Free CFA Level II Practice Exam for the 2027 Curriculum

This free set contains 22 original Finance Prep cases and 88 attached questions for the 2027 CFA Level II curriculum. Each case has four questions with three answer choices. Use the set to check case reading, calculations and reasoning before continuing with more cases in Finance Prep.

These are original independent practice questions, not official CFA Institute questions, copied live-exam content or exam dumps. Finance Prep is not affiliated with or endorsed by CFA Institute.

How to use this set

For a pacing check, allow up to 264 minutes across the 88 questions, with a break between two 132-minute working sessions. The official exam has scored and trial items; this public set is educational practice and does not reproduce official scoring or difficulty. Answers and explanations are visible below each question, so cover them while attempting the set.

The set covers all ten topics using an editorial practice mix. Check the official outline for CFA Institute’s topic-weight ranges.

Practice cases

Practice Vignette 1

Topic: Quantitative Methods

Solara Inflation Outlook

Mara Seth, a macro analyst at Calden Asset Management, is preparing a January 2027 inflation outlook for the firm’s fixed-income investment committee.

Inflation observations and fitted trends

Seth analyzes 36 monthly observations of Solara’s annualized one-month CPI inflation rate, from January 2024 through December 2026. The dependent variable, \(y_t\), stores the numeric percentage rate: inflation of 3.20% is entered as 3.20, not 0.032. All observations are positive.

The time index is zero in January 2024 and increases by one each calendar month. It continues without resetting during the forecast period. Selected observations are shown below.

Using all 36 observations, Seth estimates a linear trend:

\[ \widehat{y}_t = 3.20 - 0.020t. \]

She also estimates a log-linear alternative using the natural logarithm:

\[ \widehat{\ln(y_t)} = 1.167 - 0.0070t. \]

For comparisons between fitted paths, Seth exponentiates the fitted log values without a retransformation adjustment.

Estimation uncertainty and forward conditions

Historical residual diagnostics for the linear model are consistent with independent, homoskedastic, approximately normal disturbances. Its estimation statistics are summarized below.

For two-sided 95% intervals, use a critical value of 2.03.

In January 2027, Solara’s central bank announced a new monetary-policy framework scheduled to take effect in January 2028. Seth has not estimated its potential effect on inflation dynamics or adjusted either trend model for the announcement.

Question 1

Using the linear trend, Seth’s inflation forecast for June 2027 is closest to:

• A. 3.08%.
• B. 2.38%.
• C. 2.34%.

Best answer: B

Explanation

A deterministic trend forecast uses the time index measured from the model’s original calendar origin, not the number of months beyond the sample. January 2024 is indexed zero, January 2027 is indexed 36, and June 2027 is indexed 41.

\[ \widehat{y}_{41}=3.20-0.020(41)=2.38. \]

Because the dependent variable is recorded in percentage units, this result represents an annualized inflation rate of 2.38%. The December 2026 observation of 2.46% includes a realized residual around its fitted trend value. Starting from that observation and adding six monthly trend changes would therefore produce a different forecasting procedure from the specified linear trend.

Why each answer fits or falls short

• A. This substitutes the six-month forecast horizon for the original time index, incorrectly calculating \(3.20-0.020(6)=3.08\).
• B. June 2027 corresponds to \(t=41\), so the fitted trend gives \(3.20-0.020(41)=2.38\), representing inflation of 2.38%.
• C. This adds six months of trend change to the last actual observation, giving \(2.46-6(0.020)=2.34\), rather than evaluating the fitted trend.

Related terms: Linear trend; Time index; Point forecast.

Question 2

Under the linear trend, the expected decline in the reported inflation rate over a 12-month interval is closest to:

• A. 0.24 percentage points, equivalent to 24 basis points.
• B. 0.02 percentage points, equivalent to 2 basis points.
• C. 24.00 percentage points, equivalent to 2,400 basis points.

Best answer: A

Explanation

The slope’s units follow from the dependent variable and time index. Inflation is entered as a numeric percentage rate, while time advances monthly, so the slope represents a decrease of 0.020 percentage points per month.

\[ \left|\Delta\widehat{y}\right|=12(0.020)=0.24\text{ percentage points}. \]

One percentage point equals 100 basis points, making the 12-month decline 24 basis points. This is an absolute change in the reported annualized inflation rate, not a 0.24% proportional decline from its starting level. Moving 12 steps along the trend also does not require compounding a return: the specified model adds the same percentage-point change at each monthly step.

Why each answer fits or falls short

• A. Twelve monthly steps imply a decline of \(12(0.020)=0.24\) percentage points, and each percentage point equals 100 basis points.
• B. This is the decline over one monthly time step; using it for a 12-month interval omits multiplication by 12.
• C. This treats the slope as a decimal-rate change rather than a percentage-point change, overstating the 12-month decline by a factor of 100.

Related terms: Percentage point; Basis point; Rate scaling; Trend coefficient.

Question 3

As the forecast horizon increases, which description best compares the sizes of the month-to-month decreases in the two fitted inflation paths?

• A. Decreases remain constant under both the log-linear and linear models.
• B. Decreases shrink under the log-linear model and remain constant under the linear model.
• C. Decreases grow under the log-linear model and remain constant under the linear model.

Best answer: B

Explanation

The exponentiated log-linear trend implies a constant ratio between successive fitted inflation rates. Writing its fitted path as \(\widetilde{y}_t\):

\[ \frac{\widetilde{y}_{t+1}}{\widetilde{y}_t}=e^{-0.0070}\approx0.9930. \]

Thus, the fitted inflation rate decreases by approximately 0.70% of its preceding value each month. Its percentage-point decrease is:

\[ \widetilde{y}_t-\widetilde{y}_{t+1}=\widetilde{y}_t\left(1-e^{-0.0070}\right). \]

As the fitted rate falls, this absolute decrease becomes smaller. The linear specification instead imposes an unchanged absolute decrease each month. The log-linear fitted path also remains positive and approaches zero, whereas an unrestricted negative linear trend can eventually project negative inflation. These are implications of the specifications, not guarantees about future economic behavior.

Why each answer fits or falls short

• A. The log-linear coefficient fixes the proportional change in inflation, not its percentage-point change, so its absolute monthly decrease is not constant.
• B. The log-linear path applies a constant proportional decrease to a shrinking inflation rate, while the linear path maintains a fixed percentage-point decrease.
• C. The negative log slope produces progressively smaller fitted inflation rates, making successive percentage-point decreases smaller rather than larger.

Related terms: Log-linear trend; Proportional change; Exponential decay.

Question 4

Which assessment of the linear model’s two-sided 95% prediction interval for a single December 2029 inflation observation is most appropriate?

• A. Its half-width is approximately 0.49 percentage points; potential policy-regime changes are incorporated.
• B. Its half-width is approximately 0.49 percentage points; potential policy-regime changes are not incorporated.
• C. Its half-width is approximately 0.32 percentage points; potential policy-regime changes are not incorporated.

Best answer: B

Explanation

A prediction interval for one future observation includes both coefficient estimation uncertainty and a new disturbance. Let \(s_f\) denote the forecast standard error, \(s\) the residual standard error, and \(S_{tt}\) the sum of squared time deviations. December 2029 corresponds to \(t_f=71\).

\[ s_f=s\sqrt{1+\frac{1}{n}+\frac{(t_f-\bar t)^2}{S_{tt}}}=0.18\sqrt{1+\frac{1}{36}+\frac{(71-17.5)^2}{3{,}885}}\approx0.239. \]

The 95% half-width is therefore \(2.03(0.239)\approx0.49\) percentage points. The leading 1 inside the square root captures the future disturbance; the remaining terms capture coefficient uncertainty. Estimation uncertainty increases as the forecast date moves farther from the sample’s mean time index.

This interval remains conditional on the historical model being applicable. The new policy framework could change the trend, disturbance variance, or both. Widening the statistical interval with forecast distance does not automatically incorporate that structural-break risk.

Why each answer fits or falls short

• A. The numerical half-width reflects historical disturbance and coefficient uncertainty, not the effects of the announced policy framework absent from the estimated model.
• B. Including future disturbance and coefficient uncertainty gives approximately 0.49 percentage points, but the historical-model interval does not incorporate an unmodeled policy-regime change.
• C. The 0.32 percentage-point half-width omits the future disturbance, measuring uncertainty in the fitted conditional mean rather than a single future observation.

Related terms: Prediction interval; Parameter uncertainty; Forecast variance; Structural break.

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Practice Vignette 2

Topic: Quantitative Methods

Cedar Vale’s Equity Forecasting Pilot

Maya Iqbal, a quantitative analyst at Cedar Vale Asset Management, is planning a US equity forecasting project. The proposed predictors combine earnings-release and conference-call text with market data and analyst estimates.

Trading mandate

Forecasts are frozen at 18:00 New York time on each scheduled forecast date. Orders execute at the following trading session’s opening auction. Each portfolio holds the highest-ranked fifth of eligible stocks, equally weighted, until the opening auction 20 trading sessions after entry. Forecasts recur every 20 trading sessions.

The investment committee wants to maximize average benchmark-relative total return after transaction costs. Every candidate portfolio must satisfy the same sector and risk limits. Relative performance is measured as an arithmetic percentage-point difference, not a relative wealth ratio.

Individual-stock training targets must exclude transaction costs. Portfolio evaluation must deduct 0.15% per one-way dollar traded. All returns are in USD. Cash dividends are retained without interest until exit; ignore taxes and other corporate actions.

Completed historical observation

Iqbal has the following completed observation for constructing a training label. Its realized outcomes are not proposed as predictors.

Research archive and pilot cutoff

The development archive covers 2015–2024 and preserves document versions, receipt timestamps, and return-label ending dates. There is sufficient history for rolling chronological validation and a separate final holdout. At every simulated forecast, training observations must have completed their holding periods. The team has not yet selected text transformations, a model, or a primary evaluation criterion.

The pilot forecast is frozen at 18:00 on 30 June 2025, with execution at 09:30 on 1 July. Its feature snapshot uses the team’s research archive. The following timestamps are New York time in 2025 and refer to the specific candidate versions shown.

An original transcript was available earlier, but the proposed transcript feature uses the corrected version shown.

Question 5

Using the completed historical observation, the stock’s training target is closest to:

• A. 2.00%
• B. 3.00%
• C. 5.14%

Best answer: B

Explanation

The target must represent the benchmark-relative total return over the period the strategy can actually invest. Let \(P_0\) and \(P_1\) denote entry and exit prices, \(D\) the cash dividend per share, and \(R_B\) the benchmark return over that same interval. The training label is:

\[ y = \frac{P_1-P_0+D}{P_0}-R_B = \frac{104-100+1}{100}-0.02 = 0.03 = 3.00\%. \]

The forecast-date close precedes execution, so using it would include a price movement the strategy could not capture. Including the dividend aligns the label with total return. Transaction costs remain outside this security-level label because the mandate applies them during portfolio evaluation.

Why each answer fits or falls short

• A. This result subtracts the benchmark return from the stock’s price return but omits the $1.00 dividend required for total return.
• B. The investable stock total return is 5.00%, and subtracting the matching 2.00% benchmark return produces a 3.00% target.
• C. This result incorrectly uses the $98.00 forecast-date close rather than the $100.00 executable entry price as the return’s starting value.

Related terms: Target variable; Forecast horizon; Total return; Benchmark-relative return.

Question 6

Which proposed project sequence would best support an unbiased assessment of future forecasting performance?

• A. Define the target and cutoff; split chronologically; fit text transformations and tune models within development folds; lock the pipeline and test once on the final holdout.
• B. Define the target and cutoff; fit text transformations on the complete archive; split chronologically and tune within development folds; lock the pipeline and test once on the final holdout.
• C. Define the target and cutoff; split chronologically; fit and tune pipelines within development folds; compare candidates on the final holdout to select the deployed model.

