.

The retention ratio is 60%. Lowering ROE from 12% to 10% reduces sustainable growth from 7.2% to 6%:

\[ g = (1 - 0.40) \times 0.10 = 0.06 \]

The revised justified forward multiple is:

\[ \frac{P_0}{E_1} = \frac{0.40}{0.10 - 0.06} = 10.0 \]

Thus, the justified multiple falls from approximately 14.3 to 10.0. The observed peer multiple remains 14.3, but that trading ratio is not proof that the company’s revised fundamentals support the same valuation.

• A. A justified forward P/E of 14.3 reflects the original growth forecast; an unchanged peer multiple does not offset the reduction in forecast ROE.
• B. The revised sustainable growth rate is 6%, giving a justified forward P/E of 0.40 divided by 0.04, or 10.0.
• C. Including a factor of 1.06 in the numerator produces the justified trailing P/E, rather than the justified forward P/E.

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Question 89

Topic: Financial Statement Analysis

An IFRS-reporting company’s profit after tax, before preferred dividends, was $1,625,000 for the year ended 31 December 2027.

Capital structure:

• 600,000 ordinary shares were outstanding on 1 January.
• A 2-for-1 ordinary share split occurred on 1 July.
• 200,000 additional ordinary shares were issued on 1 October, after the split.
• Non-participating convertible preferred shares were outstanding throughout the year. Their annual dividends were $125,000, and full conversion would produce 200,000 ordinary shares on a post-split basis.

There were no other share transactions or potential ordinary shares. Use monthly weighting.

An analyst calculates:

Which pair of corrected basic and diluted EPS is most accurate?

• A. Basic EPS of $1.20 and diluted EPS of $1.03.
• B. Basic EPS of $1.20 and diluted EPS of $1.12.
• C. Basic EPS of $1.07 and diluted EPS of $1.02.

Best answer: B

Explanation: A share split restates the share-count basis; it is not weighted only from its effective date. The 600,000 opening ordinary shares therefore become 1,200,000 shares for the entire year. Only the October issuance is time-weighted:

\[ 1{,}200{,}000 + 200{,}000 \times \frac{3}{12} = 1{,}250{,}000 \]

Basic EPS uses profit available to ordinary shareholders, after deducting preferred dividends. Thus, basic EPS is \( 1{,}500{,}000 / 1{,}250{,}000 = 1.20 \), or $1.20 per share.

Under the if-converted method, the preferred shares are assumed converted at the beginning of the year. Add back the $125,000 preferred dividends and include 200,000 additional ordinary shares. Diluted EPS is \( 1{,}625{,}000 / 1{,}450{,}000 \approx 1.12 \), or $1.12 per share. Conversion lowers EPS, so the preferred shares are dilutive.

The analyst’s numerator adjustments are appropriate. The decisive error is time-weighting the split instead of restating the pre-split shares.

• A. The diluted amount continues deducting preferred dividends even though assumed conversion eliminates them, understating the diluted earnings numerator by $125,000.
• B. Restating the split gives 1,250,000 weighted-average ordinary shares; assumed preferred conversion increases diluted earnings to $1,625,000 and diluted shares to 1,450,000.
• C. These amounts use year-end ordinary shares rather than weighted-average shares, incorrectly giving the October issuance a full year’s weight.

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Question 90

Topic: Equities

An analyst is assessing the business-cycle exposure of a diagnostics company. Routine testing services are medically necessary, while hospitals can postpone equipment purchases. A long-term shift toward automated testing supports growth in recurring service revenue.

Revenue forecast for a one-year downturn:

Operating costs consist of variable costs equal to 30% of total revenue and annual fixed costs of $50 million. The variable-cost ratio and fixed costs remain unchanged during the downturn.

Which assessment of the company’s operating-profit sensitivity in the downturn is most accurate?

• A. Operating profit declines by 7.0%; defensive service demand keeps earnings sensitivity equal to revenue sensitivity.
• B. Operating profit declines by 24.5%; fixed operating costs amplify exposure to cyclical equipment demand.
• C. Operating profit declines by 35.0%; fixed operating costs make the revenue decline reduce earnings dollar for dollar.

Best answer: B

Explanation: Business-cycle exposure depends on a company’s revenue mix and cost structure, not merely its industry label. Routine testing demand is defensive, automation adoption provides structural growth, and equipment spending is cyclical.

Forecast revenue, in millions of dollars, is \(60(1.05) + 40(0.75) = 93\), compared with $100 million currently. Current operating profit is \(100(0.70) - 50 = 20\) million dollars. Forecast operating profit is \(93(0.70) - 50 = 15.1\) million dollars.

The operating-profit decline is therefore \((20 - 15.1)/20 = 24.5\%\). Although revenue falls only 7.0%, fixed costs magnify the percentage earnings decline. Defensive demand and secular growth can coexist with material cyclical earnings sensitivity. Neither characteristic, by itself, establishes low equity valuation risk.

• A. Revenue declines by 7.0%, but applying that percentage to operating profit overlooks the amplifying effect of unchanged fixed costs.
• B. Operating profit falls from $20 million to $15.1 million, a 24.5% decline, despite continued growth in recurring services.
• C. This subtracts the entire $7 million revenue loss from operating profit, ignoring the accompanying $2.1 million reduction in variable costs.

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Question 91

Topic: Quantitative Methods

An analyst uses historical simulation to estimate the one-day profit-and-loss distribution of a portfolio invested in an equity-index fund.

Baseline method:

• Use joint daily changes in the index level, option-implied volatilities, and interest rates from 1 January 2013 through 31 December 2017.
• Give each observed trading day equal weight and fully revalue current holdings under each scenario.
• The sample contains no one-day index decline greater than 5%.

Change: The index-fund holding is replaced with long positions in put options on the same index. The historical window, scenario weights, and full-revaluation method remain unchanged.

Which statement most accurately describes the revised simulated distribution?

• A. The distribution reflects nonlinear option exposures and adds market-factor scenarios inferred from current implied volatilities.
• B. The distribution reflects only linear option exposures and uses the recorded historical market-factor scenarios.
• C. The distribution reflects nonlinear option exposures and uses only the recorded historical market-factor scenarios.

Best answer: C

Explanation: Historical simulation applies recorded market-factor changes to current holdings and treats the resulting profits and losses as an empirical outcome distribution. Here, each historical trading day receives equal weight.

Changing the holdings changes the portfolio’s response to those scenarios. Full revaluation captures the puts’ nonlinear price responses, so the revised distribution need not resemble the index fund’s distribution even though the historical scenarios are unchanged.

The method does not introduce unobserved market moves. No simulated scenario includes an index decline greater than 5%, but that does not establish a bound on future declines or losses. Shocks or regimes absent from the selected window can make its distribution an unreliable representation of prospective risk.

• A. Implied volatilities help revalue the options, but this historical simulation does not use them to generate additional market-factor scenarios.
• B. Full revaluation captures nonlinear changes in option values; limiting the response to linear sensitivities would describe a first-order approximation.
• C. Repricing the puts under each recorded joint market move captures nonlinear exposures without introducing market scenarios absent from the historical window.

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Question 92

Topic: Financial Statement Analysis

An analyst compares Alder and Birch, two medical-device manufacturers, at 31 December 2027. Alder reports under IFRS; Birch reports under U.S. GAAP. Selected disclosures follow, with amounts in $ millions.

Development expenditures relate to internally generated product designs, not software. No development assets have been impaired or revalued. Ignore income taxes and other accounting differences.

After restating Alder’s development costs to U.S. GAAP treatment, Alder’s total assets would most likely be:

• A. $12 million higher than Birch’s.
• B. $12 million lower than Birch’s.
• C. $6 million lower than Birch’s.

Best answer: C

Explanation: IFRS capitalizes development expenditures that meet its recognition criteria, whereas U.S. GAAP generally expenses internally generated, non-software research and development costs as incurred. Alder’s development asset has a carrying amount of \(24 - 6 = 18\) million dollars. Restating to U.S. GAAP removes this net amount, not the gross cost, because accumulated amortization has already reduced reported assets. Alder’s adjusted assets are \(240 - 18 = 222\) million dollars, $6 million below Birch’s $228 million. Ignoring income taxes, equity also declines by $18 million and liabilities remain unchanged. The apparent asset-size advantage therefore reverses when recognition policies are aligned.

• A. The $12 million advantage uses reported assets and overlooks the $18 million development asset that must be removed under U.S. GAAP.
• B. Deducting the full $24 million cost ignores the $6 million amortization already reflected in Alder’s reported assets.
• C. Removing the $18 million net development asset yields adjusted assets of $222 million, compared with Birch’s $228 million.

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Question 93

Topic: Financial Statement Analysis

An analyst reviews a manufacturer’s draft IFRS financial statements for the year ended 31 December 2027. The enacted tax rate is 25% for all relevant years.

All amounts relate to the same tax-paying entity and tax authority. The temporary differences arise from accelerated tax depreciation. Convincing evidence supports the forecast, which excludes temporary-difference reversals. Loss utilization is unrestricted before expiry. Any deferred tax adjustment is recognized in profit or loss.

The deferred tax expense required to adjust the draft balances is most likely:

• A. $1.0 million.
• B. $2.5 million.
• C. $0.5 million.

Best answer: A

Explanation: Under IFRS, a deferred tax asset for loss carryforwards is recognized only to the extent that sufficient taxable profit is probable before the losses expire. Supporting taxable profit can arise from both future operations and reversals of taxable temporary differences for the same tax-paying entity and tax authority.

Here, $6.0 million of taxable differences reverse before expiry. Together with $2.0 million of supported additional taxable profit, this permits recovery of $8.0 million of losses. The recoverable asset is \( 8.0 \times 25\% = 2.0 \) million dollars. Reducing the draft asset from $3.0 million to $2.0 million creates $1.0 million of deferred tax expense, reducing net income and equity equally.

The deferred tax liability remains $2.0 million. Its recognition is not subject to the asset’s recoverability test. The 2030 reversals remain taxable but occur too late to support recovery of these loss carryforwards.

• A. Taxable profit available before expiry totals $8.0 million, supporting a $2.0 million asset and requiring a $1.0 million reduction.
• B. This amount uses only the $2.0 million profit forecast and ignores $6.0 million of taxable temporary differences reversing before the losses expire.
• C. This amount includes the $2.0 million of reversals in 2030, after the tax losses expire, overstating the recoverable deferred tax asset.

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Question 94

Topic: Equities

An analyst is valuing a company’s common shares today. Forecast dividends are paid at each year-end.

After year 2, growth is financed entirely through retained earnings. ROE and the payout ratio remain constant indefinitely, and earnings and dividends per share grow at the resulting sustainable rate.

Based on a two-stage dividend discount model, which valuation assessment is most accurate?

• A. Undervalued, with an estimated intrinsic value of $43.09 per share.
• B. Overvalued, with an estimated intrinsic value of $41.60 per share.
• C. Undervalued, with an estimated intrinsic value of $63.55 per share.

Best answer: A

Explanation: With constant ROE and payout, growth financed through retained earnings implies a sustainable growth rate of \(g=(1-0.60)\times0.10=4\%\).

The first stable-growth dividend is \(D_3=2.70\times1.04=2.808\) dollars per share. The terminal value at the end of year 2 uses this next dividend:

\[ V_2=\frac{2.808}{0.10-0.04}=46.80. \]

Discount the explicit dividends and terminal value to today:

\[ V_0=\frac{2.40}{1.10}+\frac{2.70+46.80}{1.10^2}=43.09. \]

The estimated intrinsic value exceeds the $42.00 market price by approximately $1.09 per share, indicating undervaluation under the forecasts. The stable-growth model requires growth below the required equity return; the assumed 4% growth satisfies that condition.

• A. Sustainable growth of 4% produces a year 2 terminal value of $46.80 and a current intrinsic value of $43.09, exceeding the market price.
• B. The $41.60 estimate uses the year 2 dividend in the terminal value, which instead requires the year 3 dividend.
• C. The $63.55 estimate treats the 60% payout ratio as retention; the retention ratio is 40%, implying growth of 4%, not 6%.

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Question 95

Topic: Ethical and Professional Standards

Maya Chen, a portfolio manager, holds the CFA charter and is an active CFA Institute member in good standing. She is writing an introductory message to prospective clients.

Which statement most appropriately represents her CFA qualification under the Standards of Professional Conduct?

• A. As a CFA charterholder, I apply knowledge gained through the CFA Program when analyzing investments for client portfolios.
• B. As a CFA, I apply knowledge gained through the CFA Program when analyzing investments for client portfolios.
• C. As a CFA charterholder, I have demonstrated the investment skills needed to achieve superior returns for client portfolios.

Best answer: A

Explanation: Standard VII(B), Reference to CFA Institute, the CFA Designation, and the CFA Program, requires accurate representation of the credential and its implications. Chen holds the charter and maintains active membership, so she may use the CFA designation in client communications.

The designation may identify her credential, and she may truthfully describe applying knowledge acquired through the CFA Program. “CFA charterholder” uses CFA appropriately as an adjective; “a CFA” improperly uses it as a noun. Earning the charter also does not establish superior investment ability or imply that client portfolios will earn superior returns.

• A. Chen’s active membership permits use of the designation, and this statement describes applying CFA Program knowledge without implying superior performance.
• B. Using “CFA” as a noun identifying a person misuses the designation; “CFA charterholder” is an appropriate expression.
• C. The CFA charter does not demonstrate an ability to achieve superior investment returns, so this statement exaggerates the designation’s implications.

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Question 96

Topic: Equities

An analyst estimates a company’s equity value at $240 million, including cash available for distribution. The company has 12 million shares outstanding and plans to distribute $60 million through either a cash dividend or a share repurchase.

The analyst concludes that a shareholder who sells no shares will have the same estimated total wealth, including any dividend received, immediately after either distribution. Assume equity value falls only by the cash distributed. Ignore taxes, transaction costs, and signaling effects.

Which assumed average repurchase price makes the analyst’s conclusion most accurate?

• A. $25 per share.
• B. $15 per share.
• C. $20 per share.

Best answer: C

Explanation: With taxes and other effects excluded, either distribution reduces total equity value by $60 million, leaving $180 million. The effect on continuing shareholders depends on the repurchase price.

The cash dividend is $5 per share. After payment, each share is worth $15, so shareholder wealth remains $20 per original share: $15 of stock plus $5 of cash.

At a $20 repurchase price, the company retires 3 million shares. The remaining 9 million shares represent $180 million of equity value, or $20 per share. A non-selling shareholder therefore has the same estimated wealth under either method.

Repurchasing below the original estimated value benefits continuing shareholders at selling shareholders’ expense; repurchasing above it has the opposite effect. A higher per-share value does not imply higher total company value.

• A. Repurchasing at $25 leaves 9.6 million shares worth $18.75 each, giving continuing shareholders less wealth than the dividend alternative.
• B. Repurchasing at $15 leaves 8 million shares worth $22.50 each, giving continuing shareholders more wealth than the dividend alternative.
• C. Repurchasing at the original estimated value of $20 leaves continuing shareholders with $20 per share, equal to their stock-plus-cash wealth after the dividend.

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Question 97

Topic: Financial Statement Analysis

On 1 January 2027, a company reporting under IFRS pays $90 million in cash to acquire 100% of another business.

Acquisition facts:

• The acquired business’s identifiable net assets, excluding its brand, have a fair value of $60 million.
• Its separately identifiable brand has a fair value of $15 million. The seller developed the brand internally and had not recognised it.
• The acquirer’s own internally generated reputation has an estimated value of $10 million.

At 31 December 2027, a correctly performed impairment test establishes a $3 million loss allocated entirely to goodwill. Ignore tax effects.

Analyst’s conclusion:

The brand and reputation were internally generated, so neither is recognised separately. Goodwill is $30 million at acquisition and $27 million after impairment. The impairment reduces total assets and equity by $3 million.

Which correction to the analyst’s conclusion is most accurate?

• A. Recognise only the acquirer’s reputation separately; report year-end goodwill of $17 million.
• B. Recognise both the brand and reputation separately; report year-end goodwill of $2 million.
• C. Recognise only the acquired brand separately; report year-end goodwill of $12 million.

Best answer: C

Explanation: Goodwill is the excess of acquisition consideration over the fair value of identifiable net assets acquired. It represents benefits that cannot be identified separately, such as expected synergies. An identifiable acquired brand is recognised separately even if the seller developed it internally. The acquirer’s own internally generated reputation remains unrecognised.

Identifiable net assets therefore total $75 million, leaving initial goodwill of $15 million. The $3 million impairment reduces goodwill to $12 million. The analyst correctly describes the impairment’s balance-sheet effect: this non-cash expense reduces total assets and retained earnings, and therefore equity, by $3 million when tax effects are ignored.

Future comparisons require care. For unchanged subsequent earnings, smaller asset and equity bases can produce higher return ratios without operating improvement. Recognition differences also remain between acquisitive businesses, which record purchased goodwill and identifiable intangibles, and businesses that develop similar benefits internally.

• A. The acquirer’s internally generated reputation cannot be recognised, whereas the acquired brand must be recognised separately; this treatment reverses those requirements.
• B. Including the acquirer’s reputation improperly increases acquired identifiable net assets by $10 million and understates year-end goodwill by the same amount.
• C. Recognising the acquired brand makes identifiable net assets $75 million; excluding the acquirer’s reputation leaves initial goodwill of $15 million and $12 million after impairment.

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Question 98

Topic: Derivatives and Risk Management

An investor shorts one equity index futures contract and posts $10,000 of initial margin. The contract multiplier is $50 per index point. The position remains open through Day 2, and daily settlement gains and losses are credited to or debited from the margin account. There are no other deposits or withdrawals; ignore fees and interest.

Immediately after Day 2 settlement, which statement about the margin-account balance and the futures contract’s value is most accurate?

• A. The margin-account balance is $11,250, and the futures contract’s value is $0.
• B. The margin-account balance is $8,750, and the futures contract’s value is $0.
• C. The margin-account balance is $8,750, and the futures contract’s value is -$1,250.

Best answer: B

Explanation: A short futures position gains when the settlement price falls and loses when it rises. Day 1 credits \( (4,180 - 4,120) \times 50 = 3,000 \) dollars to margin. Day 2 debits \( (4,205 - 4,120) \times 50 = 4,250 \) dollars. The cumulative loss is therefore $1,250, leaving a margin-account balance of $8,750.

Marking to market settles these gains and losses in cash, resetting the contract’s value to zero immediately after settlement. It does not reset the quoted futures price to zero. The Day 2 quotation remains 4,205 index points, corresponding to a notional amount of $210,250. This notional amount is distinct from both the margin cash balance and the contract’s value.

• A. The $11,250 balance treats the position as long; the overall 25-point price increase creates a $1,250 loss for the short position.
• B. The cumulative loss is $1,250, leaving $8,750 in margin; daily cash settlement resets the open contract’s value to zero.
• C. The $1,250 loss has already reduced the margin balance, so recording it again as a negative contract value after settlement double counts it.

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Question 99

Topic: Equities

An analyst plans to value a company financed with both debt and common equity by discounting expected free cash flow to equity (FCFE). The analyst proposes a 10.8% discount rate using CAPM and a beta taken from a peer company.

Inputs:

• Risk-free rate: 3.0%.
• Expected market return: 9.0%.
• Peer beta: 1.3.

Which assumption about the peer beta most directly supports using the proposed discount rate?

• A. The peer beta represents the systematic risk of the company’s operating assets over the forecast period.
• B. The peer beta represents the total risk of the company’s equity over the forecast period.
• C. The peer beta represents the systematic risk of the company’s equity over the forecast period.

Best answer: C

Explanation: CAPM estimates the return investors require for bearing systematic equity risk. The expected market risk premium is the expected market return less the risk-free rate, or 6.0%. The required equity return is:

\[ 3.0\% + 1.3 \times (9.0\% - 3.0\%) = 10.8\%. \]

Using a peer beta is defensible when it represents the company’s systematic equity risk over the forecast period. Because FCFE belongs to equity investors, this required equity return is the relevant discount rate. It is neither a guaranteed realized return nor the weighted average cost of capital for debt and equity together.

• A. An operating-asset beta does not establish the equity beta needed to discount FCFE for a company with debt financing.
• B. CAPM prices systematic risk, whereas total equity risk also includes diversifiable risk that beta does not measure.
• C. CAPM requires a beta appropriate for the equity cash flows being valued, so comparable systematic equity risk supports the proposed rate.

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Question 100

Topic: Fixed Income

A holding company owns all the shares of an operating subsidiary and has no other assets. Its notes currently have no claim against the subsidiary.

Liquidation estimates:

Simplified subsidiary waterfall:

• Secured debt receives pledged collateral proceeds first. Any deficiency ranks pari passu with senior unsecured claims against the remaining proceeds.
• Subordinated debt is paid next. Only residual proceeds pass to the holding company.

Assume each proposed amendment is enforceable and leaves principal amounts and liquidation proceeds unchanged. Ignore costs and other claims.

An analyst argues that an amendment could make the holding-company notes recover a higher percentage of principal than the subsidiary’s subordinated debt, potentially supporting a higher issue rating if default probabilities are equal. Which amendment most supports this conclusion?

• A. The holding company fully guarantees the subsidiary’s senior unsecured debt, with the guarantee ranking pari passu with the holding-company notes.
• B. The holding company secures its notes with a first-priority pledge of all the shares it owns in the subsidiary.
• C. The subsidiary fully guarantees the holding-company notes, with the guarantee ranking pari passu with the subsidiary’s senior unsecured debt.

Best answer: C

Explanation: Structural subordination means holding-company creditors depend on distributions remaining after subsidiary creditors are paid. Senior status at the holding company does not override the subsidiary’s payment priorities. An enforceable senior unsecured guarantee creates a direct subsidiary claim ahead of the subsidiary’s subordinated debt.

With the guarantee, collateral pays $40 million toward the $60 million secured claim. The $20 million deficiency, $30 million senior unsecured debt, and $40 million guarantee share the remaining $60 million. Their recovery rate is \( 60 / (20 + 30 + 40) = 66.7\% \). Thus, the holding-company notes recover 66.7%, while subordinated debt recovers zero. The secured claim recovers $53.3 million, or 88.9%, illustrating that collateral does not guarantee full repayment.

For equal default probabilities, lower loss severity can support a higher issue credit rating. A debt label alone does not establish recovery priority across separate legal entities.

• A. The holding-company guarantee creates no claim on subsidiary proceeds for the holding-company notes, which still receive zero after the subsidiary’s creditors are paid.
• B. The subsidiary shares have no residual value because subsidiary creditors exhaust the proceeds, so securing the notes with those shares leaves their recovery at zero.
• C. The subsidiary guarantee places the holding-company notes in the senior unsecured tier, giving them a 66.7% recovery while subordinated debt receives zero.

Questions 101-125

Question 101

Topic: Fixed Income

On 30 June 2028, an analyst reviews a convertible bond with the following terms and market data:

• Face value: $1,000; current bond price: $1,180.
• The investor may exchange each bond for 25 newly issued common shares from 30 June 2027 through maturity on 30 June 2030.
• Current issuer share price: $44.

Assume conversion does not affect the share price. Ignore accrued interest, taxes, and transaction costs.

Which statement about an immediate conversion is most accurate?

• A. Conversion reduces the holding’s market value by $80 and retains the issuer’s $1,000 principal repayment obligation.
• B. Conversion increases the holding’s market value by $100 and cancels the issuer’s $1,000 principal repayment obligation.
• C. Conversion reduces the holding’s market value by $80 and cancels the issuer’s $1,000 principal repayment obligation.

Best answer: C

Explanation: A conversion right allows the investor to exchange a debt claim for equity; it does not provide shares in addition to principal repayment. The right is currently exercisable because the stated conversion period has begun.

The conversion value is \(25 \times 44 = 1,100\) dollars. Compared with the bond’s $1,180 market price, immediate conversion sacrifices $80 of market value. Face value is not the appropriate basis for this comparison.

Conversion extinguishes the issuer’s debt obligation and increases its shares outstanding. The investor becomes a common shareholder rather than a creditor. A rising share price increases conversion value, but the conversion right does not guarantee repayment or provide protection against equity losses.

• A. The $80 value reduction is accurate, but conversion replaces the debt claim with shares rather than preserving the principal repayment obligation.
• B. The $100 compares the shares’ value with face value rather than the bond’s $1,180 market price; conversion instead sacrifices $80.
• C. The shares are worth $1,100, which is $80 below the bond price, and exchanging the bond for equity extinguishes its principal claim.

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Question 102

Topic: Fixed Income

An analyst evaluates a portfolio of option-free, fixed-rate bonds. The table reports full market values, including accrued interest. Modified durations are in years and convexities are in years squared; both use annual yields expressed as decimals.

Each bond’s yield to maturity rises immediately by 100 basis points, with cash flows unchanged. Using the duration-convexity approximation, the estimated percentage change in the portfolio’s full market value is closest to:

• A. A 5.67% decrease.
• B. A 4.82% decrease.
• C. A 5.90% decrease.

Best answer: A

Explanation: Portfolio duration and convexity are weighted by each bond’s share of full market value. The $10,000,000 portfolio has weights of 20%, 30%, and 50%, giving:

• Portfolio modified duration: \(D_p = 0.20(2) + 0.30(5) + 0.50(8) = 5.9\).
• Portfolio convexity: \(C_p = 0.20(6) + 0.30(30) + 0.50(72) = 46.2\).

For portfolio value \(V\) and a common yield increase of \(\Delta y = 0.01\), the approximate proportional value change is:

\[ \frac{\Delta V}{V} \approx -D_p\Delta y + \frac{1}{2}C_p(\Delta y)^2 \]

Substituting gives \(-0.059 + 0.00231 = -0.05669\), or a 5.67% decline. Positive convexity reduces the loss relative to the duration-only estimate.

Applying one yield change to these aggregates assumes equal component yield shifts and unchanged cash flows. Unequal yield movements require component-specific calculations; rate-dependent cash flows may require effective duration and convexity.

• A. Market-value weights of 20%, 30%, and 50% give duration of 5.9 and convexity of 46.2, producing an estimated 5.669% decline.
• B. This estimate uses equal weights, giving duration of 5.0 and convexity of 36.0, rather than weighting by full market value.
• C. This estimate applies the value-weighted duration of 5.9 but omits the positive convexity adjustment of 0.231 percentage points.

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Question 103

Topic: Fixed Income

An analyst evaluates a one-year corporate loan immediately after the borrower posts additional collateral.

Loan estimates:

• Exposure at default: $5,000,000.
• Probability of default over the next year: 2%, unchanged by the additional collateral.
• Recovery if default occurs: 60% of exposure at default, increased from 40%.
• Quoted annual credit spread: 180 basis points.

Ignore discounting. The analyst reports:

Expected one-year credit loss equals the credit spread multiplied by exposure at default, or $90,000.

The most accurate corrected estimate of expected one-year credit loss is:

• A. $40,000.
• B. $100,000.
• C. $60,000.

Best answer: A

Explanation: Expected credit loss combines exposure at default, the probability of default over the specified horizon, and loss given default. Loss given default is the unrecovered proportion of exposure, so a 60% recovery rate implies 40% loss severity.

Expected one-year credit loss is therefore \(5{,}000{,}000 \times 0.02 \times (1 - 0.60) = 40{,}000\), or $40,000.

The additional collateral reduces expected loss from $60,000 to $40,000 by improving recovery; the stated default probability remains unchanged. The analyst’s error is treating the quoted spread as the expected loss rate. Credit spreads can also include credit-risk and liquidity premiums, so they cannot simply replace probability of default multiplied by loss given default.

• A. Expected loss is $5,000,000 multiplied by the 2% default probability and the 40% loss given default.
• B. This estimate multiplies exposure by default probability but assumes no recovery, despite the estimated 60% recovery.
• C. This estimate applies the previous 60% loss given default; the additional collateral reduces loss given default to 40%.

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Question 104

Topic: Fixed Income

An investor bought a fixed-rate bond immediately after a coupon payment. The purchase record shows:

The investor held the bond to maturity and received all payments on schedule. The first coupon was kept as non-interest-bearing cash until maturity. Ignore taxes and transaction costs.

The investor’s annualized compound return based on total wealth at maturity is closest to:

• A. 7.61%.
• B. 7.80%.
• C. 5.26%.

Best answer: A

Explanation: Yield to maturity (YTM) is the internal rate of return that equates promised coupon and principal payments to the purchase price. Realizing that rate as a compound return through maturity also requires reinvesting interim coupons at that yield.

The first $50 coupon earns no interest. Wealth at maturity therefore equals $1,000 of principal plus both $50 coupons, or $1,100. The annualized realized return is \( (1{,}100/950)^{1/2} - 1 \approx 7.61\% \). This is below the quoted 7.80% YTM despite receiving every payment on schedule.

Current yield is \( 50/950 \approx 5.26\% \). It measures annual coupon income relative to price and excludes both reinvestment income and the gain from repayment at par.

• A. Wealth at maturity is $1,100; annualizing its growth from the $950 purchase price over two years gives approximately 7.61%.
• B. Matching the quoted yield as a compound return requires reinvesting the first coupon at that yield rather than holding it as non-interest-bearing cash.
• C. The $50 annual coupon divided by the $950 purchase price gives current yield, which ignores the gain from buying the bond below par.

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Question 105

Topic: Portfolio Construction

An analyst compares the historical risk of Asset B alone with a portfolio rebalanced to 50% in Asset A and 50% in Asset B at the beginning of each year. Ignore rebalancing costs.

The paired annual total returns are:

Use sample estimates with a divisor of 3 and express covariance using decimal returns. Which conclusion most appropriately compares historical risk using standard deviation?

• A. Sample covariance is 0; portfolio volatility is 3.06%, below Asset B’s 3.27%.
• B. Sample covariance is -0.000533; portfolio volatility is 2.58%, below Asset B’s 3.27%.
• C. Sample covariance is +0.000533; portfolio volatility is 3.46%, above Asset B’s 3.27%.

Best answer: B

Explanation: Historical diversification depends on covariance as well as individual asset volatility. Both assets have arithmetic mean returns of 4.00%. Using decimal returns, their sample variances are \(s_A^2=0.002667\) and \(s_B^2=0.001067\). The sample covariance is \(s_{AB}=-0.0016/3=-0.000533\).

For equal portfolio weights, sample variance is:

\[ s_p^2=0.25s_A^2+0.25s_B^2+0.50s_{AB}\approx0.000667 \]

The portfolio’s sample standard deviation is therefore \(\sqrt{0.000667}\approx0.02582\), or 2.58%. Asset B’s sample standard deviation is \(\sqrt{0.001067}\approx0.03266\), or 3.27%. The negative covariance makes the portfolio less volatile than Asset B alone over these observations.

Covariance calculated from decimal returns is expressed in squared decimal-return units, whereas standard deviation can be reported as a percentage. These historical estimates support a diversification assessment but do not establish that future covariance or portfolio risk will remain unchanged.

• A. The paired returns have negative covariance rather than zero; omitting the covariance term overstates the portfolio’s sample volatility.
• B. With sample covariance of -0.000533, the equal-weight portfolio’s variance is approximately 0.000667 and its standard deviation is 2.58%.
• C. The cross-products of paired deviations sum to -0.0016, so the sample covariance is negative rather than +0.000533.

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Question 106

Topic: Fixed Income

A credit analyst must choose one of three loans based solely on minimizing expected credit loss in dollars over the next year. Exposure at default is fixed, and discounting is ignored.

Which loan is most appropriate?

• A. Alder
• B. Cedar
• C. Birch

Best answer: C

Explanation: Expected credit loss equals exposure at default multiplied by probability of default and loss given default. Loss given default measures the fraction of exposure lost conditional on default, incorporating expected recoveries.

The one-year expected losses are:

• Alder: \(2{,}000{,}000 \times 0.012 \times 0.70 = 16{,}800\) dollars.
• Birch: \(3{,}000{,}000 \times 0.010 \times 0.50 = 15{,}000\) dollars.
• Cedar: \(5{,}000{,}000 \times 0.008 \times 0.40 = 16{,}000\) dollars.

Birch therefore minimizes expected dollar credit loss. Comparing default probabilities or loss severities alone is insufficient because exposure also matters. These probability-weighted amounts are expected losses, not worst-case losses or losses conditional on default.

• A. Alder’s expected loss is $16,800; its smaller exposure does not offset its higher default probability and loss given default.
• B. Cedar’s expected loss is $16,000; its lower default probability and loss given default are offset by its larger exposure.
• C. Birch’s expected loss is $15,000, the lowest probability-weighted dollar loss among the three loans.

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Question 107

Topic: Portfolio Construction

A client’s $1,000,000 portfolio has the following holdings:

Investment policy:

• Target allocation: 60% equities, 35% government bonds, and 5% cash.
• Exposure to any single equity issuer, including indirect exposure through funds, must not exceed 20% of total portfolio value.

The sector equity fund holds 20% of its assets in Orion shares. Proceeds from selling direct Orion shares would be reinvested in a diversified equity fund with no Orion exposure. All other issuer exposures would remain within the limit. Assume unchanged prices and ignore taxes and trading costs.

Which recommendation is most appropriate to satisfy the policy using the smallest reallocation?

• A. Reduce the direct Orion holding to $30,000.
• B. Keep the direct Orion holding at $150,000.
• C. Reduce the direct Orion holding to $110,000.

Best answer: C

Explanation: Meeting an asset allocation target does not ensure compliance with issuer-concentration limits. This portfolio meets its 60% equity, 35% bond, and 5% cash targets, but its fund holdings create additional Orion exposure.

The fund contributes $90,000 of indirect exposure, calculated as \(0.20 \times 450,000\). Combined with the direct shares, Orion exposure is $240,000, or 24% of the portfolio. The policy permits only $200,000, calculated as \(0.20 \times 1,000,000\).

Because $90,000 remains within the sector fund, the maximum permitted direct holding is $110,000. Reallocating $40,000 to the replacement equity fund reduces Orion exposure to 20% while preserving the asset allocation. The concentration limit applies to total portfolio value, not just the equity allocation.

• A. This complies with the concentration limit but requires reallocating $120,000, exceeding the minimum necessary reallocation of $40,000.
• B. The $150,000 direct holding plus $90,000 held through the fund gives $240,000 of issuer exposure, exceeding the $200,000 policy limit.
• C. Fund holdings add $90,000 of Orion exposure, leaving $110,000 as the maximum direct holding under the $200,000 issuer limit.

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Question 108

Topic: Portfolio Construction

An analyst is reviewing an equity holding using the following one-year estimates. The stock’s expected total return is based on its current market price.

Which assessment of the stock relative to the CAPM security market line (SML) is most accurate?

• A. The stock is 1.2 percentage points above the SML and appears undervalued; immediate price correction is assured.
• B. The stock is 1.2 percentage points below the SML and appears overvalued; immediate price correction is not assured.
• C. The stock is 1.2 percentage points above the SML and appears undervalued; immediate price correction is not assured.

Best answer: C

Explanation: The security market line represents the return required for a given beta under CAPM. The required return is \(3.0\% + 0.60 \times 6.0\% = 6.6\%\). Model-implied alpha equals expected return minus required return, so \(7.8\% - 6.6\% = 1.2\%\), or 1.2 percentage points.

Positive alpha places the stock above the SML and suggests that its current price is low relative to the CAPM equilibrium benchmark. Negative alpha would instead indicate a position below the line and model-relative overvaluation. These are conditional pricing judgments, not guaranteed trading profits. CAPM and a forecast return do not establish that a pricing difference will close immediately or that the forecast will be realized.

• A. A positive forecast alpha is conditional on the CAPM benchmark and return estimates; it does not force prices to correct immediately.
• B. Comparing 7.8% with the market’s 9.0% expected return ignores beta; the stock’s CAPM-required return is 6.6%.
• C. The expected return exceeds the 6.6% CAPM requirement by 1.2 percentage points, indicating model-relative undervaluation rather than certain immediate repricing.

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Question 109

Topic: Corporate Finance

A components manufacturer discloses a supplier wastewater-compliance policy. Its purchasing rules permit annual contracts only with suppliers that pass an independent pre-year environmental audit.

Baseline annual budget:

• Net operating cash inflow: $20 million.
• Capital expenditure: $18 million.
• Cash payments for materials: $50 million, including $30 million to one supplier.
• All suppliers are assumed to pass the audit. A compliant replacement for the $30 million supplier would charge a 20% premium for the same full-year quantity and quality.

No existing cash is available to fund capital expenditure, and no dividends or other financing outflows are planned.

Changed condition: The independent audit establishes that the $30 million supplier fails the wastewater standard. Sales volume, selling prices, cash taxes, capital expenditure, and all other operating cash flows remain unchanged.

Using annual cash-flow totals, the manufacturer’s minimum external financing requirement most likely increases by:

• A. $4 million.
• B. $6 million.
• C. $8 million.

Best answer: A

Explanation: An environmental exposure can be financially material through an issuer’s supply chain. A disclosed compliance policy does not establish actual supplier compliance; the independent audit provides evidence that changes the purchasing decision.

Replacing the affected supplier increases annual cash payments by \(30 \times 0.20 = 6\) million dollars. The baseline budget has a surplus of \(20 - 18 = 2\) million dollars and therefore requires no external financing. After replacement, operating cash inflow falls to \(20 - 6 = 14\) million dollars, leaving a funding gap of \(18 - 14 = 4\) million dollars.

The economic channel is higher material spending, lower operating cash flow, and increased financing needs. Planned capital expenditure itself remains unchanged.

• A. Replacement increases material cash payments by $6 million, absorbing the baseline $2 million surplus and creating a $4 million funding gap.
• B. The $6 million replacement premium is the incremental cash outflow, but the $2 million baseline surplus reduces the external funding need.
• C. Applying the premium to all $50 million of material payments overstates the affected spending; only the $30 million supplier must be replaced.

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Question 110

Topic: Economics

A monopolist faces the demand schedule below and charges the same price for every unit sold. Output is restricted to zero or one of the quantities shown. Fixed costs are unavoidable during the period.

An analyst recommends producing 400 units and charging $70 per unit to maximize profit. Which assumption about marginal cost would make this recommendation profit-maximizing?

• A. Marginal cost is constant at $30 per unit.
• B. Marginal cost is constant at $70 per unit.
• C. Marginal cost is constant at $15 per unit.

Best answer: A

Explanation: A single-price monopolist maximizes profit using marginal revenue, not the selling price. Selling extra units requires reducing the price on all units, so marginal revenue is below price.

Total revenue at 300, 400, and 500 units is $24,000, $28,000, and $30,000. Thus, the fourth 100-unit batch adds $4,000 of revenue and the fifth adds $2,000. At constant marginal cost of $30, each batch costs $3,000. The fourth batch increases profit by $1,000, while the fifth decreases it by $1,000. Earlier batches also increase profit, making 400 units optimal at a price of $70. Unavoidable fixed costs do not affect this comparison.

• A. The fourth batch has marginal revenue of $40 per unit and the fifth has $20, so a $30 marginal cost supports stopping at 400 units.
• B. At $70 marginal cost, the third batch’s $60 marginal revenue lowers profit, making 200 units optimal rather than 400.
• C. At $15 per unit, the final 100-unit batch has marginal revenue of $20 per unit, so expanding to 500 units increases profit.

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Question 111

Topic: Financial Statement Analysis

A manufacturer prepares its financial statements under IFRS and presents the following reconciliation of non-GAAP adjusted operating profit. Amounts are in millions of dollars.

Additional information:

• Each year’s restructuring charges relate to a separate plant closure.
• Employees receive equity-settled awards annually as part of their regular compensation.
• Management applies the same exclusions in all three years.

Which approach is most appropriate for assessing the trend in recurring operating performance?

• A. Use adjusted operating profit, because the reconciliation is clear and the exclusions are consistent across years.
• B. Use operating profit excluding only restructuring, because the closures involve separate plants and equity compensation is recurring.
• C. Use reported operating profit, because both recurring restructuring costs and employee equity compensation are economically relevant.

Best answer: C

Explanation: A non-GAAP reconciliation establishes how management moves from reported profit to an adjusted measure; it does not establish that the exclusions are analytically appropriate. Reported operating profit decreases from $68 million to $62 million, while adjusted operating profit remains at $90 million as the excluded costs rise.

Restructuring charges recur across the three years, even though each closure affects a different plant. Share-based compensation also recurs and represents a cost of employee services despite being noncash. Removing both costs therefore presents an overly favorable view of recurring performance. Consistency improves comparability, but consistently excluding recurring economic costs can still reduce a measure’s usefulness. Reported operating profit is the more representative measure for this comparison.

• A. Transparent, consistent reconciliation makes the adjustments understandable, but it does not justify excluding costs that recur and reduce economically meaningful operating profit.
• B. Closures at different plants are separate projects, but restructuring occurs every year and is therefore not isolated at the company level.
• C. Both categories occur annually, so retaining them captures the economic cost of operating the business and the decline masked by adjusted profit.

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Question 112

Topic: Financial Statement Analysis

An analyst prepares a sales-based forecast for a company with current-year sales of $100 million and net income of $10 million. At year-end, net operating working capital (receivables plus inventories less trade payables) is $25 million. Internally available cash after reinvestment was $5 million during the current year.