Best answer: A

Explanation

A defensible project begins with the economic objective, target horizon, and information boundary. Chronological partitions then reproduce the direction in which information becomes available during deployment. Within rolling development folds, learned text transformations, such as vocabulary selection and term weighting, must be estimated using only the training portion. Hyperparameters and model choices are evaluated on subsequent development observations, with training labels already observable at each forecast cutoff.

After development, the selected pipeline is locked and assessed once on the final holdout. This separation distinguishes model selection from performance estimation. Even an unsupervised text transformation can transmit future information when fitted on the complete archive, while repeated comparisons on the final holdout make its results part of the selection process.

Why each answer fits or falls short

• A. This sequence establishes the investment task first, confines model development to historical folds, and preserves an untouched sample for final assessment.
• B. Fitting transformations on the complete archive allows future validation and holdout documents to influence features before chronological separation.
• C. Using final-holdout results to select the deployed model turns that sample into selection data and biases its performance estimate.

Related terms: Time-series cross-validation; Data leakage; Holdout sample; Text preprocessing.

Question 7

Which proposed predictor would introduce look-ahead bias into the pilot forecast?

• A. Uncertainty-word frequency calculated from the corrected call transcript.
• B. Estimate dispersion calculated from the archived analyst-estimate snapshot.
• C. Sentiment calculated from the archived earnings-release text.

Best answer: A

Explanation

Predictor availability is determined by the frozen forecast cutoff and the exact data version used, not merely by the date of the underlying event. Although the conference call occurred on 27 June, the corrected transcript was first received at 07:05 on 1 July. Its contents were unavailable at 18:00 on 30 June.

Receipt before the opening auction does not make that version valid for an already-frozen forecast. Using it would reconstruct a prediction with information unavailable when the prediction was made. Point-in-time testing therefore requires archived document vintages and receipt timestamps; replacing historical text with a later corrected version can create look-ahead bias even when the original document was available.

Why each answer fits or falls short

• A. The corrected transcript arrives after the frozen forecast cutoff, even though the call occurred earlier and the correction arrives before trade execution.
• B. The analyst-estimate snapshot was received at 17:10 on 30 June and was therefore available before the forecast was frozen.
• C. The specified earnings-release version was received at 16:12 on 30 June, before the 18:00 forecast cutoff.

Related terms: Look-ahead bias; Point-in-time data; Data vintage; Information set.

Question 8

Which primary out-of-sample evaluation criterion best matches the investment committee’s stated objective?

• A. Average squared error across all individual-stock holding-period return forecasts.
• B. Average cross-sectional Spearman rank correlation across all eligible stocks.
• C. Average after-cost benchmark-relative return of the strategy’s implemented portfolio.

Best answer: C

Explanation

Evaluation should reflect the operational decision that consumes the forecasts. Cedar Vale buys only the highest-ranked fifth of stocks, so improvements elsewhere in the ranking or in numerical forecast precision need not improve investment results.

For each out-of-sample forecast, the team should construct the prescribed portfolio, apply the actual entry and exit timing, deduct 0.15% per one-way dollar traded, and calculate its benchmark-relative return. Averaging those returns directly addresses the committee’s objective, given that all candidates satisfy the same risk constraints. Rank correlation and squared forecast error remain useful diagnostic measures, but neither captures the complete selection-and-trading process. In particular, attractive gross forecasts can produce disappointing net results when they induce excessive turnover.

Why each answer fits or falls short

• A. Squared error measures forecast accuracy across all stocks rather than the economic performance of the highest-ranked fifth after implementation costs.
• B. Rank correlation measures ordering across the entire universe but does not directly measure the selected portfolio’s returns or trading costs.
• C. This criterion directly measures the committee’s desired economic outcome using the actual selection rule, holding period, benchmark, and trading costs.

Related terms: Economic significance; Rank information coefficient; Transaction costs; Portfolio turnover.

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Practice Vignette 3

Topic: Economics

Marston Components’ Currency Execution Review

Nadia Kline is a treasury analyst at Marston Components, a U.S.-based manufacturer whose functional currency is the U.S. dollar. She obtains simultaneous executable quotations from Alder Bank and Birch Bank for two planned currency transactions.

Treasury requirements

• Sell EUR4 million currently held to fund immediate USD operating payments.
• Purchase EUR2.5 million for a supplier payment due on the three-month forward value date.

Treasury is also evaluating a possible separate EUR15 million spot sale, executed as one all-or-none ticket.

Dealer quotations

All exchange rates are expressed as USD per EUR: EUR is the base currency and USD is the price currency. Bid and offer refer to the dealer buying and selling EUR, respectively.

Spot transactions settle in two business days. Three-month forwards settle three calendar months after the spot value date. Forward points are signed and expressed in units of USD0.0001 per EUR for the full tenor.

The following quotations are firm for transactions of up to EUR5 million per ticket. Execution charges are flat USD amounts per transaction, payable on its value date. There are no other charges or taxes.

Larger-order inquiry

For the potential EUR15 million spot transaction, Alder provides a separate firm quotation of 1.0843 bid and 1.0852 offer, with no execution charge. This quotation is obtained at the same time as the standard-size quotations. Market volatility, settlement terms, and Marston’s credit standing are unchanged.

Question 9

Using Alder’s quotation, the USD amount Marston must pay on the forward value date to purchase EUR2.5 million is closest to:

• A. $2,721,750.
• B. $2,702,750.
• C. $2,701,000.

Best answer: B

Explanation

Marston is purchasing the base currency, EUR, so the executable side is the dealer’s offer. An outright forward quotation is obtained by adding the signed forward points to the corresponding spot quotation. Alder’s three-month forward offer, in USD per EUR, is:

\[1.0849+(-38)(0.0001)=1.0811\]

The required value-date payment is therefore:

\[2{,}500{,}000(1.0811)=2{,}702{,}750\]

The three-month tenor does not require annualizing the points or discounting this contractual settlement amount. Alder charges no execution fee. Its bid would apply to a customer selling EUR, which is the opposite transaction direction.

Why each answer fits or falls short

• A. This amount incorrectly subtracts the negative offer points, producing 1.0887 instead of adding the signed adjustment to the spot offer.
• B. Alder’s forward offer is \(1.0849-0.0038=1.0811\) USD per EUR, producing a payment of $2,702,750.
• C. This amount uses Alder’s forward bid of 1.0804, which applies when Marston sells EUR rather than purchases EUR.

Related terms: Forward points; Outright forward rate; Offer rate; Base currency.

Question 10

Excluding execution charges, Alder’s standard-size spot bid-offer spread, expressed as a percentage of the quotation midpoint, is closest to:

• A. 0.0553%.
• B. 0.0138%.
• C. 0.0277%.

Best answer: C

Explanation

A midpoint-based percentage spread divides the full difference between the offer and bid by their arithmetic midpoint. Alder’s midpoint, in USD per EUR, is:

\[\frac{1.0846+1.0849}{2}=1.08475\]

Its quoted percentage spread is:

\[\frac{1.0849-1.0846}{1.08475}\times100=0.027656\%\approx0.0277\%\]

The denominator matters. For an immediate USD-to-EUR-to-USD round trip at unchanged quotations, the percentage loss relative to starting USD would instead divide the bid-offer difference by the offer. Thus, a quoted percentage spread and a round-trip percentage cost need not be identical. Neither measure includes separate execution charges unless explicitly adjusted for them.

Why each answer fits or falls short

• A. This percentage doubles the full bid-offer difference, incorrectly counting the quoted spread twice.
• B. This percentage divides only the half-spread of 0.00015 by the midpoint, rather than using the full quoted spread.
• C. The full spread is 0.0003 USD per EUR, and dividing it by the midpoint of 1.08475 gives approximately 0.0277%.

Related terms: Bid-offer spread; Midpoint quotation; Round-trip transaction cost; Price currency.

Question 11

For Marston’s planned EUR4 million spot sale, which dealer provides the highest net USD proceeds after the stated execution charge?

• A. Birch, with net proceeds of $4,338,800.
• B. Birch, with net proceeds of $4,339,800.
• C. Alder, with net proceeds of $4,338,400.

Best answer: C

Explanation

Marston sells EUR, so each dealer’s bid determines gross USD proceeds. The flat USD charge must then be deducted before comparing executable outcomes. Let \(N_A\) and \(N_B\) represent net USD proceeds from Alder and Birch, respectively:

\[N_A=4{,}000{,}000(1.0846)-0=4{,}338{,}400\]\[N_B=4{,}000{,}000(1.0847)-600=4{,}338{,}200\]

Alder provides $200 more. Birch’s higher bid improves gross proceeds by $400, but that improvement is smaller than its $600 charge. Dealer selection therefore requires comparing total proceeds for the actual transaction size, not simply choosing the highest displayed bid.

Why each answer fits or falls short

• A. This is Birch’s gross bid-side proceeds; deducting its $600 execution charge reduces net proceeds to $4,338,200.
• B. This amount applies Birch’s offer and deducts its fee, but a customer selling EUR receives the dealer’s bid.
• C. Alder’s bid-side proceeds are $4,338,400 with no charge, exceeding Birch’s net proceeds of $4,338,200.

Related terms: Bid rate; Net proceeds; Transaction costs; Executable quotation.

Question 12

Using each quotation’s midpoint as the reference value, which interpretation of Alder’s pricing for the EUR15 million spot sale is most appropriate relative to its standard-size quotation?

• A. The larger trade has a lower liquidity cost per euro, reflecting fixed processing costs spread over more euros.
• B. The larger trade has a higher liquidity cost per euro, consistent with greater market-depth and inventory risk.
• C. The larger trade has an unchanged liquidity cost per euro, reflecting the unchanged midpoint of the quotations.

Best answer: B

Explanation

A larger transaction can consume more available market depth and leave a dealer with greater inventory exposure. A wider spread can compensate for these risks even when the quotation midpoint is unchanged.

Both Alder quotations have a midpoint of $1.08475 per EUR. For a customer selling EUR, the concession relative to that midpoint rises from $0.00015 per EUR under the standard quote to $0.00045 per EUR under the large-order quote. The liquidity cost per euro therefore increases. The unchanged market conditions and credit standing support a transaction-size explanation rather than a change in market volatility or counterparty risk.

Why each answer fits or falls short

• A. Any processing economies do not produce a lower quoted execution cost, because Alder’s bid moves farther below the midpoint.
• B. Alder’s lower bid increases the seller’s concession relative to the unchanged midpoint, consistent with greater risk from the larger order.
• C. An unchanged midpoint does not preserve execution cost when the executable bid moves farther below that reference value.

Related terms: Market depth; Dealer inventory risk; Liquidity cost; Order size.

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Practice Vignette 4

Topic: Financial Statement Analysis

Asteron Europe’s Year-End Review

Lina Shah, an analyst at Asteron Instruments, is reviewing the financial statements of Asteron Europe for consolidation. The group reports under IFRS in US dollars. Asteron Europe’s functional currency is also the US dollar, although it maintains its accounting records in euros. Shah must remeasure those records into dollars for the year ended 31 December 2027.

Assets and liabilities

The following table contains all asset and liability balances in Asteron Europe’s euro ledger at year-end. There are no hedging instruments. Ignore income taxes throughout the analysis.

The external bank loan was issued at par on 1 July 2027. There have been no principal repayments, and there are no discounts or unamortized fees. All interest was paid by year-end.

Trade payables include an unpaid €240,000 inventory purchase made on 1 November 2027.

Inventory and plant records

Inventory is measured using FIFO at historical cost. Ending inventory consists entirely of these two layers:

All plant was acquired on 1 January 2024 and is measured using the historical-cost model. No inventory write-downs, plant impairments, or revaluations are required in either currency.

Exchange rates

Rates are quoted as US dollars per euro; a lower rate indicates a weaker euro.

Question 13

What US dollar carrying amount should Shah report for the long-term bank loan at 31 December 2027?

• A. $696,000
• B. $684,000
• C. $624,000

Best answer: C

Explanation

A monetary liability requires payment of a fixed or determinable number of currency units. Because Asteron Europe’s functional currency is the US dollar, its euro bank loan must be remeasured using the closing exchange rate. Its long-term classification does not change this treatment.

\[ \text{Loan carrying amount in dollars} = 600{,}000 \times 1.04 = 624{,}000 \]

The issuance-date rate establishes the liability’s initial dollar amount, not its subsequent year-end measurement. An annual average rate may approximate transaction-date rates for certain income statement items, but it does not measure an outstanding monetary balance.

Why each answer fits or falls short

• A. This amount uses the loan’s issuance-date rate, but a monetary liability must be remeasured using the reporting-date rate.
• B. This amount uses the annual average rate, which is inappropriate for measuring an outstanding monetary liability at the reporting date.
• C. The loan is a monetary liability, so its carrying amount is \(600{,}000 \times 1.04 = 624{,}000\) dollars at year-end.

Related terms: Monetary liabilities; Closing exchange rate; Functional currency.

Question 14

What is the remeasured US dollar carrying amount of ending inventory at 31 December 2027?

• A. $312,000
• B. $332,000
• C. $342,000

Best answer: B

Explanation

Inventory measured at historical cost is a nonmonetary asset. When local-currency records are remeasured into the functional currency, each remaining inventory layer retains the exchange rate applicable when that layer was acquired. The case identifies the FIFO layers directly, so no estimate of purchase timing is necessary.

\[ \text{Inventory in dollars} = (200{,}000 \times 1.12) + (100{,}000 \times 1.08) = 332{,}000 \]

The closing rate does not replace these historical rates merely because inventory appears on the year-end balance sheet. No separate valuation adjustment is needed because the case excludes inventory write-downs.

Why each answer fits or falls short

• A. This amount applies the closing rate to all inventory, incorrectly treating a historical-cost nonmonetary asset as a monetary balance.
• B. The remaining September and November layers retain their historical rates, giving \(200{,}000 \times 1.12 + 100{,}000 \times 1.08 = 332{,}000\) dollars.
• C. This amount applies the annual average rate to ending inventory instead of the historical rates associated with its remaining purchase layers.

Related terms: Nonmonetary assets; Historical exchange rate; FIFO inventory; Temporal method.

Question 15

Which foreign exchange effect attributable solely to the unpaid €240,000 supplier liability originating on 1 November should be reported for 2027?

• A. A $9,600 loss in profit or loss.
• B. A $9,600 gain in other comprehensive income.
• C. A $9,600 gain in profit or loss.

Best answer: C

Explanation

A liability denominated in a currency other than the entity’s functional currency is initially recognized at the transaction-date rate and subsequently remeasured at the closing rate. The supplier payable was initially recorded at $259,200 and has a year-end carrying amount of $249,600.

\[ \text{Exchange gain in dollars} = 240{,}000(1.08 - 1.04) = 9{,}600 \]

The weaker euro reduces the dollars needed to settle the fixed euro obligation. Under IFRS, this exchange difference is recognized in profit or loss. It is not a translation adjustment from converting financial statements prepared in a different functional currency into the group’s presentation currency.

Why each answer fits or falls short

• A. The payable’s dollar value decreases from $259,200 to $249,600, reducing the obligation and producing a gain rather than a loss.
• B. The gain arises from remeasuring a foreign-currency monetary liability into the subsidiary’s functional currency, so it belongs in profit or loss.
• C. The payable’s dollar value falls by \(240{,}000 \times (1.08 - 1.04) = 9{,}600\), producing an exchange gain recognized in profit or loss.

Related terms: Foreign exchange gain; Profit or loss; Functional currency; Other comprehensive income.

Question 16

Immediately after year-end, the USD-per-euro exchange rate falls by 5% from its 31 December level. All euro balances remain unchanged, and no transactions, depreciation, or valuation write-downs occur. What incremental remeasurement effect on pretax profit would this movement produce?

• A. A $26,000 loss.
• B. A $36,400 gain.
• C. A $36,400 loss.

Best answer: B

Explanation

Immediate remeasurement exposure is determined by the net foreign-currency monetary position, not total net assets. Cash and receivables are monetary assets; trade payables and the bank loan are monetary liabilities. Net monetary assets, measured in euros, are:

\[ M = 100{,}000 + 300{,}000 - 500{,}000 - 600{,}000 = -700{,}000 \]

The exchange rate falls from 1.04 to \(1.04 \times 0.95 = 0.988\) dollars per euro, a decline of 0.052. Therefore:

\[ \text{Remeasurement gain in dollars} = (-700{,}000)(-0.052) = 36{,}400 \]

Dollar liabilities decline more than dollar monetary assets, generating a gain in pretax profit. Historical-cost inventory and plant retain their historical dollar measurements and do not contribute to this immediate exchange-rate effect.

Why each answer fits or falls short

• A. This loss applies the exchange-rate change to total euro net assets, incorrectly including historical-cost inventory and plant in the remeasurement exposure.
• B. Net euro monetary liabilities are €700,000, so the rate decline of $0.052 per euro produces a \(700{,}000 \times 0.052 = 36{,}400\) dollar gain.
• C. The magnitude reflects the net monetary position, but euro depreciation benefits a net euro monetary liability position rather than causing a loss.

Related terms: Net monetary exposure; Remeasurement gain; Currency depreciation; Historical-cost accounting.

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Practice Vignette 5

Topic: Financial Statement Analysis

Asteron’s Investment Portfolio Review

Lena Maric, an equity analyst, is reviewing Asteron Manufacturing plc’s consolidated financial statements for the year ended 31 December 2027. Asteron applies IFRS and is not an investment entity. All amounts are in € millions unless otherwise indicated. Ignore taxes, impairment, transaction costs and foreign exchange effects.

Debt and minority equity holdings

Rovel notes: Asteron manages these notes within a portfolio whose objective is both collecting contractual cash flows and selling financial assets. The notes repay principal in full at maturity in 2031. Annual payments equal 4% of principal plus 0.5% of Rovel’s positive EBITDA. The EBITDA-linked payment is uncapped and economically significant. Asteron has not elected the fair value option.

Selia shares: Asteron acquired a 6% interest in Selia for €4.0 million during 2026. The shares were not held for trading, and Asteron had no board representation or participation in Selia’s policy decisions. At initial recognition, Asteron irrevocably elected to present subsequent fair value changes in other comprehensive income. The holding’s fair value was €5.2 million on 1 January 2027. During 2027, Asteron received €0.24 million of ordinary dividends from Selia’s earnings and subsequently sold the entire holding for its then fair value of €6.0 million.

Governance arrangements

Dorsen: Asteron owns 42% of the ordinary voting shares. Throughout 2027, an enforceable shareholder agreement gives Asteron the current, substantive right to appoint and remove four of Dorsen’s seven directors. The board directs the relevant operating and financing activities by simple majority. Other shareholders cannot override these decisions. A lender can veto liquidation and changes to Dorsen’s constitution, but cannot participate in ordinary operating or financing decisions.

Orton: Asteron owns 30% of the ordinary voting shares and appoints two of seven directors. Through these directors, Asteron participates in financial and operating policy decisions. The other shareholders appoint the remaining directors. Board decisions require a simple majority, and Asteron has no special veto or other contractual decision-making rights.

Ventra: Asteron and an unrelated partner each own 50% of this separate incorporated entity. Their binding agreement requires unanimous consent for decisions about Ventra’s relevant activities. The agreement gives the shareholders rights only to Ventra’s net assets, rather than direct rights to its assets or obligations for its liabilities.

Acquisition amounts and annual results

Asteron acquired its Orton and Ventra interests on 1 January 2027. The following figures are the investees’ reported amounts unless identified as Asteron’s investment cost.

Each investment’s cost equaled Asteron’s share of the investee’s identifiable net assets at acquisition-date fair value. Asteron’s share of Orton’s equipment fair value uplift was €1.5 million. That equipment had a five-year remaining useful life, no residual value and straight-line depreciation. All other acquisition-date fair values equaled carrying amounts.

Orton and Ventra had no other comprehensive income, other equity changes or transactions with Asteron during 2027 apart from the dividends described.

Question 17

Under IFRS 9, Asteron’s investment in the Rovel notes should be classified as measured at:

• A. Fair value through other comprehensive income.
• B. Fair value through profit or loss.
• C. Amortized cost.

Best answer: B

Explanation

IFRS 9 classification of debt investments depends on both the business model and the contractual cash-flow characteristics. Amortized cost and debt FVOCI require cash flows that are solely payments of principal and interest, commonly called the SPPI condition. Interest under this condition compensates for basic lending risks and costs, including the time value of money and credit risk. Rovel’s uncapped, economically significant EBITDA-linked payment introduces exposure to the issuer’s operating performance. Consequently, the notes fail SPPI and must be measured at fair value through profit or loss, notwithstanding Asteron’s collect-and-sell business model. The absence of a fair value option election does not change this mandatory classification.

Why each answer fits or falls short

• A. The collect-and-sell business model supports this classification only when contractual cash flows qualify as solely payments of principal and interest.
• B. The material EBITDA-linked payment exposes Asteron to issuer performance rather than basic lending risks, causing the notes to fail the contractual cash-flow test.
• C. Amortized cost requires both a hold-to-collect business model and qualifying contractual cash flows, whereas Rovel’s notes satisfy neither condition.

Related terms: SPPI test; Business model assessment; Fair value through profit or loss.

Question 18

Which accounting treatment is most appropriate for Asteron’s Selia investment during 2027?

• A. Fair value through OCI, with €0.24 million recognized in profit or loss.
• B. Fair value through OCI, with €2.24 million recognized in profit or loss.
• C. Fair value through profit or loss, with €1.04 million recognized in profit or loss.

Best answer: A

Explanation

For an eligible equity investment not held for trading, IFRS 9 permits an irrevocable election at initial recognition to present subsequent fair value changes in OCI. Asteron made that election for Selia. The 2027 fair value increase of €0.8 million is therefore recognized in OCI rather than profit or loss. Upon disposal, the cumulative gain of €2.0 million is not reclassified to earnings, although it may be transferred between components of equity. Ordinary dividends are recognized in profit or loss unless they clearly represent recovery of investment cost. Selia’s €0.24 million dividend is a distribution of earnings, so it is the investment’s only contribution to Asteron’s 2027 profit or loss.

Why each answer fits or falls short

• A. The irrevocable equity FVOCI election keeps fair value gains outside earnings, while the €0.24 million ordinary dividend is recognized in profit or loss.
• B. This amount adds the €2.0 million cumulative fair value gain to dividends, but an equity FVOCI disposal does not recycle gains into earnings.
• C. This treatment incorrectly reverses the irrevocable FVOCI election and includes the €0.8 million current-year fair value increase in earnings.

Related terms: Equity FVOCI election; OCI recycling; Dividend income; Derecognition.

Question 19

Based on the governance arrangements, Asteron’s relationship with Dorsen is most appropriately characterized as:

• A. Significant influence without control.
• B. Control.
• C. Joint control.

Best answer: B

Explanation

Under IFRS 10, control requires power over an investee, exposure or rights to variable returns, and the ability to use that power to affect those returns. Majority ownership is not necessary when substantive contractual rights provide power. Asteron can currently appoint and remove four of seven directors, and that board directs Dorsen’s relevant activities by simple majority. Its ordinary shareholding provides exposure to variable returns. The lender’s vetoes concern liquidation and constitutional changes, rather than ordinary relevant activities, and are protective under these facts. They do not prevent Asteron from controlling Dorsen or establish joint control. Asteron must therefore consolidate Dorsen despite owning less than half its voting shares.

Why each answer fits or falls short

• A. The 42% ownership interest does not limit Asteron to significant influence because its contractual board appointment rights provide unilateral decision-making power.
• B. Asteron’s substantive right to appoint a board majority gives it power over relevant activities and the ability to affect returns from its ownership.
• C. The lender’s protective vetoes do not require shared consent over relevant activities and therefore do not create joint control.