Next-year forecast:

Depreciation is the only noncash item. The company must maintain its opening cash balance and may raise up to $2 million in net new borrowing. No equity issuance or other cash flows are assumed.

The analyst concludes that the maximum cash dividend next year is $5.25 million. Which assumption about next-year net operating working capital is most consistent with this conclusion?

• A. Net operating working capital will equal 24% of forecast sales.
• B. Net operating working capital will equal 26% of forecast sales.
• C. Net operating working capital will equal 25% of forecast sales.

Best answer: C

Explanation: Dividend capacity depends on cash remaining after reinvestment, not accounting earnings alone. If net operating working capital remains at 25% of sales, its forecast balance is $31.25 million. The increase from $25 million absorbs $6.25 million of cash.

With amounts in millions, internally available cash is \(12.5 + 5 - 8 - 6.25 = 3.25\). Adding the $2 million borrowing capacity produces a maximum dividend of $5.25 million without reducing the required cash balance.

Net income rises by 25%, but internally available cash declines from $5 million to $3.25 million. Depreciation is added back because it is noncash, while capital expenditures and additional working capital consume cash. Borrowing expands distribution capacity but does not represent internally generated funding.

• A. A 24% ratio requires a $5 million working-capital increase, leaving $4.5 million internally and supporting a maximum dividend of $6.5 million.
• B. A 26% ratio requires a $7.5 million working-capital increase, leaving $2 million internally and supporting a maximum dividend of $4 million.
• C. A 25% ratio requires a $6.25 million working-capital increase, leaving $3.25 million internally and supporting a maximum dividend of $5.25 million.

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Question 113

Topic: Equities

An analyst is valuing a listed investment holding company with no operating subsidiaries.

• Assets and obligations: The portfolio consists of liquid listed shares and bonds. Current security prices and reliable liability valuations are available.
• Earnings and payouts: Reported earnings include recurring investment income and large unrealized gains or losses. Cash dividends are discretionary.
• Valuation inputs: Three-year dividend forecasts and estimates of holding-company costs and taxes are available.
• Peers: Listed investment holding companies have materially different portfolio compositions and leverage.

Considering the reliability of the available inputs, which approach is most appropriate as the primary basis for estimating equity value?

• A. Use asset-based valuation, measuring investments and liabilities at market value and adjusting for relevant holding-company costs and taxes.
• B. Use a dividend discount model, incorporating forecast distributions and a terminal value based on sustainable dividend growth.
• C. Use peer-based P/E valuation, applying leverage-adjusted multiples to normalized earnings that exclude unrealized investment gains and losses.

Best answer: A

Explanation: Asset-based valuation is particularly useful for investment holding companies whose assets have observable market values and whose value does not depend on a separate operating business. Here, liquid listed securities provide a direct basis for measuring the portfolio. The equity estimate starts with market asset values, subtracts market-valued liabilities, and incorporates any additional holding-company cost and tax adjustments.

Dividend discount valuation remains possible, but it depends on payout and terminal-growth assumptions beyond the available forecasts. Relative valuation can provide a cross-check, although differences in portfolio composition weaken peer comparability. Asset-based valuation is not assumption-free: liability valuations and the treatment of future costs and taxes still require judgment.

• A. Observable prices for liquid investments provide a strong valuation basis, with liabilities, holding-company costs, and taxes incorporated into the equity estimate.
• B. Dividend forecasts cover only three years, while discretionary payouts make long-term dividend assumptions less directly supported than current portfolio values.
• C. Even after adjusting for leverage, differences in portfolio composition limit how closely peer P/E multiples reflect the company’s investment risks and returns.

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Question 114

Topic: Fixed Income

Harbor Bank originates auto loans and securitizes them through Juniper, a bankruptcy-remote special-purpose entity (SPE). Counsel confirms that the loan transfer is an enforceable true sale.

Transaction record:

Harbor subsequently files for bankruptcy, temporarily disrupting its collection processing. Which conclusion about the noteholders is most accurate?

• A. Juniper SPE owns the loans; payment delays may arise from interruptions in Harbor’s loan-servicing operations.
• B. Noteholders directly own the loans; payment delays may arise from arranging their own collections from borrowers.
• C. Harbor’s bankruptcy estate owns the loans; payment delays may arise from the estate’s creditor-settlement process.

Best answer: A

Explanation: In this true-sale securitization, the SPE owns the collateral. At closing, investors fund Juniper by purchasing its notes, and Juniper pays Harbor for the auto loan pool.

Ongoing payments follow a different path: borrowers pay Harbor as servicer, Harbor remits collections less its fee to Juniper, and Juniper pays investors. Harbor therefore acts as both originator and servicer, but no longer owns the transferred loans.

The enforceable sale and bankruptcy-remote structure keep the pool outside Harbor’s bankruptcy estate. Nevertheless, Harbor’s servicing disruption can delay cash reaching Juniper and the noteholders. Bankruptcy remoteness limits exposure to the originator’s creditors; it does not eliminate borrower credit risk, servicing risk, or every legal risk.

• A. Harbor collects borrower payments and remits them to Juniper, making its servicing relevant to payment timing despite the pool’s legal separation.
• B. Investors own Juniper’s notes rather than the underlying auto loans; Juniper remains the collateral owner and recipient of servicer remittances.
• C. The enforceable true sale places loan ownership with Juniper, so Harbor’s bankruptcy does not make the transferred pool part of its estate.

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Question 115

Topic: Portfolio Construction

An investment management firm uses the following risk-governance arrangements:

• The board sets risk tolerance and approves portfolio risk limits.
• The chief investment officer (CIO) is accountable for compliance with those limits, and portfolio managers execute investment trades.
• The chief risk officer (CRO), separate from the investment team, monitors exposures and promptly reports limit breaches directly to the board risk committee.

Policy change: The CRO must now obtain the CIO’s approval before reporting a limit breach to the board risk committee. Risk tolerance, portfolio limits, trade-execution authority, and all other responsibilities remain unchanged.

Compared with the original arrangements, the revised risk governance is most likely:

• A. Equally effective because the board retains risk-tolerance decisions and the CIO remains accountable for complying with portfolio limits.
• B. More effective because the CIO’s authority over breach reporting is now aligned with accountability for managing portfolio risks.
• C. Less effective because the CIO can restrict independent escalation of breaches in investment activities under the CIO’s oversight.

Best answer: C

Explanation: Effective risk governance aligns the board’s risk-tolerance decisions with management accountability and independent oversight. The board establishes acceptable risk, management implements limits, and an independent risk function monitors exposures and escalates breaches.

The revised policy gives the CIO control over whether breaches reach the board risk committee. Because the CIO is also accountable for compliance with those limits, this approval requirement creates a conflict and weakens independent oversight. The board’s unchanged formal authority does not offset the restricted reporting channel.

Governance of risk-taking is distinct from trade execution. Portfolio managers may continue executing trades, and management may direct corrective action. The CRO needs effective monitoring and escalation authority, not authority to execute investment trades.

• A. The board’s retained authority does not preserve effective oversight when the CIO can prevent risk-limit breaches from reaching its risk committee.
• B. Management accountability for implementing risk limits should not extend to controlling whether independent monitors disclose breaches to the board.
• C. Requiring approval from the executive accountable for investment risk compromises the CRO’s independent escalation of breaches to the governing body.

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Question 116

Topic: Quantitative Methods

An analyst proposes using a sample covariance calculation for the three economic-state return pairs below.

The research director confirms that these mutually exclusive and exhaustive states describe the complete prospective one-year probability distribution, not three historical observations.

Given this confirmation, which unconditional covariance estimate is most accurate when returns are expressed as decimals?

• A. The unconditional covariance is -0.01200.
• B. The unconditional covariance is -0.00564.
• C. The unconditional covariance is -0.00360.

Best answer: B

Explanation: Unconditional covariance uses the probabilities of all possible states. Because the table represents a complete prospective distribution, no sample degrees-of-freedom adjustment applies.

Let \(R_E\) and \(R_B\) denote the equity and bond returns. Their probability-weighted expected returns are:

\[ \begin{aligned} E[R_E] &= 0.20(-0.20)+0.50(0.08)+0.30(0.20)=0.060, \\ E[R_B] &= 0.20(0.10)+0.50(0.04)+0.30(-0.02)=0.034. \end{aligned} \]

The expected product is \( E[R_E R_B] = 0.20(-0.20)(0.10)+0.50(0.08)(0.04)+0.30(0.20)(-0.02)=-0.00360 \). Therefore:

\[ \operatorname{Cov}(R_E,R_B)=E[R_E R_B]-E[R_E]E[R_B]=-0.00564. \]

The negative covariance indicates that deviations from the two expected returns tend to move in opposite directions under this distribution.

• A. This is the unweighted sample covariance of the three return pairs; it ignores the stated probabilities and treats prospective states as historical observations.
• B. The probability-weighted expected product is -0.00360, so covariance is \( -0.00360 - (0.060)(0.034) = -0.00564 \).
• C. This is the expected product of the returns; covariance requires subtracting the product of their expected returns.

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Question 117

Topic: Quantitative Methods

A bond analyst is developing a screen to estimate an issuer’s probability of missing a scheduled debt payment during the next 12 months. The analyst plans to develop the model using the larger historical archive.

Data inventory:

Historical outcomes are labeled missed payment or no missed payment for the 12 months after the ratios were measured. Both outcomes occur in each archive. The archives cover the same years, do not overlap, and represent their respective issuer populations.

Which analytical approach and evaluation method are most appropriate for the intended screen?

• A. Fit a supervised classifier and assess predictive performance on a random industrial-issuer holdout.
• B. Fit a supervised classifier and assess predictive performance on the independent software-issuer sample.
• C. Fit an unsupervised clustering model and assess group separation on the independent software-issuer sample.

Best answer: B

Explanation: Predicting a known binary outcome is a supervised classification task. Historical financial ratios provide the predictors, and subsequent missed-payment status provides the labels. A suitable classifier can estimate event probabilities. Unsupervised clustering instead discovers similarity groups without directly learning the specified outcome.

Evaluation should reflect the population in which the model will operate. A random industrial holdout can assess performance among industrial issuers, but relationships learned there may not generalize to software issuers. The independent software archive matches the intended investment universe and uses verified outcomes over the same forecast horizon, making it the more relevant out-of-sample assessment. Successful validation supports deployment but does not guarantee future performance if financial conditions or issuer characteristics change.

• A. An industrial holdout evaluates performance in the development population, but does not establish performance for the software issuers the screen will cover.
• B. Verified binary outcomes support supervised classification, and the independent software sample evaluates predictive performance in the intended investment population.
• C. Group separation measures clustering quality rather than predictive performance for the specified future payment outcome.

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Question 118

Topic: Derivatives and Risk Management

A three-year fixed-for-floating interest rate swap is initiated at par, giving it zero initial value. The fixed-rate payer pays 3.97% annually (rounded) and receives an annually reset benchmark rate on a constant notional. Net settlements occur at the end of years 1, 2, and 3, with no exchange of notional.

Standalone forward commitments with the same notional, one-year accrual periods, and settlement dates have the following fair fixed rates:

Ignoring counterparty risk, which statement about the forward commitments replicating the swap is least accurate?

• A. The year 1 component forward has a negative initial value to the fixed-rate payer.
• B. The three component forwards each have zero initial value to the fixed-rate payer.
• C. The three component forwards have a combined initial value of zero to the fixed-rate payer.

Best answer: B

Explanation: A fixed-for-floating swap can be decomposed into forward commitments that all use the swap’s contractual fixed rate. A standalone forward has zero initial value only when its fixed rate equals the fair forward rate for that particular period.

For the fixed-rate payer, a one-year component’s value is \(N D_i(F_i-K)\), where \(N\) is the notional, \(D_i\) is the payment-date discount factor, \(F_i\) is the fair forward rate, and \(K\) is the swap rate. Here, the first component is negative and the later components are positive. The par swap rate is the discount-weighted average of the forward rates, so these component values sum to zero. Using the three different fair forward rates instead would change the swap’s contracted settlements.

• A. The first period’s fair forward rate of 3.00% is below the swap’s 3.97% fixed rate, making that component negative for the fixed-rate payer.
• B. The common 3.97% rate differs from every period’s fair forward rate, so none of the swap’s individual components has zero initial value.
• C. The swap is initiated at par, so the initial values of the forwards replicating its settlements must sum to zero.

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Question 119

Topic: Quantitative Methods

An analyst uses the following mutually exclusive and exhaustive economic scenarios to model a fund’s return over the next year:

The fund’s expected one-year return and standard deviation are closest to:

• A. Expected return of 8.0%; standard deviation of 14.8 percentage points.
• B. Expected return of 5.0%; standard deviation of 12.8 percentage points.
• C. Expected return of 8.0%; standard deviation of 12.5 percentage points.

Best answer: C

Explanation: Expected return is the probability-weighted mean, not the most likely individual outcome. The scenarios contribute -2.0%, 2.5%, and 7.5%, respectively, giving an expected return of 8.0%.

The deviations from this mean are -18, -3, and 17 percentage points. Weighting their squares gives the variance:

\[ \sigma^2 = 0.20(-18)^2 + 0.50(-3)^2 + 0.30(17)^2 = 156. \]

The variance is 156 squared percentage points, so the standard deviation is \(\sqrt{156} \approx 12.5\) percentage points. This measures dispersion around the 8.0% expectation. The 5% return is the most likely outcome, with a 50% probability, but the expectation incorporates all scenarios and need not equal any possible realized return.

• A. The 14.8-point figure is the square root of the weighted squared returns, rather than the weighted squared deviations from the 8.0% mean.
• B. Centering on the most likely return of 5.0% gives a 12.8-point dispersion, but standard deviation must be centered on the probability-weighted mean of 8.0%.
• C. Probability weighting gives an 8.0% mean and variance of 156 squared percentage points; taking the square root yields a 12.5-point standard deviation.

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Question 120

Topic: Derivatives and Risk Management

An analyst values a one-year European call on a non-dividend-paying stock using a one-period binomial model. The current stock price is $100, the exercise price is $100, and the annual effective risk-free rate is 5%. Trading is frictionless, and borrowing and lending are available at the risk-free rate.

The analyst initially assigns real-world probabilities of 70% to the up state and 30% to the down state. The analyst revises these probabilities to 80% and 20%, respectively. All market inputs and terminal payoffs remain unchanged.

Compared with its value before the forecast revision, the call’s no-arbitrage value is most likely:

• A. Increased to $15.24.
• B. Unchanged at $13.33.
• C. Unchanged at $11.90.

Best answer: C

Explanation: Risk-neutral valuation uses pricing probabilities consistent with traded asset prices and no-arbitrage replication. It does not assume that investors are actually indifferent to risk.

The up-state pricing probability \(q\) makes the stock’s expected terminal price under those weights equal its current price compounded at the risk-free rate:

\[ q = \frac{100(1.05)-80}{120-80} = 0.625. \]

The call value is therefore \(C_0 = [0.625(20)+0.375(0)]/1.05 = 11.90\), or $11.90. Equivalently, a replicating portfolio holds 0.5 share and borrows the present value of $40. Its initial cost is \(50-40/1.05=11.90\).

Revising the subjective forecast changes the real-world expected payoff, not the cost of this unchanged replicating portfolio. Risk preferences can influence market prices without invalidating risk-neutral valuation.

• A. The calculation \(0.80 \times 20 / 1.05 = 15.24\) incorrectly discounts the revised real-world expected payoff at the risk-free rate.
• B. The calculation \(0.70 \times 20 / 1.05 = 13.33\) incorrectly uses the original real-world probability instead of the pricing probability implied by tradable assets.
• C. The pricing probability remains 62.5%, giving \(0.625 \times 20 / 1.05 = 11.90\); unchanged replication inputs leave the no-arbitrage value unchanged.

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Question 121

Topic: Equities

An analyst estimates Norvia Ltd.’s equity value per share using two methods:

The comparable estimate uses Norvia’s forecast next-year earnings per share of $3.00 and a peer median forward P/E of 18.0.

Subsequently, every peer’s share price declines by 20%, while peer earnings forecasts remain unchanged. The same peers are retained. Norvia’s earnings and cash-flow forecasts, terminal assumptions, and required return on equity are unchanged.

Which revised comparison and explanation of the valuation gap is most accurate?

• A. Present-value estimate: $38.40; comparable estimate: $43.20. Peer repricing reduces both estimates proportionately and preserves their relative ranking.
• B. Present-value estimate: $48.00; comparable estimate: $43.20. Peer repricing reverses the direction of the valuation gap.
• C. Present-value estimate: $48.00; comparable estimate: $54.00. Unchanged earnings forecasts preserve both estimates and their relative ranking.

Best answer: B

Explanation: Present-value equity estimates depend on expected cash flows, terminal assumptions, and the required return. Comparable-company estimates reflect market prices embedded in peer multiples as well as the target company’s financial forecasts.

With peer earnings unchanged, the 20% share-price decline reduces the median forward P/E to \(18.0 \times 0.80 = 14.4\). Applying that multiple to Norvia’s forecast EPS of $3.00 gives $43.20 per share. The present-value estimate remains $48.00 because its inputs have not changed.

The comparable estimate initially exceeded the present-value estimate by $6.00; it now falls below it by $4.80. This reversal reflects peer-market repricing, not a change in Norvia’s expected cash flows. Averaging the estimates would not resolve the underlying difference in valuation assumptions.

• A. Peer-price declines do not mechanically reduce the present-value estimate when Norvia’s cash-flow forecasts, terminal assumptions, and required return remain unchanged.
• B. The price decline lowers the peer multiple to 14.4 and the comparable estimate to $43.20, while unchanged present-value inputs preserve $48.00.
• C. Forward P/E depends on peer share prices as well as forecast earnings, so unchanged earnings do not preserve the 18.0 multiple.

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Question 122

Topic: Fixed Income

An analyst constructs an arbitrage-free interest-rate curve from the following default-free market quotations. Spot and forward rates use annual compounding.

The two-year bond is issued today at par with a $100 face value. It pays $5 at the end of year 1 and $105 at the end of year 2.

Which proposed method and one-year forward rate for the period from year 1 to year 2 are most appropriate for reproducing the bond’s par price?

• A. Use 6.00%, calculated as twice the two-year par rate minus the one-year spot rate.
• B. Use 6.06%, calculated from the forward-rate relationship with the two-year discount factor recovered from the par bond.
• C. Use 6.01%, calculated from the forward-rate relationship with the two-year par rate substituted for the spot rate.

Best answer: B

Explanation: An arbitrage-free forward rate must be derived from discount factors that price the underlying cash flows consistently. A par rate is a bond’s coupon rate when its price equals face value, not generally the spot rate for the same maturity.

Let \(D_t\) denote the discount factor for a payment in year \(t\). The one-year quote gives \(D_1=1/1.04=0.961538\). The par bond requires \(100=5D_1+105D_2\), so:

\[ D_2=\frac{100-5D_1}{105}=0.906593. \]

The one-year forward rate \(f_{1,1}\), beginning in one year, satisfies \(D_2=D_1/(1+f_{1,1})\). Therefore:

\[ f_{1,1}=\frac{D_1}{D_2}-1=0.060606\approx6.06\%. \]

Using the unrounded discount factors, \(5D_1+105D_2=100\), confirming that the 5% coupon bond prices at par.

• A. Doubling the par rate and subtracting the spot rate ignores coupon discounting and compounding, so it does not recover the arbitrage-free forward rate.
• B. The par bond implies a two-year discount factor of 0.906593, which combines with the one-year discount factor to give a 6.06% forward rate.
• C. The calculation \((1.05)^2/1.04-1\) treats 5% as a two-year spot rate, although the quotation is a par rate.

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Question 123

Topic: Quantitative Methods

In July 2026, an analyst completes a retrospective study of a stock-return model and reports 78% directional accuracy on a held-out test period.

Study design:

• The intended strategy fits the model once, after closing-price information is available on 31 December 2025, and then keeps it fixed.
• Each observation has a month-end forecast date and uses only features available on that date.
• The target is the stock’s total return over the next three full calendar months, observable at the end of the third month.
• Training forecast dates run from 31 January 2023 through 31 December 2025.
• Test forecast dates run from 31 January through 31 March 2026. These observations are excluded from fitting and model selection.

To evaluate performance achievable under the intended deployment schedule, which latest training forecast date is most appropriate before refitting and repeating the test?

• A. 31 December 2025.
• B. 31 October 2025.
• C. 30 September 2025.

Best answer: C

Explanation: Valid out-of-sample evaluation must reproduce the information available when the model would have been fitted, not merely separate training and test forecast dates. Each target spans the next three full calendar months. A forecast dated 30 September 2025 therefore has a target measured over October, November, and December, which is known at the intended fitting date. Targets for later forecasts finish after 31 December 2025.

Training must consequently stop at 30 September 2025. Timely features and exclusion of test observations do not cure look-ahead bias from unavailable training labels. The analyst must refit the model and recompute test accuracy; the original 78% does not establish performance achievable with information available at deployment.

• A. The December forecast’s target covers January through March 2026; separate training and test forecast dates do not prevent future outcomes from entering model fitting.
• B. The October forecast’s target covers November 2025 through January 2026, so its return would be unavailable at the intended December fitting date.
• C. The September forecast’s target covers October through December 2025 and is observable at fitting; later forecasts require prices unavailable at that time.

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Question 124

Topic: Ethical and Professional Standards

A professional association for investment analysts awards a designation based on examinations and experience. Its code requires members to put client interests first and exercise independent judgment. Member analysts receive bonuses partly linked to sales of products they recommend.

Initially, the association independently investigates alleged code violations and can suspend members. It then discontinues this enforcement process. The code, designation requirements, compensation arrangements, and observed quality of members’ research remain unchanged.

Which assessment of the resulting basis for client trust is most accurate?

• A. The basis for trust is unchanged because members remain bound by the association’s ethical obligations.
• B. The basis for trust is unchanged because members’ qualifications and the quality of their research are preserved.
• C. The basis for trust is weaker because the association has reduced accountability for members’ ethical obligations.

Best answer: C

Explanation: Professionalism supports trust through expertise, service to clients, ethical standards, and accountability. A designation can indicate competence, but the title alone does not ensure ethical conduct.

Here, sales-linked bonuses create incentives that can conflict with independent research and client interests. Ending independent investigation and discipline leaves the code intact but weakens a mechanism for holding members to it. The professional basis for confidence in research independence therefore becomes weaker, even though observed research quality has not changed.

This does not establish that any member has committed misconduct. Likewise, membership and enforcement cannot guarantee ethical behavior. The change reduces the credibility of the association’s commitment to upholding its professional obligations.

• A. Unchanged ethical duties do not preserve the same basis for trust when the association no longer holds members accountable for violations.
• B. Qualifications and research quality demonstrate competence, but they do not replace ethical accountability when financial incentives can compromise independent judgment.
• C. With sales-related incentives still present, removing independent discipline weakens the assurance that members will honor their client-focused duties.

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Question 125

Topic: Equities

An analyst uses a two-stage dividend discount model to value a manufacturer. Signed customer contracts support rapid growth over the next five years. Thereafter, the company is expected to maintain a stable share of a mature, competitive market.

Research note:

Growth rates and the required return are nominal. The company plans no equity issuance or repurchases, and leverage is expected to remain unchanged.

Which assessment of the model is most accurate?

• A. The model is economically defensible because perpetual growth of 6% is below the 9% required return.
• B. The model is mathematically invalid because first-stage growth of 12% exceeds the 9% required return.
• C. The model is economically questionable because perpetual growth of 6% exceeds the 4% sustainable growth rate.

Best answer: C

Explanation: For a mature company with stable ROE and payout policy, sustainable dividend growth is \(g = b \times \mathrm{ROE}\), where \(b\) is the earnings retention ratio. The forecasts imply \(g = 0.40 \times 10\% = 4\%\). Sustaining 6% growth at a 10% ROE would require 60% retention, above the planned 40%. Stable market share in a market forecast to grow 4% also supports a lower terminal rate.

The five-year 12% growth forecast can exceed the 9% required return because it applies for a finite period. The condition \(r > g\) applies to perpetual growth in the terminal value formula, \(V_5 = D_6/(r-g)\), where \(D_6\) is the year-6 dividend and \(r\) is the required return. Holding that dividend fixed, using 6% instead of 4% narrows the denominator from 5 to 3 percentage points and increases terminal value. These conclusions remain conditional on the forecasts.

• A. Being below the required return ensures a finite terminal value, but it does not establish consistency with mature reinvestment capacity.
• B. Growth can exceed the required return during a finite forecast period; the restriction applies to the perpetual growth rate.
• C. The mature forecasts imply 4% sustainable growth, below the 6% perpetual assumption and consistent with the expected market growth.

Questions 126-150

Question 126

Topic: Derivatives and Risk Management

A US exporter expects to receive €1,000,000 in three months from a provisional order. The buyer may cancel the order before the receipt date. If canceled, the exporter receives nothing and has no other euro exposure.

The exporter considers two hedges covering the entire potential receipt:

• Sell euros forward at $1.10 per euro, with no initial payment.
• Buy a European put on euros with a strike price of $1.10 per euro, paying a $20,000 premium upfront.

Both hedges are held to maturity on the receipt date and cash settled in US dollars. Ignore financing costs and counterparty risk.

Comparing minimum net receipts if the order proceeds and potential hedge losses if it is canceled, which conclusion is most accurate?

• A. The put provides a $1,100,000 net receipt floor. If the order is canceled, only the forward can generate hedge losses exceeding $20,000.
• B. The put provides a $1,080,000 net receipt floor. If the order is canceled, only the forward can generate hedge losses exceeding $20,000.
• C. The put provides a $1,080,000 net receipt floor. If the order is canceled, both hedges can generate hedge losses exceeding $20,000.

Best answer: B

Explanation: A currency put protects a euro receivable by paying when the dollar value of euros falls below the strike. If the order proceeds, the receipt plus the put payoff cannot fall below $1,100,000 before premium. Deducting the $20,000 premium gives a $1,080,000 net floor. The exporter retains the benefit of euro appreciation, less the premium.

The forward instead fixes completed-order proceeds at $1,100,000 and gives up favorable exchange-rate participation. If the order is canceled, the forward remains binding but no euro receipt exists to offset it. Euro appreciation can then produce a forward loss exceeding $20,000, making the position speculative. The purchased put may expire worthless, but its loss remains limited to the premium. Thus, the option exchanges a lower guaranteed net receipt for favorable participation and limited cancellation-related losses.

• A. The $1,100,000 amount is the put’s gross receipt floor; deducting its $20,000 premium reduces the net floor to $1,080,000.
• B. The premium reduces the put’s receipt floor by $20,000 and caps its loss, whereas the binding forward can lose more if euros appreciate.
• C. A purchased put’s payoff cannot be negative, so its maximum loss is the $20,000 premium even when the underlying receipt disappears.

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Question 127

Topic: Alternative Investments

An analyst reviews four proposed private capital investments:

The private loan ranks below bank debt but above common equity. Principal repayment is expected to come from a company sale at maturity; refinancing would be required if the sale does not occur.

The analyst concludes:

“If the planned sales occur, all four investors will hold residual ownership claims when exit proceeds are allocated.”

Which additional provision in the private-lending agreement would make this conclusion most defensible?

• A. Accrued interest is added to principal, and the combined balance becomes payable from sale proceeds.
• B. Principal and accrued interest become payable from sale proceeds only after all other creditors are repaid.
• C. Principal and accrued interest automatically convert into common shares before sale proceeds are distributed.

Best answer: C

Explanation: Private equity and private debt are distinguished by their claims, not solely by the financed company’s business stage. Venture capital, growth equity, and buyout investments can all provide residual ownership, despite targeting different stages of business development. Common shareholders participate in the value remaining after creditors’ claims are satisfied.

An early-stage company can also borrow private debt, and that debt need not be senior secured. The subordinated loan here initially provides contractual interest and principal entitlements. Dependence on a sale or refinancing creates financing risk but does not turn those entitlements into equity.

Mandatory conversion of the entire outstanding loan balance into common shares before the sale would make the analyst’s conclusion defensible at exit. Capitalized interest or deeper subordination alone would leave the lender with a debt claim.

• A. Capitalizing interest changes payment timing and the loan balance, but repayment remains a contractual debt entitlement rather than residual ownership.
• B. Greater subordination changes repayment priority and recovery risk, but the principal-and-interest entitlement remains a debt claim rather than residual ownership.
• C. Full conversion replaces the lender’s repayment entitlement with common-equity ownership, making its claim residual when sale proceeds are allocated.

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Question 128

Topic: Corporate Finance

An analyst is evaluating a two-year expansion using net present value. The company’s tax rate is 25%. Except for time 0 investments, all cash flows occur at year-end.

Operating estimates:

• The new product generates annual after-tax operating cash flow of $150,000, including depreciation tax shields but before effects on existing products and warehouse use.
• The expansion reduces existing products’ annual sales by $80,000 and avoids associated annual cash operating costs of $40,000.
• The expansion uses an owned warehouse that could otherwise generate annual net after-tax rental cash inflows of $20,000. The expansion does not change the warehouse’s terminal value.

Investment estimates:

• Equipment costs $200,000 at time 0 and has no terminal proceeds.
• Working capital requires $40,000 at time 0 and an additional $20,000 at the end of year 1. The entire balance is recovered at the end of year 2.
• A $15,000 feasibility study was paid for and fully deducted for tax purposes last year.

Which sequence of net cash flows is most appropriate for the expansion’s NPV analysis?

• A. An initial outflow of $240,000, followed by inflows of $100,000 and $180,000 in years 1 and 2, respectively.
• B. An initial outflow of $255,000, followed by inflows of $80,000 and $160,000 in years 1 and 2, respectively.
• C. An initial outflow of $240,000, followed by inflows of $80,000 and $160,000 in years 1 and 2, respectively.

Best answer: C

Explanation: Incremental cash flows measure the difference between undertaking an investment and not undertaking it. The feasibility study is excluded because its payment and tax deduction occurred last year. The owned warehouse creates an annual $20,000 after-tax opportunity cost through forgone rental income.

The expansion reduces existing products’ annual contribution by $40,000 before tax. At a 25% tax rate, this reduces after-tax cash flow by $30,000. Deducting this loss and forgone rent from the new product’s $150,000 gives annual operating cash flow of $100,000.

• Time 0: Equipment of $200,000 plus working capital of $40,000 produces a $240,000 outflow.
• Year 1: Operating cash flow of $100,000 less additional working capital of $20,000 produces an $80,000 inflow.
• Year 2: Operating cash flow of $100,000 plus recovery of $60,000 in working capital produces a $160,000 inflow.

Working-capital investment is a cash outflow, not an operating expense; its recovery is a cash inflow.

• A. Omitting the warehouse’s forgone rental income overstates each year’s cash flow by $20,000; using an owned asset still creates an opportunity cost.
• B. The additional $15,000 initial outflow incorrectly includes the feasibility study, whose payment and tax deduction are sunk rather than incremental.
• C. Adjusted annual operating cash flow is $100,000; additional working-capital investment reduces year 1 cash flow, and full recovery increases year 2 cash flow.

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Question 129

Topic: Equities

An analyst reviews the following calendar-year data for the US reusable water bottle market and one manufacturer. The manufacturer’s figures cover only this market. The product definition is unchanged, and industry totals include the manufacturer.

Based on these data, which conclusion is least accurate?

• A. The manufacturer increased its market share when measured using sales revenue.
• B. The manufacturer increased its market share when measured using units sold.
• C. Industry revenue growth reflected increases in both unit sales and average revenue per unit.

Best answer: B

Explanation: Market share compares company sales with total industry sales using consistent units, market coverage, and periods. Revenue-based and unit-based shares can move in different directions.

The manufacturer’s revenue share increased from \(80/800 = 10\%\) to \(105.6/960 = 11\%\). Its unit share decreased from \(4/40 = 10\%\) to \(4.2/44 \approx 9.55\%\). Thus, stronger revenue growth did not represent a gain in unit-based market share.

Industry revenue grew 20%, compared with 10% growth in units sold. Average industry revenue per unit consequently increased from $20.00 to approximately $21.82. The manufacturer’s average revenue per unit rose more sharply, from $20.00 to approximately $25.14. These averages may reflect changes in prices or product mix; they do not establish that every product’s price increased.

• A. Revenue-based market share rose from 10% to 11%, because the manufacturer’s revenue growth of 32% exceeded industry revenue growth of 20%.
• B. Unit-based market share fell from 10% to approximately 9.55%, because the manufacturer’s unit sales grew 5% while industry unit sales grew 10%.
• C. Industry revenue rose 20% while unit sales rose 10%, so average revenue per unit increased from $20.00 to approximately $21.82.

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Question 130

Topic: Equities

An analyst uses a constant-growth model of free cash flow to equity (FCFE) in an equity research report. Growth and discount rates are assumed to remain constant indefinitely.

The report concludes:

Using WACC in the constant-growth FCFE model gives an equity value of $50.00 per share. The shares are undervalued, supporting a buy recommendation.

Which correction and resulting comparison with the market price is most accurate?

• A. Use a 12% discount rate and deduct net debt: value is $19.50 per share, below the market price.
• B. Use a 12% discount rate with no net-debt deduction: value is $37.50 per share, above the market price.
• C. Use a 10% discount rate and deduct net debt: value is $32.00 per share, below the market price.

Best answer: B

Explanation: FCFE represents cash available to equity holders after debt-related cash flows, so it must be discounted at the cost of equity. WACC is appropriate for free cash flow to the firm, which is available to both debt and equity capital providers.

Because the stated FCFE is next year’s cash flow, the estimated equity value per share, in dollars, is:

\[ \frac{3.00}{0.12 - 0.04} = 37.50 \]

No net-debt deduction is needed because the model values equity directly. The corrected value remains above the $36.00 market price. Under the stated assumptions, the valuation still indicates undervaluation, but the original report materially overstates its extent.

• A. The $37.50 FCFE valuation already represents equity value, so subsequently subtracting $18.00 of net debt makes an unnecessary enterprise-to-equity adjustment.
• B. Discounting FCFE at the cost of equity directly values equity at $37.50 per share, exceeding the $36.00 market price.
• C. Subtracting net debt does not repair the discount-rate mismatch: WACC is inappropriate for FCFE, which already represents cash available to equity holders.

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Question 131

Topic: Ethical and Professional Standards

Maya Chen, CFA, prepares and approves monthly client performance reports. She verifies that returns labeled net of management fees have not been reduced by the fees charged to clients. She documents the error and informs her supervisor, who instructs her to continue using the same calculation in future reports.

The firm’s compliance officer has not yet been informed and is available to advise Maya. Applicable law prohibits misleading client reporting and permits, but does not require, Maya to notify the securities regulator.

Which advice about Maya’s responsibilities under the CFA Institute Code of Ethics and Standards of Professional Conduct is least accurate?

• A. Consult the compliance officer for guidance on addressing the misleading reports and the supervisor’s instructions.
• B. Notify the securities regulator to meet the Standards’ duty to report known violations to external authorities.
• C. Cease approving and distributing the misleading reports to meet the duty to dissociate from the violation.

Best answer: B

Explanation: Standard I(A), Knowledge of the Law, requires members and candidates to avoid knowingly participating in violations and to dissociate from continuing misconduct. Returns calculated before deducting charged management fees cannot accurately be presented as net of those fees.

Maya should seek compliance or legal advice and attempt to have the reports corrected. Her supervisor’s instructions do not justify continuing to approve or distribute misleading reports. If corrective efforts fail, she must withdraw from the offending activity; resignation may be necessary if effective dissociation is otherwise impossible.

The Standards do not generally require reporting violations to regulators. External reporting becomes mandatory when applicable law requires it. Here, the law permits reporting but does not require it, so regulatory notification cannot be described as a mandatory Standards obligation.

• A. Seeking compliance advice is a recommended response to a known violation, and this internal channel remains available despite the supervisor’s refusal to correct the reports.
• B. The Standards do not generally require external reporting, and the stated law imposes no such duty; permission to report does not create an obligation.
• C. Maya must stop participating in reporting she knows is misleading; notifying her supervisor does not discharge her duty to dissociate.

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Question 132

Topic: Fixed Income

An analyst assesses a callable corporate bond ahead of a parallel decrease in benchmark yields of 50 basis points (0.50 percentage points). The issuer’s credit spread is assumed unchanged. The bond’s risk measures incorporate its embedded call option.

Using both effective duration and effective convexity, which estimate is most appropriate for the change in the bond’s full price?

• A. An increase of 2.60%.
• B. An increase of 2.75%.
• C. An increase of 2.90%.

Best answer: A

Explanation: Effective duration and convexity estimate benchmark-rate sensitivity while allowing expected cash flows to change with option exercise. Let \(D\) denote effective duration, \(C\) effective convexity, and \(\Delta y\) the benchmark-yield change in decimal form. The approximate proportional full-price change is:

\[ \begin{aligned} \frac{\Delta P}{P} &\approx -D\Delta y + \tfrac{1}{2}C(\Delta y)^2 \\ &= -5.5(-0.005) + \tfrac{1}{2}(-120)(-0.005)^2 \\ &= 0.026 = 2.60\%. \end{aligned} \]

Negative convexity reduces the duration-only gain. As benchmark rates fall, a callable bond may become more likely to be called, limiting price appreciation. The unchanged credit spread isolates benchmark-rate sensitivity; these measures should not automatically be applied to an isolated credit-spread shock.

• A. The duration contribution is +2.75% and the convexity contribution is -0.15%, producing an estimated full-price increase of 2.60%.
• B. The 2.75% increase reflects the duration contribution alone and omits the negative convexity adjustment.
• C. The 2.90% increase treats the convexity contribution as positive, although the bond’s effective convexity is negative.

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Question 133

Topic: Derivatives and Risk Management

An investor starts with $6,000,000 in cash and takes a long equity index futures position with $6,000,000 of notional exposure instead of purchasing index constituents outright. Initial margin of 10% of notional is posted from this cash.

The broker then raises the initial margin requirement to 15%, while the index level, futures price, and number of contracts remain unchanged. Assume the futures price moves by the same percentage as the index, and ignore interest and transaction costs.

Immediately after the additional collateral is posted, which combination of cash outside the margin account and futures loss under a hypothetical 1% index decline is most accurate?

• A. Cash outside the margin account is $5,100,000; the hypothetical futures loss is $60,000.
• B. Cash outside the margin account is $5,700,000; the hypothetical futures loss is $60,000.
• C. Cash outside the margin account is $5,100,000; the hypothetical futures loss is $9,000.

Best answer: A

Explanation: Initial margin is collateral, not the size of the market position. Increasing the requirement from 10% to 15% raises posted collateral from $600,000 to $900,000. The investor must add $300,000, leaving $5,100,000 outside the margin account.

The futures exposure remains $6,000,000 because neither the contracts nor their prices change. A 1% index decline therefore produces a $60,000 futures loss, matching the price loss on an equally sized outright investment under the stated assumptions. Posting additional collateral reallocates cash; it is not itself an investment loss. Higher margin reduces available liquidity but does not reduce market sensitivity or eliminate subsequent variation-margin obligations.

• A. Total collateral is $900,000, leaving $5,100,000 outside the margin account; a 1% decline produces a $60,000 loss on unchanged notional exposure.
• B. The $5,700,000 balance subtracts only the $300,000 margin increase from original cash, overlooking the $600,000 already posted.
• C. The $9,000 loss treats posted collateral as market exposure; futures gains and losses depend on the $6,000,000 notional exposure.

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Question 134

Topic: Corporate Finance

An analyst is evaluating a project with the same operating risk as a company’s existing assets. The company plans to maintain the financing mix represented by these market values:

All costs are annual rates on a common basis, and the debt cost is pre-tax. Outstanding debt has an annual coupon rate of 5.0%.

The corporate tax rate is 25%. For additional borrowing, 60% of interest expense is deductible and the remainder is permanently nondeductible. The company has sufficient taxable income to use the deductions immediately. Preferred and ordinary dividends are not deductible.

The WACC used to evaluate the project is closest to:

• A. 8.50%
• B. 9.18%
• C. 8.90%

Best answer: B

Explanation: WACC combines current marginal financing costs using the financing proportions the company expects to maintain. Total market value is $300 million, giving weights of 40% debt, 10% preferred equity, and 50% ordinary equity.

Only deductible interest creates a tax shield. The after-tax marginal debt cost is \( 7.0\% \times (1 - 0.25 \times 0.60) = 5.95\% \). Preferred and ordinary equity costs receive no tax adjustment.

Therefore:

\[ \text{WACC} = 0.40(5.95\%) + 0.10(8.0\%) + 0.50(12.0\%) = 9.18\% \]

The historical coupon reflects past financing terms, not the current cost of raising debt capital. Because the project has the same operating risk as existing assets and uses the maintained financing mix, this WACC is the appropriate discount rate.

• A. Using the historical 5.0% coupon produces an after-tax debt cost of 4.25%; the calculation instead requires the current marginal borrowing cost.
• B. Market-value weights of 40%, 10%, and 50%, combined with a 5.95% after-tax debt cost, produce a WACC of 9.18%.
• C. Applying the 25% tax rate to all debt interest produces 8.90%, but only 60% of the interest expense is deductible.

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Question 135

Topic: Ethical and Professional Standards

An analyst’s draft recommendation uses an EPS figure that a data provider initially classifies as an actual reported result. The draft states:

The company’s actual reported annual EPS is $4.00. We recommend buying its shares and forecast a 9% one-year return before advisory fees. Estimates are opinions; actual outcomes may differ.