Related terms: IFRS 10 control; Substantive rights; Protective rights; Relevant activities.

Question 20

For Orton and Ventra combined, the amounts included in Asteron’s consolidated total assets at 31 December 2027 and consolidated 2027 profit or loss are closest to:

• A. €29.7 million in assets and €3.8 million in profit or loss.
• B. €30.5 million in assets and €3.5 million in profit or loss.
• C. €29.4 million in assets and €3.5 million in profit or loss.

Best answer: C

Explanation

Orton is an associate because Asteron has significant influence, while Ventra is a joint venture because unanimous consent governs relevant activities and the parties have rights to net assets. Both investments use the equity method in Asteron’s consolidated financial statements. Equity-method income includes the investor’s share of earnings after acquisition-date fair value adjustments; dividends reduce the investment carrying amount.

All calculations below are in € millions. Orton’s additional annual depreciation is \(1.5/5 = 0.3\). Asteron’s adjusted share of income is \(0.30 \times 6.0 - 0.3 = 1.5\), giving a closing investment balance of \(15.0 + 1.5 - 0.30 \times 2.0 = 15.9\).

Ventra contributes income of \(0.50 \times 4.0 = 2.0\) and a closing investment balance of \(12.0 + 2.0 - 0.50 \times 1.0 = 13.5\).

The combined contributions are therefore €29.4 million to assets and €3.5 million to profit or loss.

Why each answer fits or falls short

• A. These amounts omit the €0.3 million annual depreciation adjustment for Asteron’s share of Orton’s acquisition-date equipment fair value uplift.
• B. The earnings amount is properly adjusted, but the asset amount fails to deduct Asteron’s €1.1 million share of dividends from the investment balances.
• C. Adjusted equity-method income totals €3.5 million, and the combined carrying amount is €27.0 million plus that income less €1.1 million of dividends.

Related terms: Equity method; Joint venture; Significant influence; Acquisition-date fair value adjustments.

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Practice Vignette 6

Topic: Financial Statement Analysis

Alder Industrial Systems: Growth and Cash Generation

Mira Sen, CFA, is reviewing the earnings quality of Alder Industrial Systems, a fictional equipment manufacturer reporting under IFRS. Alder introduced a new product line during 2026. Management cites higher earnings and year-end cash as evidence of improved financial performance.

All monetary amounts are in € millions. Financial years end on 31 December. There were no acquisitions, foreign currency translation effects, revaluations, or noncash debt transactions.

Reported Results and Financial Position

Operating cash flow was 45 in 2025.

All assets other than cash are operating assets. Trade payables and other operating liabilities are the company’s only operating liabilities; the latter include payroll, warranty, and income tax accruals.

Cash Movements and Reconciliations

• Net property, plant and equipment changed only through cash purchases of 48, depreciation of 24, and disposal of equipment with a carrying amount of 12.
• Equipment-sale proceeds were 18. The resulting gain of 6 is included in 2026 net income.
• The debt increase consists entirely of cash borrowing net of principal repayments. Cash dividends were 24. There were no other investing or financing cash flows.
• Interest and income taxes paid are classified as operating cash flows; dividends paid are financing cash flows.
• Using changes in net receivables, the indirect operating cash flow reconciliation requires no adjustments beyond depreciation, the disposal gain, and changes in the operating assets and liabilities shown.

Working-Capital Review

Gross receivables increased from 95 to 143, while the expected credit loss allowance remained at 5. During 2026, impairment expense and receivable write-offs were each 3. Receivables more than 90 days overdue increased from 6 to 18. Customer credit terms remained unchanged at 60 days.

Of the 36 increase in inventory, Sen verifies that 24 supports signed, noncancelable customer orders scheduled for delivery in the first quarter of 2027 at positive expected margins. The remaining increase consists of ordinary finished goods. Alder made no change to its inventory valuation policy.

Question 21

Alder’s 2026 ratio of operating cash flow to net income is closest to:

• A. 80%
• B. 20%
• C. 40%

Best answer: B

Explanation

The indirect method adjusts net income for noncash items, investing gains, and changes in operating working capital. Increases in receivables and inventory consume cash, whereas increases in operating liabilities provide cash. Using the reported net receivable balances avoids double-counting the allowance adjustment.

For 2026, operating cash flow, in € millions, is:

\[ \mathrm{CFO}=60+24-6-(138-90)-(156-120)+(96-84)+(32-26)=12. \]

Therefore, operating cash flow represents only \(12/60=20\%\) of reported net income, compared with \(45/48=93.75\%\) in 2025. Reported earnings have grown, but their immediate operating cash support has weakened substantially. This divergence warrants investigation rather than automatically establishing improper accounting.

Why each answer fits or falls short

• A. This ratio results from omitting the 36 inventory increase, incorrectly producing operating cash flow of 48.
• B. Operating cash flow is 12 after the noncash and working-capital adjustments, giving a ratio of \(12/60=20\%\).
• C. This ratio results from adding the disposal gain rather than subtracting it, incorrectly producing operating cash flow of 24.

Related terms: Operating cash flow; Indirect method; Cash conversion; Working capital.

Question 22

Alder’s 2026 balance-sheet-based accruals ratio, using average net operating assets, is closest to:

• A. 18.2%
• B. 22.4%
• C. 16.7%

Best answer: A

Explanation

The balance-sheet approach measures aggregate accruals as the change in net operating assets. Cash is excluded from operating assets, and interest-bearing debt is excluded from operating liabilities.

Beginning and ending net operating assets, in € millions, are:

\[ \mathrm{NOA}_{2025}=(540-40)-(84+26)=390. \]\[ \mathrm{NOA}_{2026}=(684-88)-(96+32)=468. \]

The accruals ratio is therefore:

\[ \frac{468-390}{(390+468)/2}=\frac{78}{429}=18.18\%. \]

The positive ratio reflects accumulation of net operating assets. Higher accruals ratios generally warrant greater scrutiny of earnings persistence, but interpretation requires business context and comparisons over time or with peers. Operating expansion can legitimately increase receivables, inventory, and productive assets; the ratio alone does not establish a misstatement.

Why each answer fits or falls short

• A. Net operating assets increase from 390 to 468, so the accruals ratio is \(78/429=18.2\%\).
• B. This percentage divides the 96 increase in operating assets by average net operating assets, ignoring the 18 increase in operating liabilities.
• C. This percentage divides the 78 increase in net operating assets by ending net operating assets of 468 rather than the average.

Related terms: Net operating assets; Balance-sheet accruals ratio; Operating liabilities; Earnings persistence.

Question 23

For a sources-of-cash analysis, Alder’s 2026 net change in cash after removing net borrowing and equipment-sale proceeds, with all other cash flows held constant, is closest to:

• A. A decrease of €60 million
• B. A decrease of €36 million
• C. A decrease of €42 million

Best answer: A

Explanation

A rising cash balance does not identify the activity that generated the cash. Borrowing and asset disposals can increase cash even when operating cash generation is weak.

Alder’s reported cash increase is \(88-40=48\). Because the debt change contains no noncash transactions, net cash borrowing equals \(290-200=90\). Removing that borrowing and the full equipment-sale proceeds gives, in € millions:

\[ \Delta\mathrm{Cash}_{\text{excluding selected sources}}=48-90-18=-60. \]

The relevant disposal amount is the cash proceeds of 18, not the accounting gain of 6. This analytical bridge holds capital expenditures, dividends, interest, taxes, and other cash flows unchanged. It shows that the reported cash increase depended on financing and asset-sale receipts rather than sufficient internally generated cash.

Why each answer fits or falls short

• A. Removing net borrowing of 90 and disposal proceeds of 18 from the reported cash increase of 48 produces a decrease of 60.
• B. This amount also excludes the 24 cash dividend, which must remain included because all other cash flows are held constant.
• C. This amount removes the 90 of net borrowing from the cash increase but leaves the 18 of equipment-sale proceeds included.

Related terms: Financing cash flow; Asset-sale proceeds; Cash flow sustainability; Sources of liquidity.

Question 24

Which conclusion about Alder’s 2026 earnings quality is best supported by the combined evidence?

• A. Higher cash balances support improved earnings quality; the disposal gain is the main item requiring normalization.
• B. Weak operating cash support and worsening receivable aging raise quality concerns; order-backed inventory growth has a plausible operating explanation.
• C. Stable allowance balances suggest stable receivable risk; inventory growth exceeding sales growth is the main quality concern.

Best answer: B

Explanation

Earnings quality assessment combines profitability, operating cash generation, asset realizability, and sources of liquidity. Alder’s earnings growth is accompanied by weak operating cash support, while borrowing and equipment-sale receipts support the increase in cash.

Net receivables grow by approximately 53%, compared with revenue growth of 20%. Receivables more than 90 days overdue triple, yet the allowance remains unchanged. The allowance also falls relative to gross receivables, making collectibility and the expected credit loss estimate important review areas.

Inventory growth is not automatically evidence of earnings distortion. Verified, noncancelable orders explain 24 of the 36 increase and provide an operating rationale for much of the buildup. The combined evidence warrants caution about earnings sustainability and receivable valuation, but it does not establish fraudulent reporting or justify automatically writing down the inventory increase.

Why each answer fits or falls short

• A. Borrowing and disposal proceeds explain the cash increase, while weak operating cash support and deteriorating receivable aging create concerns beyond the disposal gain.
• B. Poor cash conversion and overdue receivable growth warrant scrutiny, while verified customer orders explain a substantial portion of the inventory buildup.
• C. An unchanged allowance does not demonstrate stable credit risk when overdue receivables triple, and signed orders provide context for much of the inventory increase.

Related terms: Earnings sustainability; Receivables aging; Expected credit losses; Inventory recoverability.

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Practice Vignette 7

Topic: Corporate Finance

Ordan Ceramics’ Capital Investment Review

Maya Desai, an investment analyst, is evaluating Ordan Ceramics’ proposed capital allocation. The company operates one plant in a drought-prone region. Its board seeks to maximize expected net present value while complying with applicable environmental and employment requirements.

Ordan has a €24 million capital budget. It may undertake either of two indivisible, mutually exclusive projects or retain the existing plant. Both projects satisfy applicable permit requirements, and unused funds can earn the required return.

Current operating exposures

The regional water authority gives residential supply priority during droughts. Independent engineers estimate a 35% annual probability of restricted industrial water allocations and a 65% probability of normal availability throughout the five-year forecast period.

Finance has identified the following annual exposures for the existing plant. The costs do not overlap.

Lost contribution equals forgone revenue less avoided variable cash costs; fixed cash costs remain unchanged. Purchased water itself costs only €150,000 annually.

Customer contracts reimburse 75% of each plant configuration’s actual carbon charges without affecting sales volumes. The baseline carbon charge remains €50 per tonne throughout the forecast. The cash tax rate is 25%, and all operating tax effects occur in the same year.

Investment alternatives and forecasts

Retrofit combines kiln upgrades with closed-loop water recycling. It preserves production capacity, reduces annual covered emissions to 40,000 tonnes, and lowers water withdrawals by 70%.

Expansion adds conventional production equipment, increasing capacity by 30% and annual covered emissions to 100,000 tonnes. Higher water demand increases its interruption exposure during restrictions.

The independent investment committee has validated the scenario assumptions and reconciled the forecasts with engineering, finance, and workforce estimates. The following amounts are in € millions and are incremental to retaining the existing plant.

The nominal, after-tax, unlevered free cash flows occur at each year-end for five years. They incorporate all forecast carbon charges, customer reimbursements, water interruptions, workforce costs, maintenance investment, and working-capital effects. There are no additional initial or terminal cash flows. An annual discount rate of 10% is appropriate for both projects; the five-year annuity factor is 3.7908.

Board accountability

The CEO’s current project bonus depends only on commissioned nameplate capacity. The CEO favors Expansion, citing its higher normal-water cash flow. The compensation committee is considering a replacement metric covering the full project life. The independent audit committee will verify the financial and environmental inputs to whichever metric is adopted.

Question 25

For the existing plant, which ESG exposure creates the largest expected annual pretax operating cash-flow loss?

• A. Skilled-worker turnover.
• B. Carbon pricing.
• C. Water availability.

Best answer: C

Explanation

Financial materiality depends on an exposure’s effect on cash flows, not simply its environmental prominence or direct purchase cost. Water interruptions have an expected annual pretax loss of:

\[ 0.35 \times 15 \times 300{,}000 = 1{,}575{,}000 \]

The amount is in euros. Carbon charges must be evaluated net of contractual customer reimbursements: 80,000 tonnes at €50 creates a €4 million gross charge, but Ordan bears only 25%, or €1 million. Expected turnover costs are €1.2 million annually. Water availability therefore creates the largest expected loss. The €150,000 direct water bill does not capture water’s financial importance because restricted access also interrupts production and eliminates contribution margin.

Why each answer fits or falls short

• A. The €1.2 million expected turnover cost is financially material, but it is below the €1.575 million expected loss from water interruptions.
• B. Customer reimbursements reduce the €4.0 million gross annual carbon charge to €1.0 million, below the expected water-interruption loss.
• C. The expected annual interruption loss is €1.575 million, exceeding the €1.0 million net carbon charge and €1.2 million turnover cost.

Related terms: Financial materiality; Water stress; Contribution margin; Carbon cost pass-through.

Question 26

For this question only, the carbon charge rises from €50 to €80 per tonne, with all other assumptions unchanged. By how much does this change increase Retrofit’s annual incremental after-tax operating cash flow relative to retaining the existing plant?

• A. €225,000.
• B. €300,000.
• C. €900,000.

Best answer: A

Explanation

A higher carbon charge strengthens Retrofit’s financial advantage because it produces fewer covered emissions than the existing plant. However, customers reimburse most carbon charges, so the avoided gross charge is not entirely retained by Ordan. Lower charges also reduce reimbursement revenue.

Using tonnes and euros per tonne, the increase in annual incremental after-tax operating cash flow, in euros, is:

\[ (80{,}000 - 40{,}000) \times (80 - 50) \times (1 - 0.75) \times (1 - 0.25) = 225{,}000 \]

Both configurations experience higher absolute carbon costs, but Retrofit’s increase is smaller. The €225,000 is the improvement in its relative cash-flow advantage, not an increase in either configuration’s absolute cash flow. No probability weighting is needed because the charge increase applies in both water states.

Why each answer fits or falls short

• A. Avoiding 40,000 tonnes at an extra €30 per tonne leaves a 25% unreimbursed share and a 75% after-tax share.
• B. This amount correctly nets the reduction in customer reimbursements but excludes the 25% cash tax on the incremental benefit.
• C. This amount applies the 25% tax rate to the full emissions-related saving and omits the reduction in contractual customer reimbursements.

Related terms: Carbon pricing; Cost pass-through; Incremental cash flow; Marginal tax rate.

Question 27

Which replacement bonus metric would most closely align the CEO’s capital-allocation incentive with the board’s stated objective?

• A. Multi-year incremental EBITDA incorporating ESG operating effects and actual production and sales.
• B. Multi-year incremental economic profit incorporating ESG operating effects and a charge for invested capital.
• C. Multi-year improvements in emissions and water-use intensity measured against actual production volumes.

Best answer: B

Explanation

Effective governance links management rewards to the capital-allocation objective rather than to a project characteristic such as additional capacity. Economic profit deducts a required return on invested capital from after-tax operating profit. Incorporating carbon costs, reimbursements, resource constraints, and other operating effects therefore connects financially material ESG issues with the cost of the capital used to address them.

A multi-year measurement period helps evaluate outcomes over the project’s life rather than rewarding commissioning alone. Independent verification supports accountability and limits discretion over reported results. EBITDA remains incomplete because it omits a capital charge, while resource-intensity measures track environmental efficiency rather than financial value. Such measures can supplement oversight but should not replace the value-creation metric for this bonus.

Why each answer fits or falls short

• A. EBITDA reflects operating effects but does not charge for invested capital, so it can reward expansion that fails to earn the required return.
• B. Economic profit incorporates ESG-related operating effects and deducts a capital charge, linking compensation to returns above the required return.
• C. Intensity improvements can accompany higher absolute exposure or negative-NPV spending, so they do not directly establish financial value creation.

Related terms: Economic profit; Capital charge; Executive compensation; Board oversight.

Question 28

Using the independently validated baseline forecasts, which allocation of the €24 million budget best meets the board’s stated objective?

• A. Approve Retrofit.
• B. Approve Expansion.
• C. Retain the existing plant and undertake neither project.

Best answer: A

Explanation

For mutually exclusive projects, the board should select the feasible alternative with the highest expected NPV. Annual expected free cash flow is €7.05 million for Retrofit and €6.25 million for Expansion:

\[ \mathrm{E}(FCF_R) = 0.65(6.0) + 0.35(9.0) = 7.05 \]\[ \mathrm{E}(FCF_E) = 0.65(8.0) + 0.35(3.0) = 6.25 \]

Using the five-year annuity factor, the NPVs in € millions are:

\[ NPV_R = -24.0 + 7.05(3.7908) = 2.72514 \]\[ NPV_E = -22.0 + 6.25(3.7908) = 1.69250 \]

Retrofit creates more expected value despite its higher initial outlay and lower normal-water cash flow. Its resilience benefits appear in incremental cash flows during restrictions. The independent review supports using these forecasts rather than the CEO’s preferred normal-water comparison. Adding separate carbon or water deductions would double-count effects already included.

Why each answer fits or falls short

• A. Retrofit’s probability-weighted annual cash flow is €7.05 million, producing the higher expected NPV of approximately €2.73 million.
• B. Expansion has a positive expected NPV of approximately €1.69 million, but this is below Retrofit’s approximately €2.73 million.
• C. Retaining the existing plant has zero incremental NPV, whereas both available projects have positive expected incremental NPVs.

Related terms: Expected net present value; Mutually exclusive projects; Scenario analysis; Free cash flow.

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Practice Vignette 8

Topic: Equity Investments

Harbor Vale Utilities Equity Review

Maya Sen, an equity analyst at Bracken Asset Management, is comparing the preferred and common shares of Harbor Vale Utilities. She values both securities immediately after the current annual dividends have been paid.

All amounts are in U.S. dollars per share. Future dividends are paid annually, beginning one year from the valuation date. Required returns are annual effective rates. Ignore taxes and transaction costs.

Preferred issue

The preferred shares are noncallable, nonconvertible, nonparticipating, and perpetual. Their dividend rate is fixed, no dividends are in arrears, and Sen assumes all future preferred dividends will be paid in full.

Common-share forecasts

Sen forecasts two years of common dividends before a stable-growth period begins.

Beginning with the year 3 dividend, common dividends grow by 4.0% annually from the preceding year’s dividend, indefinitely.

Question 29

Sen’s base-case intrinsic value per preferred share is closest to:

• A. $60.00
• B. $100.00
• C. $80.00

Best answer: C

Explanation

A fixed-rate perpetual preferred share is valued as a level perpetuity. Its dividend is determined by applying the stated dividend rate to par, while its value depends on the required return for the preferred claim. Let \(D_p\) denote the annual preferred dividend and \(r_p\) its required return.

\[D_p = 100(0.06) = 6\]\[V_p = \frac{D_p}{r_p} = \frac{6}{0.075} = 80\]

There is no separate repayment of par in this going-concern perpetual valuation. Because investors require more than the stated dividend rate, the shares are worth less than par. The common-share required return applies to a different cash-flow claim.

Why each answer fits or falls short

• A. Discounting the $6 annual preferred dividend at the common shares’ 10% required return produces $60, but uses the wrong discount rate.
• B. Par determines the dividend amount, but intrinsic value is below par because the 7.5% required return exceeds the 6% dividend rate.
• C. The preferred dividend is $6 annually, and dividing it by the preferred required return of 7.5% gives $80.

Related terms: Perpetual preferred stock; Dividend discount model; Required return; Dividend rate.

Question 30

Using Sen’s staged dividend forecast, the current intrinsic value per common share is closest to:

• A. $42.18
• B. $45.96
• C. $40.73

Best answer: A

Explanation

The common shares require a two-stage dividend discount model because stable growth begins after the two explicit forecast dividends. Let \(D_t\) be the common dividend in year \(t\), and \(P_2\) the ex-dividend terminal value at year 2. The common required return is 10%, and perpetual dividend growth is 4%.

\[D_3 = 2.64(1.04) = 2.7456\]\[P_2 = \frac{D_3}{0.10-0.04} = 45.76\]\[P_0 = \frac{2.40}{1.10} + \frac{2.64+45.76}{1.10^2} = 42.18\]

The terminal value represents dividends beginning in year 3, so the year 2 dividend remains a separate cash flow. Both that dividend and the terminal value occur two years from today.

Why each answer fits or falls short

• A. Discounting the first two dividends and the year 2 terminal value, calculated using the year 3 dividend, gives approximately $42.18.
• B. This value discounts the year 2 terminal value for only one year while correctly discounting the two explicit dividends.
• C. This value uses the $2.64 year 2 dividend rather than the year 3 dividend in the terminal-value numerator.

Related terms: Two-stage dividend discount model; Terminal value; Constant dividend growth; Equity required return.

Question 31

If only the preferred shares’ required return increases to 8.25%, what is the percentage change in their intrinsic value relative to Sen’s base case?

• A. A decrease of 10.00%
• B. A decrease of 9.09%
• C. A decrease of 17.65%

Best answer: B

Explanation

With a fixed perpetual dividend, intrinsic value varies inversely with the required return. Because the dividend is unchanged, it cancels when calculating the ratio of the revised value to the base-case value. Let \(V_{\mathrm{new}}\) and \(V_{\mathrm{base}}\) denote those two values.

\[\frac{V_{\mathrm{new}}}{V_{\mathrm{base}}} = \frac{0.075}{0.0825} = 0.90909\]\[\frac{V_{\mathrm{new}}-V_{\mathrm{base}}}{V_{\mathrm{base}}} = 0.90909-1 = -9.09\%\]

The required return rises by 10% relative to its original level, but the exact price decline is smaller. An equal percentage decline would be a linear approximation, not the exact result from the perpetuity relationship.

Why each answer fits or falls short

• A. This treats the 10% relative increase in required return as an equal percentage price decline rather than applying the reciprocal relationship.
• B. With the preferred dividend unchanged, the new-to-base value ratio is \(0.075/0.0825\), implying a 9.09% decline.
• C. Subtracting the common shares’ 4% growth rate from both preferred yields produces this decline, but the preferred dividend does not grow.

Related terms: Price-yield relationship; Perpetuity; Yield sensitivity.

Question 32

A colleague proposes using the common shares’ 4% perpetual growth rate as the preferred dividend-growth assumption while retaining the preferred required return. Which assessment is most appropriate?

• A. The input is appropriate because both share classes are supported by the same issuer’s earnings growth.
• B. The input is appropriate because the proposed growth rate is below the preferred shares’ required return.
• C. The input is inappropriate because the preferred terms do not link its dividend to common-dividend growth.

Best answer: C

Explanation

A dividend-growth assumption must describe the cash flows of the security being valued, not merely the issuer’s prospects. Harbor Vale’s common dividends are forecast to grow, but its preferred shares have a fixed dividend rate and no participation rights. The preferred dividend-growth assumption is therefore zero under the stated terms.

Retaining the preferred required return does not correct an unsupported growth assumption. Likewise, having growth below the discount rate only satisfies the convergence condition for a growing perpetuity; it does not justify the forecast economically. Improved business prospects could affect the preferred required return, but they do not themselves alter its contractual dividend amount.