Additional disclosures:

• Process: The valuation applies an assumed price-to-earnings multiple to the EPS input.
• Limitation and risk: The model does not simulate recessions; earnings declines and multiple contraction can cause losses.
• Services and cost: Ongoing portfolio advice and monitoring cost 0.60% of assets annually.

Before distribution, the provider corrects the classification: $4.00 is management’s forecast for the coming year, rather than actual reported earnings. All amounts, model methods, services, and fees remain unchanged.

Following the correction, which assessment of the unchanged draft is most accurate?

• A. The draft remains fair because company-issued earnings guidance qualifies as an actual reported financial result.
• B. The draft remains fair because the general disclaimer identifies the earnings figure as an opinion rather than a fact.
• C. The draft requires revision because it presents management’s earnings forecast as an actual reported financial result.

Best answer: C

Explanation: Standard V(B), Communication with Clients and Prospective Clients, requires analysts to distinguish facts from opinions and communicate investment processes, significant risks and limitations, and the nature and costs of services.

Management’s issuance of guidance is a fact, but the anticipated earnings amount remains a forecast. Once the source classification is corrected, describing $4.00 as actual reported EPS misrepresents the input, even though its numerical value and the model’s calculated return remain unchanged.

The recommendation should identify $4.00 as management guidance, clarify its use as a valuation assumption, and continue to present the 9% return as a forecast. The model-risk and advisory-fee disclosures remain relevant, but a general disclaimer cannot cure a specific misleading factual statement.

• A. Company-issued guidance concerns expected future earnings, so publication does not convert the $4.00 figure into an actual reported result.
• B. A blanket disclaimer about estimates does not correct a specific earnings figure that the draft expressly presents as actual reported data.
• C. The analyst must identify the EPS input as management guidance; its unchanged value does not preserve the accuracy of the existing description.

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Question 136

Topic: Equities

An analyst reviews Vireo plc’s ordinary-share register. The holding categories are non-overlapping and included in the issued total. All remaining holdings are unrestricted and non-strategic.

Under the analyst’s convention, treasury shares and strategic or sale-restricted holdings are excluded from free float.

The company’s free float as a percentage of shares outstanding is closest to:

• A. 37.8%
• B. 60.0%
• C. 54.0%

Best answer: B

Explanation: Free float measures outstanding shares eligible for public trading under the specified exclusions. Treasury shares are issued but not outstanding, so shares outstanding equal \(150 - 15 = 135\) million. Removing strategic founder holdings and sale-restricted employee holdings leaves \(135 - 45 - 9 = 81\) million free-float shares. Unrestricted, non-strategic institutional ownership does not reduce free float.

The free-float proportion is \(81/135 = 0.60\), or 60.0%. Free float is a stock of eligible shares, not trading volume during a period or the number of newly issued shares. Total market capitalization uses all outstanding shares multiplied by the share price; free-float-adjusted capitalization uses only free-float shares.

• A. Excluding the unrestricted institutional holdings reduces free float to 51 million shares; these holdings remain eligible for public trading under the stated convention.
• B. There are 135 million outstanding shares and 81 million free-float shares after removing strategic and sale-restricted holdings, giving 60.0%.
• C. Dividing 81 million free-float shares by 150 million issued shares gives 54.0%, but the denominator must exclude treasury shares.

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Question 137

Topic: Portfolio Construction

A client holds 60% in an equity fund and 40% in a government bond fund. An adviser proposes replacing the entire bond allocation with an income fund to reduce total portfolio volatility while preserving expected net return and daily liquidity.

Risk estimates:

All estimates use the same one-year horizon. The equity and government bond funds have an estimated correlation of -0.20. The bond and income funds have identical expected returns after fees and both offer daily liquidity.

Analyst’s conclusion:

The income fund’s lower standalone volatility means that replacing the bond fund will reduce total portfolio volatility.

Which missing input is most important to correct the analyst’s conclusion before making the switch?

• A. The income fund’s correlation with the government bond fund being replaced.
• B. The income fund’s correlation with the equity fund being retained.
• C. The income fund’s correlation with its designated bond-market benchmark.

Best answer: B

Explanation: Portfolio volatility depends on the holdings’ volatilities, weights, and correlations. A lower-volatility replacement can increase portfolio volatility if it is sufficiently more positively correlated with the retained assets.

Here, the government bond fund’s negative correlation with the equity fund contributes to diversification. The analyst must obtain the income fund’s correlation with the equity fund and combine it with the stated weights and volatilities to assess the proposed portfolio. Equal expected net returns and liquidity do not resolve this risk comparison. Lower standalone volatility is therefore insufficient evidence that the switch will reduce total portfolio volatility.

• A. The government bond fund will no longer be held, so its correlation with the income fund does not enter the proposed portfolio’s variance.
• B. The replacement’s correlation with the retained equity fund determines its diversification effect and is necessary to compare current and proposed portfolio volatility.
• C. Correlation with a bond-market benchmark describes benchmark comovement, rather than the comovement between the two holdings in the proposed portfolio.

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Question 138

Topic: Alternative Investments

An analyst compares a fully leased office building with a toll-road concession over a three-year investment horizon.

Contract and operating terms:

• Office building: A creditworthy tenant has a noncancelable lease with eight years remaining. Base rent adjusts annually with CPI and is unrelated to tenant sales. The owner bears structural-maintenance costs.
• Toll road: The concession has 25 years remaining. Regulated toll rates adjust annually with CPI. Revenue depends on traffic volume, with no minimum-revenue guarantee. The concessionaire bears maintenance and resurfacing costs.

The analyst concludes:

Both investments remain exposed to maintenance-cost increases. The toll road has lower demand-driven income risk because its longer concession secures inflation-linked revenues.

Which correction is most accurate?

• A. Both assets’ revenues are equally sensitive to usage declines while their current contracts remain in force.
• B. The toll road’s user-fee revenue is less sensitive to usage declines than the building’s contracted rent.
• C. The building’s contracted rent is less sensitive to usage declines than the toll road’s user-fee revenue.

Best answer: C

Explanation: Income stability depends on the payment mechanism, not simply on contract duration. During the three-year horizon, the building’s noncancelable lease commits the tenant to rental payments, so reduced space utilization does not directly reduce rent. Toll-road revenue depends on both the toll rate and traffic volume. CPI indexation protects the rate against inflation but does not protect revenue against declining traffic.

A longer concession secures operating rights, not guaranteed receipts. Both contracts extend beyond the investment horizon, so their different remaining terms do not reverse this income-risk comparison. Both investments also retain operating risk from their maintenance obligations. Inflation-linked revenues do not guarantee that maintenance costs will increase at the same rate.

• A. Contracts extending beyond the investment horizon do not equalize demand risk: the lease commits rental payments, whereas the concession provides traffic-dependent fees.
• B. CPI indexation adjusts toll rates rather than traffic volumes, so declining road usage reduces revenue despite the concession’s longer duration.
• C. The noncancelable lease keeps rent payable over the investment horizon, while lower traffic directly reduces the road’s user-fee revenue.

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Question 139

Topic: Portfolio Construction

An adviser is setting a one-year return objective for a retired client with $2,000,000 of investable assets. There are no cash flows before year-end.

• The client needs an $80,000 withdrawal at year-end, stated in that date’s nominal dollars.
• Expected annual inflation is 3.00%.
• After the withdrawal, the remaining portfolio must retain its current purchasing power.
• For planning, 20% of the entire year’s investment return is paid as tax at year-end, separately from the withdrawal.
• The highest expected before-tax nominal return among available portfolios consistent with the client’s assessed risk capacity is 7.50%.

Which conclusion about the client’s required return objective is most accurate?

• A. The required before-tax nominal return is 8.75%, above the highest expected return consistent with the risk limit.
• B. The required before-tax nominal return is 7.00%, below the highest expected return consistent with the risk limit.
• C. The required before-tax nominal return is 8.00%, above the highest expected return consistent with the risk limit.

Best answer: A

Explanation: A measurable return objective must account for spending, inflation, and taxes using consistent cash-flow timing. With 3.00% inflation, the client needs $2,060,000 remaining at year-end to preserve the portfolio’s purchasing power. Investment earnings after tax must therefore provide $60,000 of capital growth plus the $80,000 withdrawal, totaling $140,000. The withdrawal is already stated in year-end nominal dollars and is not inflated again.

\[ r_{\text{required}} = \frac{140{,}000}{2{,}000{,}000 \times 0.80} = 8.75\%. \]

This requirement exceeds the 7.50% highest expected return available within the client’s risk capacity. The current resources, spending requirement, and capital-preservation goal are therefore incompatible on an expected-return basis; increasing risk would not respect the stated risk limit.

• A. After-tax earnings must cover $80,000 of spending and $60,000 of capital growth, requiring an 8.75% before-tax return, which exceeds 7.50%.
• B. The 7.00% calculation covers spending and inflation but ignores the tax on investment returns, understating the required before-tax return.
• C. Grossing up only the spending component gives 8.00%; the return needed to preserve purchasing power is also taxed under the stated assumptions.

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Question 140

Topic: Quantitative Methods

An analyst studies a strategy’s population mean monthly excess return, \(\mu\), using 25 independent observations from a normal population with unknown variance. The null hypothesis is \(H_0:\mu=0\), and the significance level is 5%, but documentation of the alternative hypothesis is missing.

Sample evidence:

• Mean monthly excess return: 0.60%
• Sample standard deviation: 1.50%

For a t-distribution with 24 degrees of freedom:

The draft report states:

The strategy’s mean excess return is significantly positive, with the test’s Type I error probability controlled at 5%.

Which missing fact about the alternative hypothesis makes this conclusion most defensible?

• A. The alternative was one-sided, with its direction selected to match the sample mean’s sign.
• B. The alternative was a positive mean, specified before the sample was examined.
• C. The alternative was a nonzero mean, specified before the sample was examined.

Best answer: B

Explanation: With independent normal observations and unknown population variance, the appropriate statistic follows Student’s t-distribution with \(25-1=24\) degrees of freedom:

\[ t=\frac{0.006-0}{0.015/\sqrt{25}}=2.00. \]

A positive alternative specified before examining the data requires an upper-tailed test. Because 2.00 exceeds 1.711, the null is rejected at 5%. A two-tailed test would instead require the statistic to exceed 2.064 in absolute value.

The significance level controls the probability of rejecting a true null; it is not the probability that the null is true after rejection. Choosing the rejection direction from the observed data undermines that error control. For a specified positive true mean, power is the probability of rejecting the false null and equals one minus the Type II error probability. A 5% significance level does not imply 95% power or establish economic importance.

• A. Selecting the tail from the observed sign and applying a 5% one-tailed cutoff produces a 10% overall Type I error probability under the null.
• B. The t-statistic of 2.00 exceeds the pre-specified upper-tailed critical value of 1.711, permitting rejection with a 5% Type I error probability.
• C. A two-tailed 5% test requires an absolute t-statistic above 2.064; the observed statistic of 2.00 would not lead to rejection.

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Question 141

Topic: Quantitative Methods

An investor controls all external transfers to and from a portfolio managed by an investment adviser. The following valuations cover two equal six-month periods:

Cash-flow details:

• The opening value follows the investor’s initial $100,000 contribution.
• Immediately after the July valuation, the investor contributes $400,000 and withdraws $45,000.
• All dividends are retained as cash within the portfolio and included in its reported values. No other external transfers occur.

Using net cash flows from the investor’s perspective and the closing value as the terminal inflow, the IRR is -5.00% per six-month period. Annual returns are reported on an effective basis.

Which interpretation of performance is least accurate?

• A. The investor’s effective annual money-weighted return is -10.00% because a six-month IRR is annualized by doubling.
• B. The manager’s effective annual time-weighted return is 8.00% because the two subperiod returns are geometrically linked.
• C. The manager’s annual performance is better evaluated using time-weighted returns because the investor controls the external transfers.

Best answer: A

Explanation: Time-weighted return isolates investment performance from external cash-flow timing. Retained dividends remain part of portfolio value and are not investor withdrawals. The July transfers net to a $355,000 contribution, raising portfolio value from $120,000 to $475,000.

The first six-month return is 20%. The second is \(427{,}500/475{,}000-1=-10\%\). Linking these returns gives \(1.20\times0.90-1=8.00\%\) for the full year. This measure is appropriate for evaluating the manager because the investor controls the transfers.

Money-weighted return reflects the investor’s cash-flow timing. The reported IRR applies to six months, so the effective annual return is \((1-0.05)^2-1=-9.75\%\). This is lower than the time-weighted return because substantially more capital was invested during the losing second half. Doubling the periodic IRR produces a simple annual rate, not an effective annual return.

• A. Effective annualization requires compounding: \( (1-0.05)^2-1=-9.75\% \), rather than doubling the six-month IRR.
• B. The net July contribution is $355,000, so the subperiod returns are 20% and -10%; geometrically linking them gives 8.00%.
• C. Time-weighted return removes the effect of external cash-flow timing and size, which are controlled by the investor rather than the manager.

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Question 142

Topic: Equities

An equity analyst is evaluating domestic manufacturers of standardized solar panels.

Developments expected next year:

• The government will eliminate tariffs on imported finished panels. Tariffs on imported manufacturing components will remain unchanged.
• Foreign suppliers have spare capacity and plan to reduce their selling prices in the domestic market after the tariff removal.
• The leading domestic manufacturer will introduce a patented process that reduces its production costs. It will not license the process to competitors.

Which assessment of the domestic industry’s prospects is most accurate?

• A. Industry prospects are likely to remain stable as the leading manufacturer’s efficiency gains preserve industry-wide cost competitiveness.
• B. Industry prospects are likely to weaken as tariff removal intensifies price competition from foreign suppliers.
• C. Industry prospects are likely to improve as tariff removal lowers domestic manufacturers’ input costs.

Best answer: B

Explanation: A tariff change is a political or legal development in a PESTLE assessment. Removing tariffs on finished panels makes foreign products more competitive. Foreign suppliers’ spare capacity and planned price reductions strengthen this threat, creating downward pressure on domestic manufacturers’ prices and margins. Component tariffs remain unchanged, so the policy does not provide an offsetting reduction in domestic production costs.

The patented process is a firm-specific response rather than an industry-wide improvement. It may help the leading manufacturer withstand foreign competition or improve its relative position, but those benefits cannot be generalized to domestic rivals.

• A. The patented process benefits the leading manufacturer alone; its cost savings do not preserve the cost competitiveness of domestic rivals.
• B. Foreign suppliers’ planned price reductions and spare capacity increase competitive pressure on domestic manufacturers, threatening their selling prices and margins.
• C. The tariff reduction applies to competing finished panels, not manufacturing components, so it does not reduce domestic manufacturers’ input costs.

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Question 143

Topic: Quantitative Methods

At a scheduled rebalancing date, an analyst reviews an equal-weighted index and a market-capitalization-weighted index containing the same three stocks. Each company has 1 million shares outstanding throughout the period. The membership review requires no additions or deletions.

The analyst concludes:

Both indexes began with one-third constituent weights, so both must sell some Arden shares to restore those weights and preserve their weighting methods.

Which correction is most accurate?

• A. Restore the initial constituent weights only in the equal-weighted index.
• B. Retain the post-price-change constituent weights in both indexes.
• C. Restore the initial constituent weights only in the capitalization-weighted index.

Best answer: A

Explanation: Rebalancing restores weights according to an index’s weighting method, not necessarily to its initial weights. Arden’s price increase raises its weight in both indexes to 50%, while Benton and Crest each have a 25% weight.

The equal-weighted index must sell some Arden shares and buy Benton and Crest shares to restore one-third weights. For the capitalization-weighted index, current market capitalizations are $80 million, $40 million, and $40 million. Its existing holdings already produce the appropriate 50%, 25%, and 25% weights, so these price changes alone require no trading.

Reconstitution changes constituent membership. None is required because the membership review specifies no additions or deletions. Rebalancing changes exposures mechanically; it does not by itself establish expected excess returns.

• A. Equal weighting requires restoring one-third weights, whereas Arden’s current market capitalization justifies its increased weight in the capitalization-weighted index.
• B. Retaining Arden’s increased weight at the scheduled rebalance would leave the equal-weighted index inconsistent with its weighting method.
• C. Capitalization weighting follows current market values rather than initial weights; the equal-weighted index is the one requiring a weight reset.

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Question 144

Topic: Equities

An analyst revises a report on a mature consumer-products company. Higher sales guidance supports a larger expected dividend next year, while a new low-cost competitor is expected to pressure future margins.

The shares trade at $36. The analyst uses a constant-growth dividend discount model. Dividends are paid annually, with the next dividend in one year and constant growth indefinitely thereafter.

Which investment conclusion based on the revised assumptions is most accurate?

• A. The shares are undervalued, with an estimated intrinsic value of $40.00 per share.
• B. The shares are undervalued, with an estimated intrinsic value of $48.00 per share.
• C. The shares are overvalued, with an estimated intrinsic value of $34.29 per share.

Best answer: C

Explanation: Equity value reflects expected cash flows and the return required for their risk. For constant-growth dividends, intrinsic value per share \(V_0\) uses the next annual dividend \(D_1\), annual required return \(r\), and perpetual annual dividend growth \(g\):

\[ V_0 = \frac{D_1}{r-g} = \frac{2.40}{0.10-0.03} \approx 34.29. \]

The estimated value of $34.29 is below the $36 market price. The higher near-term dividend forecast is more than offset by lower long-run growth and a higher required return. The shares therefore offer no valuation discount under the revised assumptions. Favorable company forecasts do not necessarily imply an attractive investment at the prevailing price.

• A. The $40.00 estimate uses the previous 9% required return with the revised dividend and growth rate, ignoring the updated risk assessment.
• B. The $48.00 estimate retains the previous 5% growth assumption rather than the revised 3% rate reflecting stronger competition.
• C. The revised dividend, growth rate, and required return imply a value of $34.29, below the $36 market price.

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Question 145

Topic: Ethical and Professional Standards

A CFA charterholder manages discretionary equity portfolios using her firm’s proprietary factor model. Client disclosures state that factor forecasts are updated monthly and that the model imposes an internal 20% sector-weight limit. Client mandates permit sector weights up to 35%.

The firm removes the internal limit, and revised recommendations include a 30% sector allocation. The manager confirms that the portfolios remain suitable and comply with client mandates, then rebalances them using the revised model. She writes:

This is routine implementation within our mandates, so clients can be informed at their annual reviews, nine months from now.

Under the CFA Institute Standards of Professional Conduct, which correction is most accurate?

• A. The manager must obtain written client consent to remove the sector limit before applying the revised model to portfolios.
• B. The manager must provide clients with the revised model’s complete inputs and formulas before applying it to portfolios.
• C. The manager must promptly explain the removal of the sector limit and its significant risk implications to clients.

Best answer: C

Explanation: Standard V(B), Communication with Clients and Prospective Clients, requires prompt disclosure of changes that might materially affect the investment process. Updating factor forecasts monthly is contemplated by the disclosed approach and is ordinarily routine implementation. Removing the sector cap changes the portfolio-construction process itself, allowing recommendations with substantially greater sector concentration.

Remaining suitable and complying with client mandates does not eliminate the communication duty. Waiting nine months is inappropriate. Clients should promptly receive an understandable description of the change and its significant risk implications. Meaningful disclosure does not require reproducing the entire proprietary model.

• A. The revision remains within the discretionary mandates; Standard V(B) requires disclosure, not mandatory written approval of every investment-process change.
• B. Clients need the process’s basic principles and significant risks, not every proprietary model input or formula.
• C. Removing the disclosed sector cap changes portfolio construction, requiring prompt communication under Standard V(B), even though the portfolios remain suitable and mandate-compliant.

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Question 146

Topic: Fixed Income

A portfolio manager compares a primary subscription with purchases of two outstanding bonds from the same issuer.

Primary placement: An underwriter is offering $80 million of newly issued five-year, 5% coupon bonds at 100 per $100 of par.

Secondary market: Both outstanding issues have five years remaining and the same seniority as the new bonds. Dealer prices are per $100 of par and firm for a $500,000 par trade.

Assume no commissions and unchanged quotes for an immediate purchase and resale. Which conclusion about new issuer funding and round-trip transaction costs is most appropriate?

• A. Only the primary subscription raises new issuer capital; the smaller outstanding issue has the lower round-trip transaction cost.
• B. Only the primary subscription raises new issuer capital; the larger outstanding issue has the lower round-trip transaction cost.
• C. Both primary and secondary purchases raise new issuer capital; the larger outstanding issue has the lower round-trip transaction cost.

Best answer: B

Explanation: Primary-market subscriptions provide new funds to the issuer. Secondary-market purchases transfer existing claims, with proceeds going to the current seller, including when that seller is a dealer.

For an immediate round trip with unchanged quotes, the investor buys at the dealer’s ask and sells at its bid. The larger issue therefore costs $0.20 per $100 of par to reverse, compared with $0.80 for the smaller issue. For $500,000 par, these costs are $1,000 and $4,000, respectively. The smaller bond’s lower purchase price is not evidence of lower trading costs; its different coupon also affects its price.

The larger issue’s greater size, frequent trading, and narrower spread are consistent with greater liquidity. Compared with exchange-traded common equity, bond trading is often more decentralized and securities are less standardized across issues. Liquidity must therefore be assessed for the particular bond rather than inferred solely from the issuer’s identity.

• A. The smaller issue’s lower ask price does not imply lower trading cost: its spread is $0.80 per $100 of par, versus $0.20 for the larger issue.
• B. Primary issuance supplies new issuer funds, and the larger outstanding bond’s $0.20 spread is narrower than the smaller bond’s $0.80 spread.
• C. Purchasing an outstanding bond from a dealer transfers an existing claim; payment goes to the seller rather than providing new funds to the issuer.

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Question 147

Topic: Financial Statement Analysis

A manufacturer is preparing its IFRS financial statements for the year ended 31 December 2027. It incurred and paid the following costs on 1 January 2027:

The upgrade was available for use immediately and has a five-year useful life with no residual value. The draft statements capitalize both expenditures, depreciate both over five years using straight-line depreciation, and classify both payments as investing outflows. Ignore taxes, impairment, and disposals through 2031.

Relative to the draft treatment, which assessment of applying IFRS-compliant accounting is most accurate?

• A. 2027 operating profit and year-end assets decrease by $90,000, operating cash flow decreases by $90,000, and annual operating profit in 2028-2031 increases by $18,000.
• B. 2027 operating profit and year-end assets decrease by $72,000, operating cash flow decreases by $90,000, and annual operating profit in 2028-2031 increases by $18,000.
• C. 2027 operating profit and year-end assets decrease by $72,000, operating cash flow is unchanged, and annual operating profit in 2028-2031 increases by $18,000.

Best answer: B

Explanation: The capacity-increasing upgrade creates future economic benefits and is capitalized. Routine servicing maintains existing operating condition and must be expensed.

The draft accounts record annual servicing depreciation of $18,000, calculated as \(90,000 / 5\). Replacing that depreciation with the full $90,000 servicing expense reduces 2027 operating profit by $72,000. Removing the servicing asset also reduces year-end assets by its $72,000 net carrying amount.

The servicing payment is an operating cash outflow, not an investing outflow. Correcting its classification reduces operating cash flow by $90,000 and increases investing cash flow by the same amount; total cash flow remains unchanged.

In each year from 2028 through 2031, eliminating servicing depreciation increases operating profit by $18,000 relative to the draft treatment. Improper capitalization temporarily inflates profitability by deferring expenses rather than improving underlying operations.

• A. The correction reverses $18,000 of servicing depreciation already recorded, so operating profit and net assets decrease by $72,000 rather than $90,000.
• B. Expensing servicing while reversing its depreciation reduces current profit and assets by $72,000; its payment becomes an operating outflow, and future servicing depreciation disappears.
• C. Total cash flow is unchanged, but reclassifying the $90,000 servicing payment from investing to operating reduces operating cash flow by $90,000.

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Question 148

Topic: Ethical and Professional Standards

A credit analyst’s proposed buy recommendation for an issuer’s bond relies on a forecast that assumes a refinancing. The analyst records the following decisions:

During the meeting, the analyst’s respected, experienced desk head states that publication today would secure a bonus for every team member. He adds:

“Our last similar recommendation was profitable. You can trust my judgment on this one.”

No new issuer-specific information is presented at the meeting. Which interpretation of the analyst’s reversal is most accurate?

• A. The reversal primarily reflects situational pressure and rationalization, supported by the team incentive and reliance on prior success.
• B. The reversal primarily reflects an evidence-based reduction in refinancing uncertainty, supported by the desk head’s experience and prior success.
• C. The reversal primarily reflects an enduring weakness in ethical character, supported by the analyst’s acceptance of an unconfirmed forecast.

Best answer: A

Explanation: Ethical decision-making is affected by incentives and social context, not only by personal character. The analyst initially requires verification, then approves publication after a team bonus and a respected manager’s reassurance become salient. Because the refinancing evidence remains unchanged, the sequence supports situational pressure and rationalization. The analyst has a personal stake in the team reward, while the manager uses past success to justify proceeding with incomplete information. A profitable previous recommendation does not confirm the current refinancing assumption. A sound decision process separates the assessment of evidence from rewards and authority. The record alone does not establish an enduring character weakness.

• A. Approval follows the bonus incentive and managerial reassurance while the refinancing evidence remains unchanged, supporting situational influence rather than improved information.
• B. The desk head’s experience and a previous profitable recommendation do not provide new evidence confirming this issuer’s refinancing.
• C. A single decision following a pressured meeting does not establish an enduring character weakness, particularly when the analyst initially sought verification.

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Question 149

Topic: Corporate Finance

An analyst compares an initial public offering (IPO) followed by an exchange listing with a private placement for a founder-owned company. Both proposals would raise $30 million of new equity for expansion. The founder would retain all 1,000,000 existing shares, and no other voting arrangements apply.

Which conclusion about the ownership tradeoffs is most accurate?

• A. The private placement avoids periodic public reporting while preserving the founder’s majority voting control.
• B. The IPO broadens access to public investors while transferring majority voting control to the new investors.
• C. The IPO offers new investors exchange-traded liquidity while preserving the founder’s majority voting control.

Best answer: C

Explanation: Public ownership generally provides access to a broader investor base and more liquid share transfers, at the cost of ongoing public disclosure. Private ownership can limit public disclosure but often restricts transfers and funding access. Neither form alone determines voting control.

Under the IPO, the founder holds \(1,000,000 \times 10 = 10,000,000\) votes, and new investors hold 3,000,000 votes. The founder therefore retains approximately 76.9% of voting rights despite owning only 25% of the shares. Under the private placement, equal voting rights leave the founder with \(1,000,000/2,500,000 = 40\%\) of votes.

The listing therefore improves new investors’ liquidity without requiring the founder to surrender majority voting control. Public ownership refers here to exchange-listed equity, not government ownership, and listing alone does not establish stronger governance.

• A. With one vote per share, the founder retains \(1,000,000/2,500,000 = 40\%\) of votes, so the placement does not preserve majority voting control.
• B. New investors would own 75% of shares but only \(3,000,000/13,000,000 \approx 23.1\%\) of votes; economic ownership does not equal voting control.
• C. The IPO permits exchange trading, and the founder retains \(10,000,000/13,000,000 \approx 76.9\%\) of votes through the higher-vote shares.

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Question 150

Topic: Quantitative Methods

An equity analyst uses the following fitted relationship to project a firm’s price-to-book (P/B) ratio:

\[ \widehat{\ln(P/B)} = a + 0.040\,ROE \]

ROE is entered in percentage points, so 10% is entered as 10. The model-implied P/B ratio is 1.80 when ROE is 10%.

Using the same fitted relationship, the model-implied P/B ratio when ROE rises to 20% is closest to:

• A. 2.52
• B. 2.69
• C. 2.20

Best answer: B

Explanation: This is a log-lin model: the dependent variable, P/B, is logged, while the explanatory variable, ROE, is not. Because ROE is entered in percentage points, the increase from 10% to 20% is a 10-unit change.

The fitted log ratio therefore increases by \(0.040 \times 10 = 0.40\). A change in a natural logarithm translates into a multiplicative change on the original scale:

\[ (P/B)_{\text{new}} = 1.80e^{0.40} \approx 2.69. \]

The exact proportional increase is \(e^{0.40}-1\), or approximately 49.18%. Interpreting the log change as a 40% increase is only a first-order approximation, which becomes less accurate for larger changes.

• A. Multiplying 1.80 by 1.40 uses a first-order percentage-change approximation rather than the exponential conversion required for the fitted log change.
• B. The fitted log ratio increases by 0.40, so the model-implied P/B ratio becomes \(1.80e^{0.40} \approx 2.69\).
• C. Adding 0.40 directly to 1.80 treats the coefficient as a change in P/B rather than a change in its natural logarithm.

Questions 151-175

Question 151

Topic: Portfolio Construction

An investor holds 24% of a portfolio in one stock, compared with a 10% target weight. The shares trade below their purchase price. Following a substantial downward revision in earnings forecasts, the investor rejects an adviser’s recommendation to rebalance. Ignore taxes and transaction costs.

The adviser proposes that anchoring on an earlier optimistic price target is sustaining the concentrated position. Which additional observation would make this conclusion most defensible?

• A. The investor resists selling shares below their purchase price but readily sells comparable appreciated holdings with the same expected returns and risk.
• B. The investor gives more weight to research supporting the earlier valuation and dismisses equally credible research that challenges that valuation.
• C. With identical information, the investor’s valuation is higher when the earlier optimistic price target is presented first rather than last.

Best answer: C

Explanation: Anchoring occurs when an investor relies excessively on an initial reference and adjusts insufficiently when considering subsequent information. Here, presenting the earlier optimistic target first produces a higher valuation even though the available information is identical. The presentation order, rather than a change in fundamentals, influences the investor’s estimate.

An upward-biased valuation can make the stock appear more attractive than updated analysis supports, delaying rebalancing and maintaining the 24% holding against its 10% target. This prolongs exposure to company-specific risk. Holding a stock below its purchase price alone does not establish anchoring; the decision process provides the distinguishing evidence.

• A. Different willingness to realize gains and losses under comparable investment prospects supports loss aversion and the disposition effect rather than valuation anchoring.
• B. Selective acceptance of supportive research demonstrates confirmation bias rather than excessive reliance on an initial numerical reference.
• C. Dependence on the initial price target despite identical information demonstrates anchoring and can sustain an upward-biased valuation.

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Question 152

Topic: Portfolio Construction

An investor chooses one attainable portfolio from the proposals below using annual mean-variance utility:

\[ U = E(r) - \frac{1}{2}A\sigma^2 \]

Expected return and standard deviation are expressed as decimals, and \(A\) is the investor’s risk-aversion coefficient.

Opportunity set:

• Portfolios are fully invested in risky assets, with unrestricted short selling.
• The lowest attainable annual standard deviation is 10%.
• The highest attainable expected returns at standard deviations of 10% and 15% are 4% and 7%, respectively.
• Portfolios P, Q, and R are attainable; S is a proposed target.

The investor initially has \(A = 6\) and selects P among these proposals. The coefficient then decreases to \(A = 2\), while all asset forecasts and portfolio constraints remain unchanged.

Which displayed portfolio is most appropriate for maximizing the investor’s utility after this change?

• A. Portfolio P.
• B. Portfolio S.
• C. Portfolio Q.

Best answer: C

Explanation: The global minimum-variance portfolio has the lowest variance in the feasible set. P meets this definition. The efficient frontier is the upper branch of the minimum-variance boundary, beginning at that portfolio. Q lies on this efficient branch. R is feasible but dominated by Q, which offers a higher expected return at the same risk. S is unattainable because its return exceeds the feasible maximum at 10% standard deviation.

Changing risk aversion changes preferences, not the feasible set or efficient frontier. At \(A = 2\):

\[ \begin{aligned} U_P &= 0.04 - \tfrac{1}{2}(2)(0.10)^2 = 0.0300 \\ U_Q &= 0.07 - \tfrac{1}{2}(2)(0.15)^2 = 0.0475 \\ U_R &= 0.05 - \tfrac{1}{2}(2)(0.15)^2 = 0.0275 \end{aligned} \]

Q therefore maximizes utility among the displayed attainable portfolios. Minimum variance need not maximize an investor’s utility because expected return also matters.

• A. Its utility is now 0.0300, below the attainable utility of 0.0475, so minimizing variance no longer maximizes utility among the proposals.
• B. Its 6% expected return at 10% standard deviation exceeds the 4% attainable maximum, so its apparent utility of 0.0500 cannot be achieved.
• C. Its utility is now 0.0475, the highest among the displayed attainable portfolios, reflecting the investor’s reduced penalty for variance.

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Question 153

Topic: Financial Statement Analysis

A manufacturing company reporting under IFRS has consolidated net profit of $96 million for the year ended 31 December 2027. Net profit includes depreciation expense of $24 million.

Consolidated operating balances ($ millions):

Acquisition details:

• During the year, the company acquired a subsidiary for $40 million in cash, net of cash acquired.
• Acquisition-date balances were trade receivables of $12 million, inventory of $18 million, and trade payables of $9 million. These balances are included in the year-end consolidated balances.

All changes in the listed balances, other than the acquisition additions, arose from ordinary operating transactions. No other adjustments are required to reconcile net profit to operating cash flow.

Which conclusion about operating cash flow relative to net profit is most appropriate?

• A. Operating cash flow is $103 million, which is $7 million above net profit.
• B. Operating cash flow is $82 million, which is $14 million below net profit.
• C. Operating cash flow is $63 million, which is $33 million below net profit.

Best answer: A

Explanation: To reconcile net profit to operating cash flow analytically, add back noncash expenses and adjust for operating working-capital changes. Balances added through a business acquisition must be excluded from those changes because they do not represent operating cash movements.

After removing acquisition-date balances, receivables increased by $17 million (99 - 70 - 12), inventory increased by $8 million (111 - 85 - 18), and payables increased by $8 million (63 - 46 - 9). Asset increases reduce operating cash flow; liability increases raise it.

Operating cash flow, in millions, is therefore \(96 + 24 - 17 - 8 + 8 = 103\). Depreciation of $24 million exceeds the $17 million working-capital cash outflow, making operating cash flow $7 million higher than net profit. The $40 million acquisition payment is an investing cash outflow.

• A. Acquisition-adjusted working capital consumed $17 million, so adding $24 million of depreciation to $96 million of net profit yields operating cash flow of $103 million.
• B. Using unadjusted balance changes produces $82 million, incorrectly treating the $21 million of acquired net operating working capital as an operating cash outflow.
• C. Subtracting the $40 million acquisition payment from correctly reconciled operating cash flow produces $63 million, but that payment belongs in investing activities.

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Question 154

Topic: Ethical and Professional Standards

Mara Chen, CFA, is considering an issuer-paid equity research assignment. Her firm’s conduct statement includes this commitment:

Use independent judgment when conducting investment analysis.

Chen would disclose the issuer’s sponsorship and compensation arrangement in the report. She would retain control of the analysis and recommendation.

A compliance officer concludes that Chen cannot accept the assignment on the proposed terms, even with those disclosures. Which additional fact would most likely support that conclusion under the CFA Institute Code of Ethics and Standards of Professional Conduct?

• A. The issuer will review draft business descriptions for factual accuracy, with no authority over the recommendation.
• B. The issuer will pay a fixed fee agreed before the research begins, regardless of the recommendation.
• C. The issuer will pay a base fee plus a bonus if the report recommends purchasing its shares.

Best answer: C

Explanation: The Code of Ethics calls for reasonable care and independent professional judgment in investment analysis and recommendations. The Standard on Independence and Objectivity makes this a specific professional duty: members and candidates must protect their judgment from influences that could compromise it.

Issuer-paid research is not inherently prohibited. A fixed fee agreed in advance, independent analysis, and appropriate disclosure can support an acceptable arrangement. Compensation contingent on a favorable recommendation creates an incentive to shape the research conclusion for personal financial benefit. Disclosing that incentive does not resolve the objectivity problem. Chen must reject the contingent compensation terms or arrange acceptable terms before accepting the assignment.

• A. Limited factual review does not transfer control of Chen’s investment judgment and, by itself, does not require rejecting the assignment.
• B. A fixed fee unrelated to the recommendation does not, by itself, require rejecting issuer-paid research when sponsorship and compensation are disclosed.
• C. Linking a bonus to a purchase recommendation creates a financial incentive that compromises research objectivity; disclosure does not make these compensation terms acceptable.

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Question 155

Topic: Quantitative Methods

A risk analyst compares two methods for generating 20-trading-day paths for a two-asset portfolio. Historical paired daily returns exhibit negative skewness, positive same-day correlation between assets, and volatility clustering across consecutive days.

Simulation methods:

• Monte Carlo: Draw each day’s asset returns jointly from a bivariate normal distribution using the historical means and covariance matrix. Draws are independent across days.
• Bootstrap: Select a historical day’s complete pair of asset returns with replacement for each simulated day. Selections are independent across days.

Which conclusion is most accurate when comparing the methods’ ability to retain historical daily return asymmetry and volatility clustering?

• A. The bootstrap better represents historical daily return asymmetry; only the bootstrap preserves historical volatility clustering.
• B. Both methods represent historical daily return asymmetry equally well; neither method preserves historical volatility clustering.
• C. The bootstrap better represents historical daily return asymmetry; neither method preserves historical volatility clustering.

Best answer: C

Explanation: Bootstrap resampling uses the observed data as an empirical distribution. Selecting complete daily pairs retains same-day relationships between assets and represents the sample’s negative skewness. Its randomness comes from selecting historical observations with replacement.

Monte Carlo simulation instead draws from a specified probability model. Here, the bivariate normal model incorporates estimated means, variances, and correlation, but its symmetric marginal distributions do not reproduce historical negative skewness.

Both designs draw independently across simulated days. Consequently, neither preserves the temporal dependence underlying volatility clustering. Preserving within-day pairs is different from preserving sequences across days.

Bootstrap results remain limited by the historical sample, including any missing stress conditions. Monte Carlo can generate returns outside the observed sample, but their likelihood depends on the assumed distribution rather than direct historical evidence.

• A. Sampling complete daily pairs preserves same-day relationships between assets, but independent selection of days does not preserve the historical sequence of volatility.
• B. The bivariate normal distribution has symmetric marginal distributions, so matching historical means and covariances does not reproduce the observed negative skewness.
• C. Resampling historical pairs retains their empirical distribution, including asymmetry, while independent draws across days fail to preserve the observed temporal dependence.

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Question 156

Topic: Alternative Investments

An analyst evaluates a digital token after a new trading platform introduces access through a licensed custodian. Previously, investors held their own single private key online.

Due-diligence record:

• Custody: The custodian uses offline multisignature wallets.
• Price and liquidity: The token has no fixed-value redemption. Most displayed buy orders were withdrawn during a recent stress episode.
• Protocol: The same validators retain authority to halt transfers and approve software changes.
• Regulation (Norland case assumption): In this fictional jurisdiction, custody licensing covers safekeeping controls only. Enforceability of tokenholder claims against the issuer remains unresolved.

Which risk assessment is most accurate?

• A. Private-key theft risk is reduced; price, liquidity, and protocol-disruption risks, plus uncertainty about tokenholder claims, remain.
• B. Uncertainty about tokenholder claims is reduced; price, liquidity, protocol-disruption, and private-key theft risks remain.
• C. Protocol-disruption risk is reduced; price, liquidity, and private-key theft risks, plus uncertainty about tokenholder claims, remain.

Best answer: A

Explanation: Market access and safekeeping are distinct from the underlying asset’s investment risks. Offline multisignature custody reduces the chance that theft of a single internet-connected key causes a loss, although custody risk is not eliminated.

Without fixed-value redemption, the token’s price remains exposed to market demand. Withdrawal of buy orders during stress shows that trading availability does not assure exit liquidity. The unchanged validators can still halt transfers or modify software, leaving technological and governance exposures. Under the Norland case assumption, licensing addresses safekeeping rather than tokenholder rights against the issuer, so legal uncertainty remains. Improved custody therefore mitigates one risk without resolving the token’s broader investment risks.

• A. Offline multisignature custody reduces vulnerability to theft of a single online key but does not change the token’s market, protocol, or legal characteristics.
• B. Norland’s custody license concerns safekeeping and does not resolve the stated uncertainty over enforcement of tokenholder claims against the issuer.
• C. Custody controls do not change the validators’ authority to halt transfers or modify software, so lower protocol-disruption risk is not supported.

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Question 157

Topic: Ethical and Professional Standards

A CFA charterholder declines an outside researcher’s request for a former client’s confidential financial records. The client has not permitted disclosure, no law requires disclosure, and the records do not concern illegal client activity.

A compliance analyst assesses the refusal:

Because Standard III(E), Preservation of Confidentiality, governs these records, its requirements replace the charterholder’s broader responsibilities under the Code.

Which correction is most accurate?

• A. The Code’s broad ethical commitments and Standard III(E)’s specific confidentiality requirements are both binding when handling the former client’s records.
• B. The Code’s broad ethical commitments are advisory, while Standard III(E)’s specific confidentiality requirements are binding when handling the former client’s records.
• C. The Code’s specific confidentiality requirements and Standard III(E)’s broad ethical commitments are both binding when handling the former client’s records.