Why each answer fits or falls short

• A. A common issuer does not give both share classes identical dividend rights; earnings growth does not increase this fixed preferred dividend.
• B. Growth below the required return permits mathematical convergence, but does not establish that the preferred cash flows actually grow.
• C. The preferred is fixed-rate and nonparticipating, so the common shares’ forecast growth does not apply to its dividend stream.

Related terms: Nonparticipating preferred stock; Gordon growth model; Dividend growth rate.

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Practice Vignette 9

Topic: Equity Investments

Harbor Row Stores’ Dividend Review

Maya Desai, an equity analyst, is reviewing the growth assumptions and dividend valuation of Harbor Row Stores, a mature retailer that reports under IFRS in U.S. dollars.

Historical results and management’s initiative

Management proposes a procurement initiative that would reduce merchandise costs. The table compares fiscal 2026 results with the expected full-year ratios after implementation.

Net profit margin is after interest and taxes. Asset turnover uses average total assets, and financial leverage is average total assets divided by average common equity. All ratios within each column cover the same full-year period. Each payout ratio relates dividends to earnings for that same year.

Desai uses the conventional sustainable-growth approximation. Assume no preferred shares, common share issuance, repurchases, or changes in common equity other than retained earnings. Debt financing adjusts as needed to maintain each strategy’s target leverage.

Stable-phase valuation

At a future terminal valuation date, Desai assumes the procurement initiative has been completed. Its profit margin, asset turnover, and financial leverage will persist throughout the stable phase.

For that phase, she forecasts:

• Annual growth in sales, assets, and earnings of 4% in perpetuity.
• An annual required return on common equity of 9%.
• Earnings per common share of $3.00 for the first year after the terminal valuation date.

The stable-phase payout will be reset so retained earnings exactly fund the equity needed for growth; all remaining earnings will be distributed. Dividends are paid at year-end.

Alternative financing strategy

Instead of the procurement initiative, the board could pursue a mutually exclusive debt-financed expansion. Under this alternative, net profit margin would remain 4.0% after the additional interest expense, asset turnover would remain 2.50, financial leverage would increase to 2.00, and the payout ratio would remain 70%. The increase in financial leverage would arise entirely from additional interest-bearing debt.

Question 33

Using three-step DuPont analysis, Harbor Row’s fiscal 2026 return on common equity is closest to:

• A. 16.0%
• B. 6.4%
• C. 10.0%

Best answer: A

Explanation

Three-step DuPont analysis separates return on equity into profitability, asset utilization, and financial leverage. Because turnover and leverage use the same average asset measure, multiplying the three components yields net income divided by average common equity.

\[ \mathrm{ROE} = \text{Net profit margin} \times \text{Asset turnover} \times \text{Financial leverage} = 0.04 \times 2.50 \times 1.60 = 16.0\%. \]

The 4.0% margin measures earnings per dollar of revenue, while turnover converts that profitability into a return on assets. The equity multiplier then incorporates the financing structure. Omitting either turnover or leverage does not measure the return earned on common equity.

Why each answer fits or falls short

• A. The aligned DuPont components give return on equity of \(4.0\% \times 2.50 \times 1.60 = 16.0\%\).
• B. Multiplying the 4.0% margin by 1.60 financial leverage produces 6.4%, but omits the contribution from asset turnover.
• C. Multiplying the 4.0% margin by 2.50 turnover produces 10.0%, but omits the financial leverage needed to calculate return on equity.

Related terms: DuPont analysis; Net profit margin; Asset turnover; Equity multiplier.

Question 34

After the margin initiative is fully implemented, and while the 70% payout is retained, Harbor Row’s sustainable annual growth rate is closest to:

• A. 3.75%
• B. 6.00%
• C. 14.00%

Best answer: B

Explanation

The conventional sustainable-growth rate equals return on common equity multiplied by the earnings retention ratio. It measures growth supported by internally generated equity while the target financing structure is maintained.

The initiative’s return on equity is:

\[ \mathrm{ROE} = 0.05 \times 2.50 \times 1.60 = 20\%. \]

With 70% of earnings distributed, the retention ratio is 30%. Therefore:

\[ g = (1 - 0.70) \times 0.20 = 6.00\%. \]

The higher margin increases earnings generated from the equity base. Only the retained portion supports additional equity investment; dividends paid to shareholders cannot simultaneously finance that growth. Debt may increase proportionately without changing target financial leverage.

Why each answer fits or falls short

• A. Applying 30% retention to the 12.5% return on assets gives 3.75%, incorrectly omitting financial leverage from return on equity.
• B. The initiative produces 20% return on equity, and retaining 30% of earnings supports sustainable growth of \(20\% \times 30\% = 6\%\).
• C. Applying the 70% payout ratio to the initiative’s 20% return on equity gives 14%, but growth depends on retained earnings.

Related terms: Sustainable growth rate; Retention ratio; Dividend payout ratio; Return on equity.

Question 35

At the terminal valuation date, Harbor Row’s intrinsic value per common share under Desai’s stable-phase assumptions is closest to:

• A. $42.00
• B. $40.80
• C. $48.00

Best answer: C

Explanation

The stable-phase payout must be consistent with growth, profitability, and the financing assumptions before applying the Gordon growth model. The initiative’s continuing return on equity is:

\[ \mathrm{ROE} = 0.05 \times 2.50 \times 1.60 = 20\%. \]

Let \(b\) denote the retention ratio. Funding 4% growth requires:

\[ b = \frac{g}{\mathrm{ROE}} = \frac{0.04}{0.20} = 20\%, \qquad \text{Payout} = 80\%. \]

The $3.00 forecast is earnings for the first year after valuation, so the corresponding dividend is $2.40. No additional growth adjustment is needed. With annual required return \(r\) of 9%:

\[ V_T = \frac{D_{T+1}}{r-g} = \frac{3.00 \times 0.80}{0.09-0.04} = 48.00. \]

Maintaining the earlier payout would retain more earnings than the stipulated growth and target ratios require.

Why each answer fits or falls short

• A. This value applies the unchanged 70% payout to $3.00 earnings, rather than resetting payout to match the stable phase’s financing needs.
• B. Using 12.5% return on assets instead of 20% return on equity produces a 68% payout and understates common share value.
• C. An 80% sustainable payout produces a $2.40 first-year dividend, which capitalizes to $48.00 using the 5% required-return-minus-growth spread.

Related terms: Gordon growth model; Dividend payout ratio; Sustainable growth rate; Terminal value.

Question 36

At their stated 70% payout ratios, which comparison of the margin initiative and the debt-financed alternative is most appropriate?

• A. Higher sustainable growth under the margin initiative, with greater leverage-related risk under the debt-financed alternative.
• B. Equal sustainable growth, with greater leverage-related risk under the debt-financed alternative.
• C. Higher sustainable growth under the debt-financed alternative, with greater leverage-related risk under that alternative.

Best answer: B

Explanation

Equal return on equity can arise from different combinations of profitability and leverage. The two strategies produce:

\[ \mathrm{ROE}_{\text{margin}} = 0.05 \times 2.50 \times 1.60 = 20\%, \qquad \mathrm{ROE}_{\text{debt}} = 0.04 \times 2.50 \times 2.00 = 20\%. \]

Both retain 30% of earnings, so both support 6% sustainable growth under the stated approximation. Their economic sources differ, however. The procurement initiative improves earnings generated per dollar of sales while leaving leverage unchanged. The financing alternative preserves the existing margin and turnover but increases assets relative to common equity through additional borrowing. Its greater debt exposure increases leverage-related financial risk. An identical sustainable-growth estimate therefore does not imply identical operating improvement or financing risk.

Why each answer fits or falls short

• A. Although the margin initiative improves profitability, the alternative’s higher equity multiplier offsets its lower margin, leaving sustainable growth equal.
• B. Both strategies generate 20% return on equity with 30% retention, but only the financing alternative increases leverage through additional debt.
• C. The alternative’s higher leverage does increase financial risk, but its lower profit margin prevents it from supporting greater sustainable growth.

Related terms: Financial leverage; DuPont analysis; Sustainable growth rate; Financial risk.

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Practice Vignette 10

Topic: Equity Investments

Northline Components Cash Flow Review

Mira Patel, CFA, is preparing a discounted cash flow valuation of Northline Components, an industrial manufacturer. She reviews its fiscal 2026 IFRS financial statements to estimate cash flow available to all capital providers and to common shareholders. All amounts are in US$ millions.

Annual financial data

Net income is after interest and income taxes. Northline has no preferred shares. Capital expenditure represents cash spending, and there are no asset disposals. Operating working capital excludes cash, debt, interest payable, and income taxes payable. Net borrowing represents debt proceeds less principal repayments.

Cash flow presentation

Under Northline’s 2026 IFRS accounting policy, interest paid is classified as financing and all cash income taxes as operating. Cash interest equals interest expense. The 25% tax rate is both marginal and effective, all interest is immediately tax-deductible, and cash taxes equal tax expense. Depreciation and amortization are the only noncash income-statement items; no other adjustments affect the cash flow reconciliation.

Question 37

Using net income as the starting point, Northline’s 2026 free cash flow to the firm (FCFF) is closest to:

• A. $64 million.
• B. $46 million.
• C. $70 million.

Best answer: A

Explanation

FCFF measures cash available to debt and equity capital providers after operating costs, taxes, and operating investment. Starting with net income requires reversing noncash depreciation and amortization and adding back after-tax interest, because net income has already deducted financing costs. Capital expenditure and increases in operating working capital reduce available cash.

Using amounts in millions:

\[ \mathrm{FCFF}=84+20+24(1-0.25)-46-12=64. \]

The interest add-back is $18 million: the $24 million interest expense less its $6 million tax benefit. Net borrowing is excluded because borrowing is a financing source, not cash generated by the firm’s assets.

Why each answer fits or falls short

• A. Adding noncash charges and after-tax interest, then deducting operating investment, gives \(84+20+24(1-0.25)-46-12=64\) million.
• B. This amount omits the after-tax interest add-back, leaving cash flow after interest and before net borrowing.
• C. This amount adds back the full $24 million of interest instead of its $18 million after-tax cost.

Related terms: FCFF; After-tax interest; Capital expenditure; Working capital investment.

Question 38

Northline’s 2026 free cash flow to equity (FCFE) is closest to:

• A. $54 million.
• B. $38 million.
• C. $72 million.

Best answer: A

Explanation

FCFE measures cash available to common shareholders after operating investment and debt financing flows. Starting from net income, add noncash depreciation and amortization, subtract capital expenditure and working-capital investment, and add net borrowing. Interest is not added back because net income already reflects the interest cost borne before cash becomes available to shareholders.

Using amounts in millions:

\[ \mathrm{FCFE}=84+20-46-12+8=54. \]

Positive net borrowing increases current cash available to equity because debt proceeds exceed principal repayments. This measure represents potential cash available to shareholders; it need not equal the dividends actually paid during the year.

Why each answer fits or falls short

• A. Adding depreciation and net borrowing to net income, then deducting investment, gives \(84+20-46-12+8=54\) million.
• B. This amount subtracts the $8 million net borrowing, although positive net borrowing increases cash available to equity.
• C. This amount improperly adds back $18 million of after-tax interest, although FCFE is measured after lenders’ interest claims.

Related terms: FCFE; Net borrowing; Capital expenditure; Noncash charges.

Question 39

To estimate FCFF from Northline’s reported CFO, which interest-related adjustment should Patel make before deducting capital expenditure?

• A. Leave CFO unchanged.
• B. Increase CFO by $18 million.
• C. Decrease CFO by $6 million.

Best answer: C

Explanation

Reported CFO depends on cash flow classification, whereas economic FCFF should not. Northline reports interest paid as financing, so its CFO has not been reduced by the $24 million interest payment. All cash income taxes remain operating, however, and those taxes already incorporate the tax saving from interest deductibility.

To place CFO on an unlevered, after-tax basis, remove that financing-related tax benefit:

\[ \text{Interest-related CFO adjustment}=-24(0.25)=-6. \]

Capital expenditure is then deducted separately. Depreciation and operating working-capital investment require no additional adjustment because the reported operating cash flow reconciliation already incorporates these items. Adding after-tax interest would instead apply when interest paid is classified as operating.

Why each answer fits or falls short

• A. Although interest payments are outside CFO, reported CFO still includes their tax benefit because all cash income taxes are operating.
• B. Adding after-tax interest applies when interest payments have reduced CFO, whereas Northline classifies those payments as financing.
• C. Financing classification excludes interest payments from CFO, but operating taxes retain the $6 million interest tax benefit, which must be removed.

Related terms: Cash flow classification; Interest tax shield; Operating cash flow; Unlevered cash flow.

Question 40

Suppose Northline makes an additional $16 million cash equipment purchase on the last day of 2026 and receives an additional $16 million cash loan that day. The transaction has no 2026 effect on operations, interest, taxes, depreciation, or working capital. Relative to the reported case, how would 2026 FCFF and FCFE change?

• A. FCFF decreases by $16 million; FCFE decreases by $16 million.
• B. FCFF is unchanged; FCFE is unchanged.
• C. FCFF decreases by $16 million; FCFE is unchanged.

Best answer: C

Explanation

FCFF separates cash generated by the firm’s assets from the financing used to fund those assets. The additional equipment purchase is capital expenditure and therefore reduces FCFF, regardless of whether debt or equity finances it. Loan proceeds are not included in FCFF.

FCFE incorporates net borrowing because it measures cash available to common shareholders after debt financing flows. The transaction increases both capital expenditure and net borrowing by $16 million:

\[ \Delta\mathrm{FCFF}=-16,\qquad \Delta\mathrm{FCFE}=-16+16=0. \]

The unchanged operating results, taxes, and interest eliminate other current-year effects. This conclusion concerns 2026 only; future equipment operations and debt service could change subsequent cash flows.

Why each answer fits or falls short

• A. The equipment purchase reduces both measures before financing, but additional net borrowing offsets the reduction in cash available to equity.
• B. Debt proceeds offset the equipment purchase for FCFE but are excluded from FCFF, so the firm’s free cash flow declines.
• C. Additional capital expenditure reduces FCFF by $16 million, while equal additional net borrowing offsets that investment in the FCFE calculation.

Related terms: Debt financing; Capital expenditure; FCFF; FCFE.

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Practice Vignette 11

Topic: Fixed Income

Elmridge’s Credit Overlay Review

Mira Sen, CFA, manages a $100 million portfolio of USD-denominated senior unsecured corporate bonds at Elmridge Asset Management. The portfolio broadly resembles a diversified corporate credit index, but Sen maintains active issuer positions, including an overweight in Norwick Industries. She is evaluating CDS transactions with Bayhaven Bank while retaining the portfolio’s bonds.

Available contracts

Bayhaven offers the following contracts, which Elmridge may buy or sell:

Both contracts become effective on 20 September 2027 and settle in USD. Assume no upfront payments. Premiums are paid quarterly, with each full quarter treated as one-quarter of a year.

Each index constituent represents 1% of original index notional. The basket is fixed, and constituents are not replaced following credit events.

Credit-event and settlement provisions

Both contracts specify the following terms:

• Bankruptcy is a covered credit event.
• Failure to Pay requires more than $1 million to remain unpaid after the applicable 10-calendar-day grace period expires.
• Restructuring is excluded from covered credit events.

The settlement method is elected at inception: auction-based cash settlement or physical settlement. The auction final price is expressed as a percentage of par. For physical settlement, eligible deliverables are USD-denominated senior unsecured obligations of the affected reference entity. Ignore counterparty risk and transaction costs.

Monitoring note: 27 December 2027

Norwick missed a $1.4 million bond coupon due on 20 December. Its contractual grace period expires at the end of 30 December, and the coupon remains unpaid on 27 December.

On 22 December, bondholders approved a maturity extension and coupon reduction that meet the documentation’s definition of restructuring. The amendment did not cure the missed payment. No bankruptcy has occurred.

Question 41

For this question only, assume Elmridge sells $12 million of single-name protection and elects cash settlement. A covered bankruptcy occurs immediately after a full quarterly premium is paid, and the auction final price is 40% of par. Which cash flows apply to Elmridge for that premium payment and the subsequent settlement?

• A. Receive $30,000 in premium and pay $12 million at settlement.
• B. Pay $30,000 in premium and receive $7.2 million at settlement.
• C. Receive $30,000 in premium and pay $7.2 million at settlement.

Best answer: C

Explanation

A CDS protection seller receives premiums in exchange for assuming a contingent obligation to compensate the protection buyer following a covered credit event. Elmridge’s quarterly premium receipt is:

\[ 12{,}000{,}000 \times 0.01 \times \frac{1}{4} = 30{,}000. \]

Auction-based cash settlement compensates the buyer for the difference between par and the auction value of the reference obligations. Elmridge therefore pays:

\[ 12{,}000{,}000 \times (1 - 0.40) = 7{,}200{,}000. \]

The premium and settlement flow in opposite directions. Under physical settlement, the seller would instead pay full par against delivery of eligible obligations with the corresponding face amount. Paying full par without receiving those obligations would not represent the specified cash settlement.

Why each answer fits or falls short

• A. Cash settlement requires payment of the default loss, whereas full-par payment would require delivery of eligible obligations under physical settlement.
• B. These are protection buyer cash flows; Elmridge sells protection, so both the premium and settlement directions are reversed.
• C. As protection seller, Elmridge receives the quarterly coupon and pays the $12 million notional multiplied by the 60% loss given default.

Related terms: Protection seller; CDS coupon; Auction settlement; Physical settlement.

Question 42

For this question only, consider an index CDS with $80 million of original notional. One constituent other than Norwick experiences a covered credit event and is settled. What premium must the protection buyer pay for a subsequent full quarter with no additional credit events?

• A. $198,000
• B. $200,000
• C. $2,000

Best answer: A

Explanation

An index CDS provides protection on a portfolio of reference entities rather than terminating entirely when the first constituent experiences a credit event. Here, each constituent represents 1% of original notional, so the settled constituent accounts for $800,000. Because it is not replaced, protection continues on $79.2 million of surviving notional, corresponding to an index factor of 99%.

The subsequent full-quarter premium is:

\[ 79{,}200{,}000 \times 0.01 \times \frac{1}{4} = 198{,}000. \]

The settlement payment for the affected constituent is separate from these continuing premiums. Its recovery value is not needed to calculate the premium payable on the remaining index protection.

Why each answer fits or falls short

• A. Settling one 1% constituent leaves $79.2 million of surviving notional, on which the 100 bps annual coupon produces a $198,000 quarterly premium.
• B. This premium uses the original $80 million notional rather than reducing it for the settled constituent’s $800,000 allocation.
• C. This is the quarterly premium on the settled constituent’s allocation, rather than on the 99 surviving reference entities.

Related terms: Index CDS; Index factor; Notional principal; Running premium.

Question 43

Under the specified CDS terms, which conclusion follows from the 27 December monitoring note?

• A. No covered credit event has occurred as of 27 December.
• B. A covered credit event occurred when Norwick missed its payment on 20 December.
• C. A covered credit event occurred when Norwick’s debt terms were amended on 22 December.

Best answer: A

Explanation

CDS protection responds to the credit events covered by the transaction’s documentation, not automatically to every deterioration in an issuer’s financial condition. Norwick’s $1.4 million missed coupon exceeds the specified $1 million threshold, but that amount condition alone is insufficient. The contractual grace period does not expire until the end of 30 December, so Failure to Pay has not occurred as of 27 December.

The maturity extension and coupon reduction constitute restructuring under the stated definitions, but restructuring is excluded from these contracts. Bankruptcy is also absent. A Failure to Pay event would arise only after the grace period expires with more than $1 million still unpaid, assuming the other contractual conditions remain satisfied.

Why each answer fits or falls short

• A. The payment grace period remains open, restructuring is excluded, and Norwick has not experienced bankruptcy.
• B. Although the missed amount exceeds $1 million, Failure to Pay also requires expiration of the applicable grace period without payment.
• C. The amendment qualifies as restructuring, but both CDS contracts expressly exclude restructuring from covered credit events.

Related terms: Failure to Pay; Grace period; Restructuring; Credit event.

Question 44

At inception, Sen wants to reduce portfolio-wide exposure to broad investment-grade credit-spread widening while retaining issuer-specific active positions relative to the index. Assuming appropriately sized trades and negligible bond-CDS basis risk, which transaction best matches that objective?

• A. Sell protection through the corporate index CDS.
• B. Buy protection through the Norwick single-name CDS.
• C. Buy protection through the corporate index CDS.

Best answer: C

Explanation

Buying index CDS protection is a way to hedge the common credit component of a diversified bond portfolio without selling its bonds. Purchased protection generally gains value when reference credit spreads widen, offsetting part of the decline in the bonds’ values. This hedge can operate through changes in market value before any credit event occurs.

Because Elmridge’s portfolio broadly resembles the index, an appropriately sized index overlay targets its systematic credit exposure. The portfolio’s active issuer positions remain as deviations from the index. A concentrated single-name hedge would instead change a particular issuer exposure. Selling index protection has the opposite directional effect from the intended hedge because it adds exposure to credit losses and spread widening.

Why each answer fits or falls short

• A. Selling index protection adds long credit exposure, increasing sensitivity to broad spread widening rather than offsetting the bond portfolio’s exposure.
• B. Single-name protection targets Norwick’s credit exposure and would alter that active issuer position rather than hedge the portfolio’s broad credit component.
• C. Purchased index protection offsets broad credit-spread exposure across the portfolio while allowing Sen to retain its issuer-specific active positions.

Related terms: Index CDS; Credit beta; Credit hedging.

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Practice Vignette 12

Topic: Fixed Income

Alder Quay’s Bond Valuation Review

Mira Salcedo, a fixed-income analyst at Alder Quay Asset Management, is reviewing a bond valuation using the desk’s calibrated two-period binomial short-rate lattice. She also examines how individual terminal states contribute to the bond’s value.

Bond cash flows

The default-free, option-free bond has two years remaining to maturity. All amounts are in US dollars per $100 face value.

• The annual coupon rate is 5%.
• A $5 coupon is paid at time 1.
• The final $5 coupon and $100 redemption payment are paid at time 2 in every terminal state.
• Time 0 is immediately after a coupon date, so accrued interest is zero.

Ignore taxes and transaction costs.

Calibrated lattice

The lattice has two one-year branching periods and has already been calibrated to current default-free zero-coupon prices. Rates are annual effective short rates applying over the indicated interval.

At every nonterminal node, the risk-neutral probability of an upward move is 50%, and that of a downward move is 50%.

At time 2, the upper-lower and lower-upper paths recombine into the middle terminal state. The other terminal states are upper-upper and lower-lower.

Strategist’s forecast

Separately, Alder Quay’s macroeconomic strategist estimates a 70% physical probability of an upward move at each branching point, with a 30% probability of a downward move.

Question 45

When decomposing the bond’s maturity payment by terminal state, the time-zero present-value contribution of the middle terminal state, excluding the time 1 coupon, is closest to:

• A. $48.32
• B. $47.62
• C. $23.81

Best answer: A

Explanation

A recombining terminal state can be reached through paths with different discount factors. Each path’s probability-weighted cash flow must therefore be discounted using the rates encountered along that path. The middle state is reached by upper-lower and lower-upper movements, each having risk-neutral probability \(0.50 \times 0.50 = 0.25\). Both paths receive the $105 maturity payment, but their second-year discount rates differ.

\[ V_{0,\mathrm{middle}} = \frac{0.25(105)}{1.04(1.06)} + \frac{0.25(105)}{1.04(1.03)} = 48.3169. \]

Using the middle state’s combined 50% probability with only one path’s discount factor misprices its contribution. The time 1 coupon is a separate cash flow and is excluded from this decomposition.