Best answer: A

Explanation: The Code establishes broad, binding ethical commitments, including promoting the integrity and viability of capital markets. The Standards establish specific conduct requirements consistent with those commitments. Compliance with a particular Standard does not replace responsibilities under the Code.

Standard III(E), Preservation of Confidentiality, requires protecting information about current, former, and prospective clients unless the information concerns illegal client activities, disclosure is required by law, or the client permits disclosure. None of those exceptions applies here. Declining the researcher’s request therefore fulfills a specific confidentiality requirement while remaining consistent with the Code’s broader ethical principles. The end of the client relationship does not end the confidentiality duty.

• A. Standard III(E) imposes the concrete confidentiality duty, while the Code’s overarching ethical responsibilities continue to apply alongside that duty.
• B. The Code is binding on CFA Institute members and candidates, not merely advisory, even when a specific Standard directly addresses the conduct.
• C. This reverses their roles: the Code establishes overarching ethical principles, while Standard III(E) supplies the specific requirement to preserve former-client confidentiality.

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Question 158

Topic: Economics

Baseline: A central bank has a clear 2% inflation target, publishes its forecasts and policy rationale, and independently sets its policy rate. Medium-term inflation expectations are firmly anchored near the target. The government repeatedly favors lower interest rates to support employment but cannot direct the bank’s decisions.

Legal change: A new law allows the finance minister to veto policy-rate increases. The inflation mandate, public communication, government preferences, and fiscal policy remain unchanged.

For an inflationary shock of the same size, which result is most likely under the new law compared with the baseline?

• A. Less firmly anchored inflation expectations and a higher output cost of returning inflation to target.
• B. Equally well-anchored inflation expectations and an unchanged output cost of returning inflation to target.
• C. More firmly anchored inflation expectations and a lower output cost of returning inflation to target.

Best answer: A

Explanation: Central bank independence supports credibility by allowing monetary policy decisions to follow the inflation mandate rather than short-term political preferences. The ministerial veto weakens this independence even though the target and public communication remain unchanged.

Households and businesses may become less confident that the bank will undertake necessary tightening. Higher expected inflation can become embedded in wage demands and price setting, increasing the contraction in demand and output needed to return inflation to target.

Mandate clarity and transparency remain valuable, but they do not substitute for operational independence. Nor do strong institutions guarantee that inflation will always equal its target: shocks can cause temporary deviations. Credibility concerns confidence in the bank’s commitment and response.

• A. Reduced operational independence weakens confidence in inflation control, potentially requiring a larger contraction in economic activity to achieve a given reduction in inflation.
• B. An unchanged mandate and communication do not preserve credibility when political authorities gain the power to prevent necessary policy-rate increases.
• C. Giving a government that favors lower rates veto authority weakens the bank’s anti-inflation commitment rather than strengthening the anchoring of expectations.

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Question 159

Topic: Fixed Income

A securitization has the following balances before a credit-loss event:

The reserve is available in full for principal shortfalls. Losses are absorbed first by the reserve, then by overcollateralization, then by junior principal, and finally by senior principal.

The collateral pool incurs $24 million of unrecoverable principal losses. Assume no other cash flows or reserve replenishment.

The senior tranche’s principal loss is most likely:

• A. $4 million.
• B. $2 million.
• C. $7 million.

Best answer: B

Explanation: Overcollateralization is the excess of collateral principal over outstanding note principal. Here, the $100 million pool supports $95 million in notes, providing $5 million of overcollateralization. The separately funded $2 million reserve and the $5 million collateral surplus absorb the first $7 million of the $24 million loss. The remaining $17 million is allocated to the notes. The junior tranche loses its entire $15 million principal, leaving a $2 million loss for the senior tranche and $78 million of senior principal recoverable. Subordination changes which investors bear losses; it does not remove the pool’s credit losses.

• A. This amount deducts the $5 million of overcollateralization and $15 million junior principal but omits the available $2 million reserve.
• B. The reserve, $5 million of overcollateralization, and $15 million junior tranche absorb $22 million, leaving $2 million for the senior tranche.
• C. This amount deducts the reserve and junior principal but omits the $5 million excess of collateral principal over outstanding notes.

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Question 160

Topic: Ethical and Professional Standards

An equity analyst has a well-supported valuation of Hale Industries, with one unresolved input: whether a material loan’s maturity has already been extended by one year. The analysis supports a Buy recommendation if the extension is effective and a Sell recommendation otherwise.

Publication record:

• The CFO says the lender has approved the extension.
• The issuer and a major client urge publication before the market opens.
• The draft describes the extension as effective and discloses that the analyst has not personally inspected the signed agreement.

A qualified credit analyst at the same firm can verify the status directly with the lender and provide documented findings for review before publication. Which finding would most likely justify publishing the recommendation as drafted under the CFA Institute Standards of Professional Conduct?

• A. Both parties have signed an unconditional extension agreement, and the lender confirms that the revised maturity date is legally effective.
• B. The lender’s credit committee has approved the extension, and both parties are scheduled to sign the agreement later that day.
• C. The borrower has signed the proposed extension agreement, and the lender expects to complete its approval process later that day.

Best answer: A

Explanation: Standard V(A), Diligence and Reasonable Basis, requires recommendations to rest on an adequate research basis. Analysts may rely on qualified colleagues after taking reasonable steps to assess the soundness of their work; personal inspection of every underlying document is not required. Here, the extension determines the recommendation, and the draft presents its effectiveness as an established fact. Reliable, documented confirmation that the extension is legally effective supplies the missing support.

Standard V(B), Communication with Clients and Prospective Clients, requires facts to be distinguished from opinions. Disclosing a lack of personal document inspection does not turn an expected extension into an effective one. Client and issuer pressure do not reduce these duties. If confirmation remains unavailable, a revised conditional analysis may be appropriate, but it must have a reasonable basis and communicate the uncertainty honestly.

• A. Documented confirmation of an effective agreement supports the decisive valuation input, and the analyst may reasonably rely on sound work by qualified colleagues.
• B. Credit committee approval and expected signatures indicate progress toward an extension, not that the maturity change is already effective.
• C. The borrower’s signature and an expectation of lender approval do not establish an effective extension at the time of publication.

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Question 161

Topic: Portfolio Construction

An investment committee uses ex ante annualized portfolio volatility as its risk measure. The total risk limit is 10%. The committee allocates this limit into binding strategy caps; transfers between caps require committee approval.

Estimated strategy contributions incorporate correlations and sum to total portfolio volatility. All table values are percentage points of annualized volatility.

Equity accounts for 55% of invested capital. No transfers between risk caps have been approved.

Which conclusion is most appropriate when monitoring compliance with the approved risk budget?

• A. The portfolio is compliant because equity’s capital weight is below its 60% share of the risk budget.
• B. The portfolio is compliant because its estimated volatility is below the 10% total risk limit.
• C. The portfolio is noncompliant because equity’s volatility contribution exceeds its 6.0-percentage-point risk cap.

Best answer: C

Explanation: A risk budget allocates an explicit measure of permissible risk across strategies. Here, component contributions to annualized portfolio volatility are monitored against binding caps.

The contributions sum to 9.0%, below the 10% total limit. Nevertheless, equity contributes 6.3 percentage points against its 6.0-percentage-point cap. Unused capacity in other strategies does not automatically authorize additional equity risk. The breach calls for reducing equity’s risk contribution or obtaining approval to reallocate the budget.

Equity’s cap represents 60% of maximum allowable portfolio risk. It neither prescribes a 60% capital allocation nor forecasts equity returns. Governance therefore requires monitoring both aggregate risk and individual strategy contributions.

• A. The 60% budget share refers to allowable volatility contribution, not invested capital, so the 55% capital weight does not establish compliance.
• B. Total estimated volatility is 9.0%, but compliance also requires each strategy contribution to remain within its separately approved cap.
• C. Equity contributes 6.3 percentage points against a cap of 6.0, exceeding its allocated risk by 0.3 percentage points.

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Question 162

Topic: Quantitative Methods

An investor chooses a one-year allocation between a risk-free asset and a risky portfolio. The investor maximizes utility, \(U = E(R_p) - 0.5A\sigma_p^2\), where \(E(R_p)\) and \(\sigma_p\) are the combined portfolio’s expected return and standard deviation, expressed as decimals, and \(A\) is the risk-aversion coefficient.

The investor can borrow or lend at the risk-free rate, with no borrowing limit or transaction costs. Allocations are percentages of initial wealth.

Which allocation is most appropriate for maximizing the investor’s utility?

• A. Invest 22.5% in the risky portfolio and lend 77.5% at the risk-free rate.
• B. Invest 150% in the risky portfolio and borrow 50% at the risk-free rate.
• C. Invest 112.5% in the risky portfolio and borrow 12.5% at the risk-free rate.

Best answer: C

Explanation: A mean-variance investor balances expected excess return against the additional variance from risky investment. Let \(w\) denote the fraction of initial wealth invested in the risky portfolio. The optimal weight equals the expected risk premium divided by the product of risk aversion and risky-portfolio variance:

\[ w^* = \frac{0.12-0.03}{2\times(0.20)^2} = 1.125. \]

The risk-free weight is \(1-w^*=-0.125\). Thus, the investor invests 112.5% of initial wealth in the risky portfolio and finances the additional 12.5% by borrowing. A negative risk-free weight represents borrowing; a positive weight represents lending. Equal borrowing and lending rates allow leveraged allocations to remain on the same capital allocation line.

• A. A 22.5% weight results from using standard deviation in the denominator; the utility-maximizing allocation requires variance instead.
• B. A 150% weight uses the risky portfolio’s 12% expected return rather than its 9% expected return in excess of financing costs.
• C. The optimal risky weight is \(0.09/(2\times0.20^2)=1.125\), requiring borrowing equal to 12.5% of initial wealth.

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Question 163

Topic: Alternative Investments

An analyst forecasts a property’s one-year investment return using the following assumptions:

The purchase is financed with the loan and the balance is equity. All rental income, operating costs, and interest occur at year-end. There are no taxes, transaction costs, or principal repayments.

At a 5% annual interest rate, the forecast equity total return is 12.5%. The analyst revises only the interest rate to 9%, holding all other assumptions fixed.

Under the revised assumption, the equity total return and the effect of leverage relative to an unlevered investment are most accurately described as:

• A. 6.5%, with leverage now reducing total return.
• B. 10.1%, with leverage still increasing total return.
• C. 1.5%, with leverage now reducing total return.

Best answer: A

Explanation: A real asset’s total return combines net operating income and capital appreciation. Net operating income is $300,000, giving an unlevered income return of 6%. The $100,000 increase in value adds 2%, so the unlevered total return is 8%.

Initial equity is $2,000,000. At the revised 9% borrowing rate, annual interest is $270,000. The equity investor receives $30,000 of net cash income and benefits from $100,000 of appreciation. The equity total return is therefore:

\[ \frac{30,000 + 100,000}{2,000,000} = 6.5\% \]

The property’s total return remains unchanged, but the borrowing cost now exceeds its 8% return. Leverage therefore changes from enhancing to reducing equity total return. Because debt is 1.5 times equity, the four-percentage-point increase in borrowing cost reduces equity return by six percentage points.

• A. Revised interest is $270,000, leaving $130,000 of income plus appreciation on $2,000,000 of equity, a 6.5% return versus 8.0% unlevered.
• B. This applies the borrowing-rate increase to debt relative to property value rather than debt relative to equity, understating the reduction in equity return.
• C. The 1.5% cash income return excludes the $100,000 increase in property value, which must be included in total return.

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Question 164

Topic: Portfolio Construction

An analyst assesses a stock using the following estimates for the coming year:

• Risk-free rate: 3.0%.
• Expected market return: 9.0%.
• Stock beta: 1.25.

The analyst proposes treating 14.25% as the minimum one-year return an investor will earn. If the stock is fairly priced and the standard CAPM assumptions hold, which conclusion is most accurate?

• A. The required expected return is 10.5%; the realized one-year return must be at least 10.5%.
• B. The required expected return is 14.25%; the realized one-year return may be above or below 14.25%.
• C. The required expected return is 10.5%; the realized one-year return may be above or below 10.5%.

Best answer: C

Explanation: CAPM calculates a stock’s required expected return as the risk-free rate plus beta times the market risk premium. Beta measures systematic risk, the risk that diversification cannot eliminate.

The market risk premium is the expected market return minus the risk-free rate: 9.0% − 3.0% = 6.0%. Therefore:

\[ 3.0\% + 1.25 \times 6.0\% = 10.5\% \]

For a fairly priced stock under CAPM, its expected return equals this required return. The 7.5% premium above the risk-free rate represents expected compensation for systematic risk, not a guaranteed payment. Realized returns can be higher or lower than 10.5%; correct pricing does not eliminate investment uncertainty.

• A. Although 10.5% is the correct required expected return, CAPM does not establish a minimum realized stock return.
• B. The 14.25% calculation multiplies beta by the total market expected return rather than the market risk premium.
• C. The market risk premium is 6.0%, giving a required expected return of 3.0% + 1.25 × 6.0% = 10.5%, with no guaranteed realized return.

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Question 165

Topic: Quantitative Methods

An analyst models a stock’s terminal price one year from now, \(P_1\). Its current price, \(P_0\), is $100. The log price relative \(Y=\ln(P_1/P_0)\) is normally distributed with mean 0.02 and variance 0.04.

For a normal variable with mean \(m\) and variance \(v\), use:

• \(E[e^Y]=e^{m+v/2}\)
• \(\operatorname{Var}(e^Y)=e^{2m+v}(e^v-1)\)

Which statement about the modeled terminal stock price is least accurate?

• A. The terminal stock price can be below $100 and must exceed $0.
• B. The terminal stock price has a mean of approximately $102.02.
• C. The terminal stock price has a variance of approximately 442.10 dollars squared.

Best answer: B

Explanation: Normally distributed log price relatives imply lognormally distributed prices. The normal distribution’s mean parameter describes the log relative, not the arithmetic mean of the terminal price. Because exponentiation is convex, dispersion raises the mean price above the median.

The terminal price moments are:

• Mean: \(100e^{0.02+0.04/2}=100e^{0.04}\), approximately $104.08.
• Variance: \(100^2e^{2(0.02)+0.04}(e^{0.04}-1)\), approximately 442.10 dollars squared.

The value $102.02, calculated as \(100e^{0.02}\), is the median terminal price. Since \(P_1=100e^Y\), prices are strictly positive. Prices below $100 occur when \(Y<0\), which has positive probability under the stated normal distribution.

• A. The exponential transformation produces strictly positive prices, while negative log price relatives have positive probability and produce prices below $100.
• B. Exponentiating the mean log price relative gives the median price; the mean price is \(100e^{0.02+0.04/2}\), approximately $104.08.
• C. Scaling the lognormal variance by \(100^2\) gives \(100^2e^{0.08}(e^{0.04}-1)\), approximately 442.10 dollars squared.

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Question 166

Topic: Ethical and Professional Standards

Elena Voss, CFA, recommends a company’s shares using a valuation model purchased from an award-winning research firm.

Information at the recommendation date:

• Voss has reviewed the provider’s methodology, verified model inputs, and analyzed both renewal and nonrenewal of a credit facility expiring in three months.
• The model’s base-case 25% estimated one-year total return assumes renewal. Renewal is uncertain, and nonrenewal would substantially reduce the estimated value.
• Her sole client communication about the recommendation labels the return as an estimate and identifies the outside research source, but omits the renewal assumption and its associated risk.

The facility is subsequently renewed, and the shares earn a 32% total return over the following year.

Under the CFA Institute Standards of Professional Conduct, which conclusion about Voss’s conduct at the recommendation date is most appropriate?

• A. Her communication was inadequate because she omitted the credit-renewal risk underlying the return estimate.
• B. Her communication was adequate because she identified the projected return as an estimate rather than a guarantee.
• C. Her research was inadequate because she used an external valuation model rather than developing one herself.

Best answer: A

Explanation: Standard V(B), Communication with Clients and Prospective Clients, requires disclosure of significant risks and limitations associated with investment analysis. Voss’s return estimate depends on an uncertain credit renewal that materially affects valuation. Calling the return an estimate does not adequately communicate that dependency.

Standard V(A), Diligence and Reasonable Basis, permits the use of outside research when supported by appropriate due diligence. Voss reviewed the methodology, verified inputs, and assessed both renewal outcomes; developing an internal model is not required.

Conduct is evaluated using the information available when the recommendation was made. Neither the provider’s reputation nor the subsequent 32% return cures the deficient client communication.

• A. Standard V(B) requires disclosure of significant risks and limitations, including uncertain credit renewal that materially affects estimated value.
• B. Labeling the return as an estimate distinguishes opinion from fact but does not disclose the significant credit-renewal risk.
• C. Standard V(A) permits reliance on third-party research after appropriate due diligence; Voss is not required to develop the model herself.

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Question 167

Topic: Financial Statement Analysis

A manufacturer sells one product and reports the following current-year results:

An analyst makes these assumptions for next year:

• Unit sales increase by 10%.
• All variable input prices increase by 10%, with input requirements per unit unchanged.
• The percentage increase in selling price equals 50% of the percentage increase in variable input prices.
• Total fixed operating costs increase by 8%.

There are no other operating revenues or expenses. Relative to the current year, which conclusion about next year’s operating performance is most accurate?

• A. Operating profit increases, and operating profit margin decreases.
• B. Operating profit increases, and operating profit margin increases.
• C. Operating profit decreases, and operating profit margin decreases.

Best answer: A

Explanation: Forecast revenue reflects both volume growth and selling-price growth. The pricing policy implies a selling-price increase of 5%. Variable costs reflect both volume growth and input-price inflation, whereas fixed costs receive only their stated 8% increase.

Using amounts in millions of dollars:

• Revenue: \(10.00 \times 1.10 \times 1.05 = 11.55\).
• Variable costs: \(6.00 \times 1.10 \times 1.10 = 7.26\).
• Fixed costs: \(2.00 \times 1.08 = 2.16\).

Forecast operating profit is \(11.55 - 7.26 - 2.16 = 2.13\), compared with $2.00 million currently. However, operating profit margin falls from 20.0% to \(2.13/11.55 = 18.4\%\). Higher sales volume supports greater total profit even though incomplete input-price pass-through compresses the margin.

• A. Operating profit rises by 6.5% to $2.13 million, but revenue grows faster, reducing the operating profit margin to 18.4%.
• B. Operating profit margin falls from 20.0% to 18.4%, because total operating costs grow by 17.75% while revenue grows by 15.5%.
• C. Operating profit rises from $2.00 million to $2.13 million; increased sales volume more than offsets the effects of higher costs.

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Question 168

Topic: Financial Statement Analysis

A manufacturing company reports under IFRS Accounting Standards for the year ended 31 December 2026 and has not early adopted IFRS 18. It classifies interest paid as financing and dividends received as investing.

Selected data:

An analyst recasts only the cash-flow classifications under U.S. GAAP, holding all cash amounts and average current liabilities fixed. The revised ratio of operating cash flow to average current liabilities is closest to:

• A. 1.10
• B. 1.25
• C. 1.05

Best answer: A

Explanation: Before IFRS 18 adoption, IAS 7 permits a nonfinancial company to classify interest paid as operating or financing and dividends received as operating or investing, with consistent application. The company’s chosen policies exclude both amounts from its reported operating cash flow.

Under U.S. GAAP, interest paid and dividends received are operating cash flows. Recasting therefore subtracts the $12 million interest payment and adds the $4 million dividend receipt:

\[ \text{Operating cash flow ratio} = \frac{96 - 12 + 4}{80} = 1.10 \]

The ratio decreases from \(96/80 = 1.20\) to 1.10. Total net cash flow remains unchanged; the decrease reflects different classifications rather than a change in the company’s underlying cash flows.

• A. Both flows are operating under U.S. GAAP, giving operating cash flow of $88 million and a ratio of \(88/80 = 1.10\).
• B. The calculation \((96 + 4)/80 = 1.25\) adds dividends received but leaves interest paid in financing rather than reclassifying it to operating activities.
• C. The calculation \((96 - 12)/80 = 1.05\) reclassifies interest paid but omits the required addition of dividends received to operating cash flow.

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Question 169

Topic: Portfolio Construction

An analyst reviews a proposed increase in a foundation’s equity allocation.

Foundation profile:

• Willingness: Trustees are willing to accept a 12% portfolio loss under a standardized one-year adverse scenario.
• Capacity: The foundation can absorb an 8% loss under that scenario without impairing committed grants.
• Documented tolerance: The investment policy statement (IPS) permits an estimated scenario loss of up to 8%.

Risk governance: The investment committee approves the IPS and delegates a 6% scenario-loss limit to the portfolio manager, retaining authority to approve exceptions. The proposed allocation has an estimated 7% loss under the same scenario.

Analyst’s recommendation:

The proposal falls within documented tolerance, so the manager may approve the limit exception and implement the allocation.

Which correction to the analyst’s reasoning is most accurate?

• A. The committee must increase the documented tolerance before implementation; the 6% delegated limit defines the foundation’s overall risk tolerance.
• B. The committee must increase the documented tolerance to 12% before implementation; trustees’ willingness takes priority over the foundation’s loss capacity.
• C. The committee must approve a delegated-limit exception before implementation; the 8% documented tolerance can remain unchanged.

Best answer: C

Explanation: Risk tolerance must reflect both willingness and capacity to bear losses. Here, the foundation’s capacity constrains the trustees’ greater willingness, supporting the documented 8% scenario-loss tolerance.

The proposed 7% scenario loss falls within that broad tolerance but exceeds the manager’s delegated 6% limit. These thresholds serve different purposes: the IPS expresses the foundation’s tolerance, while the delegated limit bounds the manager’s authority. Consistency with the IPS does not allow the manager to approve an exception reserved for the investment committee.

The committee must authorize the exception before implementation; no tolerance amendment is required solely because the delegated limit is exceeded. A risk measure becomes actionable when it is linked to a governing threshold, decision-making authority, and an exception procedure.

• A. The delegated limit constrains the manager’s authority but does not replace the 8% IPS tolerance, which the proposed 7% scenario loss does not exceed.
• B. The foundation’s 8% loss-bearing capacity constrains the trustees’ greater willingness, so willingness alone does not justify raising tolerance to 12%.
• C. The proposed 7% scenario loss exceeds the manager’s 6% limit, and the committee retained authority to approve exceptions.

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Question 170

Topic: Equities

A company implements a 1-for-5 reverse stock split that applies to all its common shares.

Immediately before the split:

• An investor holds 250 shares.
• The company has 10,000,000 common shares outstanding.
• The closing share price is $8.00.

The first post-split closing price is $38.40. During this period, the investor makes no trades, receives no distributions, and there are no other changes in shares outstanding.

Comparing proportional ownership and holding value on a consistent share basis, which conclusion about the investor’s position is most accurate?

• A. The ownership percentage is unchanged, and the holding’s market value decreased by 4%.
• B. The ownership percentage decreased by 80%, and the holding’s market value decreased by 4%.
• C. The ownership percentage is unchanged, and the holding’s market value increased by 380%.

Best answer: A

Explanation: A reverse stock split consolidates shares without mechanically changing shareholder wealth, total earnings, or proportional ownership. The 1-for-5 split reduces the investor’s holding from 250 to 50 shares and shares outstanding from 10,000,000 to 2,000,000. Ownership remains 0.0025%.

Absent market repricing, the corresponding post-split price would be five times $8.00, or $40.00. The observed price of $38.40 is below that benchmark. The holding’s value therefore changes from $2,000 to $1,920, a decrease of 4%.

The higher quoted share price largely reflects the change in share units; it is not itself evidence of wealth creation.

• A. The holding falls from $2,000 to $1,920, while the investor’s shares and total shares outstanding decrease in the same proportion.
• B. Shares outstanding decrease by the same 80% as the investor’s share count, leaving the investor’s proportional ownership unchanged.
• C. The 380% increase compares unadjusted share prices and ignores the reduction in the investor’s share count from 250 to 50.

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Question 171

Topic: Financial Statement Analysis

An analyst revises a manufacturer’s one-year financial forecast. Both forecasts have identical opening balances. Dollar amounts are in millions.

Model assumptions:

• Net operating assets equal operating net working capital plus net property, plant, and equipment (PP&E).
• Only operating net working capital, net PP&E, retained earnings, and debt may differ between the ending balance sheets.
• Debt is the financing plug. Incremental borrowing occurs at year-end and incurs no interest expense during the forecast year.

Which conclusion about the revised forecast, relative to the original forecast, is least accurate?

• A. Year-end retained earnings are $8 million higher.
• B. Year-end debt is $35 million higher.
• C. Year-end net operating assets are $35 million higher.

Best answer: B

Explanation: A linked forecast separates additional asset investment from the financing needed to support it. Net income rises from $40 million to $48 million because the 8% net profit margin applies to higher revenue. With dividends unchanged at $16 million, additions to retained earnings rise from $24 million to $32 million.

Ending operating net working capital rises from $100 million to $120 million. Net PP&E is $15 million higher because capital expenditure increases by $15 million while depreciation is unchanged. Net operating assets therefore increase by $35 million.

With other balance sheet amounts fixed, the additional $8 million of retained earnings funds part of this investment. Required incremental borrowing is $27 million, rather than the full $35 million increase in net operating assets.

• A. Net income rises by $8 million and dividends are unchanged, so year-end retained earnings rise by the same amount.
• B. The $35 million additional asset requirement is partly funded by $8 million of additional retained earnings, leaving $27 million of additional borrowing.
• C. Operating net working capital increases by $20 million and net PP&E by $15 million, producing a $35 million increase in net operating assets.

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Question 172

Topic: Ethical and Professional Standards

An analyst recommends a company’s shares solely on a buy signal from an established external research provider. Neither the analyst nor her firm has reviewed the model’s assumptions or its suitability for the company.

Two weeks later, her employer accepts a paid advisory engagement from the company. The recommendation remains active, and the analyst remains free to form an independent investment opinion. She proposes the following response:

“I will fully and fairly disclose the advisory engagement. The provider’s reputation means the recommendation needs no further review.”

Under the CFA Institute Code of Ethics and Standards of Professional Conduct, which correction is most accurate?

• A. Assess the model’s assumptions and applicability, revise the recommendation as warranted, and communicate the result with full and fair conflict disclosure.
• B. Assess the provider’s reputation and past performance, reaffirm the recommendation if both are satisfactory, and communicate the result with full and fair conflict disclosure.
• C. Assess the model’s assumptions and applicability, withdraw the recommendation as required by the advisory engagement, and communicate the result with full and fair conflict disclosure.

Best answer: A

Explanation: Standard V(A), Diligence and Reasonable Basis, requires appropriate diligence before relying on third-party research. A provider’s reputation can inform that assessment, but it does not replace evaluating the research’s assumptions, limitations, and applicability. The analyst should reassess the recommendation and revise or withdraw it if the review warrants doing so.

The employer’s paid advisory engagement creates a conflict addressed by Standard VI(A), Avoid or Disclose Conflicts. Full and fair disclosure allows clients to evaluate that relationship, but it does not repair the missing research basis. Because independent judgment remains possible, the engagement does not itself prohibit continued coverage. The analyst should communicate the reassessed conclusion and any material changes consistently with Standard V(B), Communication with Clients and Prospective Clients.

• A. The missing research assessment requires reassessing the recommendation, while the employer’s advisory engagement requires separate, full and fair conflict disclosure.
• B. Reputation and past performance alone do not establish that the model’s assumptions are sound or applicable to the recommended company.
• C. The advisory engagement does not automatically require withdrawal; the reassessment should determine whether the recommendation remains supportable.

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Question 173

Topic: Equities

A company has the following common shares outstanding:

Both classes have identical per-share dividend and liquidation rights. The founder owns all Class B shares and no Class A shares. Ordinary shareholder decisions require a simple majority of votes.

The company declares a total cash dividend of $3,000,000. An analyst writes:

Class B has twice as many votes in total as Class A, so the founder is entitled to two-thirds of the dividend.

Which allocation most accurately corrects the analyst’s conclusion?

• A. The founder receives $500,000, and Class A shareholders receive $2,500,000.
• B. The founder receives $2,000,000, and Class A shareholders receive $1,000,000.
• C. The founder receives $1,500,000, and Class A shareholders receive $1,500,000.

Best answer: A

Explanation: Voting rights and economic rights are separate features of an equity class. The founder’s 100,000 Class B shares carry 1,000,000 votes, compared with 500,000 votes for Class A. The founder therefore has two-thirds of total voting power and can control ordinary shareholder decisions.

Identical per-share dividend rights require allocating the $3,000,000 dividend across 600,000 shares, giving $5 per share. The founder receives $500,000, while Class A shareholders receive $2,500,000. Identical liquidation rights similarly attach to each share, not each vote. Greater voting power may influence an equity class’s value through control, but it neither increases stated cash entitlements nor implies a fixed valuation multiple.

• A. The founder owns one-sixth of the outstanding shares and therefore receives one-sixth of the dividend under the identical per-share participation rights.
• B. This allocation uses voting power to divide the dividend, although the stated economic rights allocate dividends equally per share.
• C. Identical per-share dividend rights do not imply equal total dividends for the two classes because their outstanding share counts differ.

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Question 174

Topic: Derivatives and Risk Management

A treasury analyst is evaluating a commitment entered today to borrow for one year, with the loan drawn exactly one year from today. The default-free zero-coupon spot curve is:

All rates use annual compounding. Borrowing and lending are available at the stated spot rates, with no credit spread or transaction costs.

Which conclusion about the no-arbitrage forward borrowing rate is most accurate?

• A. The forward rate is 8.04%, the one-year spot rate that must prevail when the future loan begins.
• B. The forward rate is 6.00%, a borrowing rate that can be fixed today for the future loan.
• C. The forward rate is 8.04%, a borrowing rate that can be fixed today for the future loan.

Best answer: C

Explanation: A no-arbitrage forward rate equates borrowing for two years with borrowing for one year and locking in borrowing for the following year. With annual compounding, the two-year accumulation factor equals the first-year spot factor multiplied by the second-year forward factor.

Let \(f\) denote the one-year forward rate beginning in one year:

\[ f = \frac{(1.06)^2}{1.04} - 1 \approx 8.04\%. \]

This rate can be fixed today through a forward borrowing commitment. It determines the contractual financing cost for the future period, not the market spot rate that will prevail then. Actual future interest rates may differ as market conditions change.

• A. Although 8.04% is the implied forward rate, no-arbitrage pricing does not guarantee that the future one-year market spot rate will equal it.
• B. The 6.00% spot rate applies to borrowing over the full two years, not solely to the one-year period beginning in one year.
• C. The implied second-year borrowing rate is the two-year accumulation factor divided by the first-year accumulation factor, minus one.

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Question 175

Topic: Quantitative Methods

A U.S. investor buys a share of stock for $50 and holds it for one year. At year-end, the share’s ex-dividend price is $57, and the investor receives a $3 dividend, retained as cash. Ignore taxes and transaction costs.

At purchase, the investor expected inflation of 5% over the year. The U.S. dollar cost of the investor’s fixed consumption basket actually increased by 10% over that same year.

The investment’s realized purchasing-power return for this investor is closest to:

• A. 9.09%
• B. 14.29%
• C. 10.00%

Best answer: A

Explanation: A nominal holding-period return includes both price appreciation and cash income. The investor’s ending wealth is $60 per share, including the dividend, compared with an initial investment of $50:

\[ R_{\text{nominal}} = \frac{57 + 3 - 50}{50} = 20\%. \]

Realized purchasing-power growth compares the investment’s wealth-growth factor with the actual price-growth factor of the investor’s consumption basket:

\[ R_{\text{real}} = \frac{1 + R_{\text{nominal}}}{1 + \text{inflation}} - 1 = \frac{1.20}{1.10} - 1 = 9.09\%. \]

Thus, the investment can purchase approximately 9.09% more of that basket after one year. The initial inflation forecast does not measure realized purchasing power. Subtracting inflation from nominal return is only an approximation.

• A. Including the dividend gives a 20% nominal return; adjusting for the basket’s actual price increase gives \(1.20/1.10 - 1 = 9.09\%\).
• B. Adjusting the nominal return for the expected 5% inflation rate gives 14.29%, but realized purchasing-power growth requires actual inflation.
• C. Subtracting 10% inflation from the 20% nominal return gives 10.00%, which is an approximation rather than the exact purchasing-power return.

Questions 176-180

Question 176

Topic: Quantitative Methods

A price-weighted index has a current divisor of 3.00 and the following closing prices:

An analyst initially forecasts a 10% gain for Stock A over the next trading day, with Stocks B and C unchanged and no corporate actions.

The analyst then learns that Stock A will undergo a 3-for-1 share split before the next trading session. At the adjustment time, Stock A’s quoted price becomes $30, while the other stock prices remain unchanged. The forecast 10% gain still applies to Stock A’s split-adjusted price. No dividends are paid, and there are no constituent changes.

After accounting for the split, the forecast index price return from the current close to the next close is closest to:

• A. -31.67%
• B. 5.00%
• C. 2.50%

Best answer: C

Explanation: A price-weighted index equals the sum of constituent prices divided by its divisor. A split creates no economic gain or loss at the adjustment time, so the divisor must preserve index continuity.

The initial index level is \( (90 + 60 + 30)/3 = 60 \). Immediately after the split, constituent prices sum to $120, requiring an adjusted divisor of \( 120/60 = 2.00 \).

Stock A’s forecast closing price is $33 after its 10% gain. The forecast index level is therefore \( (33 + 60 + 30)/2 = 61.50 \), giving a return of \( 61.50/60 - 1 = 2.50\% \).

Although the split preserves the index level, it reduces Stock A’s price weight from 50% to 25%, changing the index’s sensitivity to its subsequent return.

• A. This result retains the original divisor of 3.00 after the split, incorrectly treating the mechanical price reduction as an investment loss.
• B. This is the no-split forecast return, which incorrectly retains Stock A’s original 50% price weight rather than its split-adjusted 25% weight.
• C. Preserving the initial index level of 60 requires a divisor of 2.00; the forecast level of 61.50 implies a 2.50% return.

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Question 177

Topic: Portfolio Construction

An analyst reviews a portfolio for the year ended 31 December 2027. Its mandate requires:

• An annual time-weighted return after all portfolio costs at least equal to the specified benchmark’s total return.
• Equity exposure no higher than 65% at any time.
• Cash available for a $200,000 withdrawal on 31 December.

Review data:

The initial review used a benchmark total return of 8.0%. The benchmark provider subsequently corrected that return to 9.0% for the same year. Portfolio results, cash needs, benchmark composition, and mandate requirements remain unchanged.

Which revised assessment is most accurate?

• A. The return objective remains satisfied; the equity-exposure limit and cash requirement remain satisfied.
• B. The return objective is missed; the equity-exposure limit and cash requirement remain satisfied.
• C. The return objective is missed; the equity-exposure limit is breached and the cash requirement remains satisfied.

Best answer: B

Explanation: Performance must be evaluated on the mandate’s specified basis and against the comparator for the same period. Deducting the 1.0-percentage-point cost drag from the 9.5% gross return gives an 8.5% net return. This exceeded the initially reported benchmark return by 0.5 percentage point but falls short of the corrected return by 0.5 percentage point. A positive absolute return therefore does not establish that the relative return objective was achieved.

The benchmark correction does not change policy compliance. Maximum equity exposure of 60% remains below the 65% limit; the benchmark’s 50% equity weight is not that limit. Available cash of $250,000 covers the $200,000 withdrawal. The revised review consequently shows a missed performance objective alongside continued compliance with exposure and liquidity requirements.

• A. The 8.5% net return falls below the corrected 9.0% benchmark return; using the 9.5% gross return ignores the mandate’s after-cost requirement.
• B. Net return falls 0.5 percentage point short of the revised benchmark, while maximum equity exposure and available cash satisfy the unchanged requirements.
• C. Exceeding the benchmark’s 50% equity weight does not breach the mandate because the portfolio’s maximum 60% exposure remains below its 65% ceiling.

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Question 178

Topic: Ethical and Professional Standards

An equity analyst regularly publishes recommendations on an issuer.

Existing arrangement:

• She also serves as a paid nonexecutive director of the issuer, with her employer’s approval.
• Her reports fully and fairly disclose the role and compensation. An independent reviewer checks her research for objectivity.
• Previously, she possessed no material nonpublic information about the issuer and used only public information in her research.

Changed condition: At a board meeting, she learns confidentially that the issuer’s largest customer has canceled its contract. The loss will materially reduce earnings and has not been publicly disseminated. All other conditions remain unchanged.

She wants to incorporate the customer loss into her next client recommendation. Which revised approach is most appropriate?

• A. Resign from the board role and update the recommendation once the resignation has taken effect.
• B. Retain the board role and defer the recommendation update until the customer loss is broadly disseminated to the public.
• C. Retain the board role and update the recommendation after expanding the conflict disclosure to describe her confidentiality duties.

Best answer: B

Explanation: A paid directorship can create competing loyalties to research clients and the issuer, as well as access to confidential information. Under Standard VI(A), conflicts must be avoided or fully and fairly disclosed, with safeguards supporting objective client service. The approval, disclosure, and independent review address the original arrangement.

The customer loss introduces a separate restriction under Standard II(A), Material Nonpublic Information. The analyst must not use this information to act or cause others to act. Neither expanded conflict disclosure nor resignation removes that restriction. She should defer a recommendation update reflecting the loss until the information is broadly publicly disseminated and continue protecting its confidentiality. Receiving the information does not, by itself, require resignation.

• A. Resignation ends the ongoing board relationship but does not make previously received confidential information public or permit its immediate use.
• B. Deferring use until broad public dissemination addresses the new information restriction while preserving the existing management of the disclosed board-role conflict.
• C. Expanded conflict disclosure cannot authorize a recommendation using material nonpublic information, even when clients understand the analyst’s confidentiality duties.

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Question 179

Topic: Corporate Finance

A manufacturer is evaluating a three-year sales contract. Forecasts for its total operations are:

All sales and purchases are on credit, and annual operating purchases equal cost of sales. Use a 360-day year and assume uniform daily activity.

Baseline working capital is already funded. Incremental working capital is invested at contract inception, remains constant, and is fully recovered at the end of Year 3 when operations return to baseline. The annual discount rate is 10%.

Which statement about the contract’s working-capital impact is least accurate?

• A. The contract produces a terminal working-capital cash inflow of $400,000.
• B. The contract requires an initial working-capital cash outflow of $900,000.
• C. Omitting working-capital cash flows overstates the contract’s NPV by approximately $99,474.

Best answer: B

Explanation: Net operating working capital equals receivables plus inventory minus trade payables. Receivables use sales as their calculation base; inventory and payables use cost of sales here. Each balance equals its annual calculation base multiplied by the associated days divided by 360.

The resulting balances, in dollars, are:

• Baseline: \(300{,}000 + 400{,}000 - 200{,}000 = 500{,}000\).
• With contract: \(600{,}000 + 600{,}000 - 300{,}000 = 900{,}000\).

Only the $400,000 increase is attributable to the contract. It reduces available cash at inception and is recovered when the contract ends; baseline working capital remains invested.

The net present-value cost of this temporary investment, in dollars, is:

\[ 400{,}000 - \frac{400{,}000}{(1.10)^3} \approx 99{,}474. \]

Excluding both working-capital cash flows therefore overstates NPV by approximately $99,474, rather than by the full initial investment.

• A. The terminal inflow equals the $400,000 incremental investment because baseline working capital remains committed to continuing operations.
• B. The $900,000 balance includes $500,000 already required by baseline operations, so the contract requires only $400,000 of additional funding.
• C. The overstatement equals the $400,000 initial outflow minus the recovery’s present value of approximately $300,526, or approximately $99,474.

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Question 180

Topic: Economics

An analyst reviews an economy’s seasonally adjusted indicators. Real GDP reached a cyclical peak of 100 in Q4 2025 and fell throughout 2026 to 93 in Q4 2026.

Potential output in Q3 2027 is 104 on the same GDP index scale. Firms’ desired inventory-to-sales ratio is 1.30.

The analyst concludes:

The economy remains in contraction because real GDP has not returned to its previous cyclical peak.

Which assessment most accurately corrects the analyst’s interpretation?

• A. Late expansion, with limited unused productive capacity.
• B. Early expansion, with substantial unused productive capacity.
• C. Contraction, with substantial unused productive capacity.

Best answer: B

Explanation: Business-cycle phases depend on the direction of broad economic activity, not whether output has regained a previous peak. Rising real GDP and employment following the 2026 decline are consistent with early expansion, or recovery. The inventory-to-sales ratio returning to firms’ desired level also supports normalization after the downturn.

Bank lending can continue contracting after production begins recovering because credit and production cycles need not turn simultaneously. Negative loan growth therefore does not overturn the evidence of recovery.

Economic slack is assessed relative to potential output, not a historical cyclical peak. Actual output of 98 remains below potential output of 104, indicating substantial unused productive capacity even though the economy is expanding.

• A. Proximity to the previous GDP peak does not imply proximity to productive capacity; current output remains substantially below potential.
• B. Output and employment are recovering, while real GDP of 98 remains materially below potential output of 104.
• C. Rising real GDP and employment indicate expansion; output remaining below its previous peak does not establish continued contraction.

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