Why each answer fits or falls short

• A. The two paths contribute \(0.25(105)/[1.04(1.06)] + 0.25(105)/[1.04(1.03)] \approx 48.32\) at time zero.
• B. This assigns the middle state’s total 50% probability to discounting entirely through the 6% upper node, ignoring the lower-node path.
• C. This includes only the upper-lower path and omits the lower-upper path reaching the same recombining terminal state.

Related terms: Arrow-Debreu securities; Risk-neutral probabilities; Short-rate lattice.

Question 46

At the upper node at time 1, immediately after the first coupon has been paid, the bond’s arbitrage-free value is closest to:

• A. $99.06
• B. $104.06
• C. $100.96

Best answer: A

Explanation

An ex-coupon bond value includes only cash flows remaining after the current coupon payment. At the upper node at time 1, the bond has one remaining payment: the $100 redemption plus the final $5 coupon at time 2. The applicable one-year short rate is 6%.

\[ B_{1,u} = \frac{100+5}{1.06} = 99.0566. \]

Here, \(B_{1,u}\) denotes the upper-node ex-coupon value. Risk-neutral weighting does not change this one-period calculation because the contractual payment is $105 in either subsequent terminal outcome. The coupon already paid at time 1 is excluded, and the initial 4% rate does not apply to discounting from time 2 back to this node.

Why each answer fits or falls short

• A. The value is \(105/1.06 \approx 99.06\), discounting the final coupon and redemption for one year at the upper-node short rate.
• B. This includes the $5 coupon paid at time 1, although the requested value is immediately after that payment.
• C. This discounts the $105 maturity payment at the initial 4% rate rather than the 6% rate applying at the upper node.

Related terms: Ex-coupon price; Coupon timing; Backward induction.

Question 47

The bond’s time-zero arbitrage-free price is closest to:

• A. $105.50
• B. $101.44
• C. $96.63

Best answer: B

Explanation

Backward induction first values the remaining cash flows at each time 1 node. The time-zero price then equals the discounted sum of the time 1 coupon and the risk-neutral expected ex-coupon continuation value. Let \(B_0\) denote the time-zero bond price.

\[ B_0 = \frac{5 + 0.50\left(\frac{105}{1.06}\right) + 0.50\left(\frac{105}{1.03}\right)}{1.04} = 101.4415. \]

The $5 first coupon must be added because the continuation values exclude the coupon paid at time 1. The entire expected time 1 amount is then discounted using the initial 4% short rate. Node-specific discounting, rather than discounting every cash flow at one arbitrarily selected rate, preserves consistency with the calibrated term structure.

Why each answer fits or falls short

• A. This is the risk-neutral expected time 1 coupon and continuation value before the required discounting at 4% to time zero.
• B. Discounting the first coupon and expected continuation value gives \([5+0.5(105/1.06)+0.5(105/1.03)]/1.04 \approx 101.44\).
• C. This omits the $5 time 1 coupon, reducing the price by its time-zero present value of \(5/1.04\).

Related terms: Backward induction; Arbitrage-free valuation; Risk-neutral expectation; Discount factors.

Question 48

Current market zero-coupon prices remain unchanged. A colleague replaces the risk-neutral probabilities with the strategist’s physical probabilities while retaining all node short rates. Compared with the calibrated valuation, which conclusion about the colleague’s result is most accurate?

• A. It produces a lower value that remains consistent with the calibrated market prices.
• B. It produces a higher value that is inconsistent with the calibrated market prices.
• C. It produces a lower value that is inconsistent with the calibrated market prices.

Best answer: C

Explanation

Risk-neutral probabilities are pricing weights, not forecasts of actual interest-rate movements. Combined with node short rates, they reproduce the market prices used to calibrate the lattice.

At time 1, the fixed $105 maturity payment has a lower value when discounted at 6% than at 3%. Increasing the upper-node probability from 50% to 70% therefore lowers the expected continuation value. The first coupon and the initial discount rate remain unchanged, so the calculated time-zero price falls.

Physical probabilities can support forecasting and scenario analysis, but they cannot simply replace calibrated pricing probabilities while the same risk-free discounting rules are retained. Because observed zero-coupon prices have not changed, the colleague’s lower value is inconsistent with the market-replicating value of the bond’s fixed payments.

Why each answer fits or falls short

• A. The greater upper-node weight lowers the calculated value, but substituting physical probabilities while retaining node rates breaks consistency with the market calibration.
• B. The substitution breaks market-pricing consistency, but assigning greater weight to the higher-rate node lowers rather than raises the expected continuation value.
• C. The upper node has the lower continuation value, so increasing its weight lowers the price and abandons the probabilities supporting current calibration.

Related terms: Physical probabilities; Risk-neutral probabilities; Term structure calibration.

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Practice Vignette 13

Topic: Fixed Income

Dollar Rates During a Collateral Disruption

Maya Sethi, a fixed-income analyst at Cedargate Asset Management, reviews Treasury securities, interest rate swaps, and a corporate bond after a disruption in the collateral market.

Market quotations

The US dollar swap curve consists of par fixed-rate quotations for swaps exchanging annual fixed payments for overnight SOFR compounded in arrears and paid annually. The swaps are centrally cleared, with daily cash variation margin remunerated at SOFR. Treasury yields and swap quotations have been normalized to a common annual-compounding basis, with matched maturities.

Selected current observations are shown below. Sethi also has the complete curves needed for valuation.

Funding and collateral conditions

Immediately before the disruption, the five-year benchmark Treasury yielded 4.30%, and the five-year swap fixed rate was 4.31%.

Demand to borrow the five-year benchmark Treasury subsequently increased sharply. Its overnight repo rate fell from 4.10% to 1.40%, while the general-collateral Treasury repo rate remained at 4.10%. Counterparty credit indicators, clearing arrangements, and margin requirements were unchanged.

At the long end, Treasury issuance is heavy, and pension funds have increased their demand to receive fixed in 30-year swaps. Dealers report binding balance-sheet limits and uncertainty about future term repo funding costs.

Corporate bond valuation

Sethi also reviews a noncallable, fixed-rate corporate bond. An issuer-specific constant spread of 95 basis points, previously calibrated over zero-coupon rates derived from the SOFR swap curve, remains appropriate. She intends to retain this spread and the existing valuation methodology. All bond cash flows are denominated in US dollars.

Question 49

The current 10-year swap spread is closest to:

• A. 140 basis points.
• B. -14 basis points.
• C. 14 basis points.

Best answer: C

Explanation

A swap spread is the par fixed swap rate minus the yield on a government security of comparable maturity, using consistent quotation conventions. For the ten-year instruments:

\[S_{10} = 4.45\% - 4.31\% = 0.14\% = 14\text{ basis points}.\]

The positive result means the swap fixed rate is above the Treasury yield. One percentage point equals 100 basis points, so the difference of 0.14 percentage points must be multiplied by 100. The floating reference rate, overnight SOFR, is not the rate subtracted from the Treasury yield.

Why each answer fits or falls short

• A. The difference is 0.14 percentage points, which equals 14 basis points; 140 basis points would equal 1.40 percentage points.
• B. This reverses the spread convention by subtracting the 4.45% swap fixed rate from the 4.31% Treasury yield.
• C. The swap fixed rate exceeds the maturity-matched Treasury yield by 0.14 percentage points, equivalent to 14 basis points.

Related terms: Swap spread; Par swap rate; Basis point; Maturity matching.

Question 50

Which discounting approach is most appropriate for Sethi’s corporate bond valuation under her stated assumptions?

• A. Discount each cash flow at its maturity-matched Treasury zero rate plus 95 basis points.
• B. Discount each cash flow at its maturity-matched SOFR swap par rate plus 95 basis points.
• C. Discount each cash flow at its maturity-matched SOFR zero rate plus 95 basis points.

Best answer: C

Explanation

The swap curve can serve as a benchmark term structure for valuation, but its par quotations must first be converted into discount factors or zero-coupon rates. A par swap rate reflects the combined valuation of multiple payments; a zero rate applies to a single maturity.

Sethi should discount each promised corporate bond payment using its maturity-matched SOFR zero rate plus the existing 95-basis-point issuer spread. This is a constant-spread, or Z-spread, approach. The spread represents issuer-specific compensation relative to the selected benchmark. Moving the same numerical spread to the Treasury curve would change the valuation basis rather than preserve the stated methodology.

Why each answer fits or falls short

• A. Applying the unchanged spread to Treasury zero rates changes its benchmark and does not preserve Sethi’s existing SOFR-based valuation methodology.
• B. Swap par rates price exchanges involving multiple cash flows and cannot generally replace zero rates when discounting individual bond payments.
• C. SOFR zero rates provide cash-flow-specific benchmark discount rates, and adding 95 basis points preserves the issuer spread on its calibrated basis.

Related terms: Zero-coupon curve; Bootstrapping; Z-spread; SOFR.

Question 51

Which development most likely explains the change in the five-year swap spread during the disruption?

• A. Increased scarcity value of the Treasury as repo collateral.
• B. Increased expectations for future overnight SOFR.
• C. Increased compensation for swap counterparty default risk.

Best answer: A

Explanation

A Treasury trading special in repo provides valuable collateral services. Its holder can finance it at a lower repo rate than general collateral, which can support a higher cash price and a lower yield.

The five-year Treasury’s repo rate fell sharply while general-collateral funding remained unchanged. Its yield declined by 26 basis points, compared with only a 3-basis-point decline in the swap fixed rate. The swap spread therefore widened primarily because the Treasury became richer relative to swaps. Stable counterparty indicators and unchanged margin arrangements provide little support for a counterparty-credit explanation. A swap spread is a relative-price measure, not a pure measure of swap counterparty risk.

Why each answer fits or falls short

• A. The sharply lower special repo rate indicates greater collateral value, consistent with investors accepting a lower yield on the five-year Treasury.
• B. Higher expected SOFR would generally put upward pressure on the swap fixed rate, whereas the observed five-year swap rate declined.
• C. Counterparty indicators and collateral arrangements were unchanged, while the swap fixed rate declined slightly rather than rising with a larger credit premium.

Related terms: Repo specialness; Convenience yield; Swap spread; Counterparty credit risk.

Question 52

Which interpretation of the current 30-year swap spread is most appropriate?

• A. The negative spread is consistent with fixed-receiving demand and limits on cash-swap arbitrage.
• B. The negative spread measures sovereign default compensation in excess of swap-counterparty default compensation.
• C. The negative spread establishes a risk-free profit from repo-financed Treasuries hedged with pay-fixed swaps.

Best answer: A

Explanation

The 30-year swap fixed rate is below the matched Treasury yield, producing a negative swap spread. This relationship is economically possible and does not itself indicate a quotation or arithmetic error.

Pension demand to receive fixed can push swap fixed rates downward. Heavy Treasury supply can place upward pressure on Treasury yields. Dealers may be unable or unwilling to eliminate the resulting difference because intermediation consumes scarce balance-sheet capacity and financing costs are uncertain. Buying a Treasury and paying fixed in a swap does not automatically lock in the quoted spread as a risk-free return: repo costs, margin liquidity, and cash-flow differences matter. Nor does the negative spread isolate sovereign versus counterparty default risk.

Why each answer fits or falls short

• A. Pension receiving demand can depress swap fixed rates, while heavy Treasury issuance and dealer constraints can sustain the negative spread.
• B. The spread also reflects supply, hedging demand, collateral characteristics, and intermediation costs, so it cannot isolate relative default compensation.
• C. Uncertain repo funding costs and binding dealer balance-sheet limits prevent the quoted yield difference from establishing a risk-free arbitrage profit.

Related terms: Negative swap spread; Liability-driven investment; Balance-sheet constraints; Repo funding risk.

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Practice Vignette 14

Topic: Derivatives

Cedar Ridge’s Bond Forward Review

On 14 June 2027, Mira Chen, a derivatives analyst at Cedar Ridge Asset Management, reviews a draft valuation of a physically settled bond forward. The hedge would use a cash bond purchase settling on 15 June 2027. All funding calculations begin on that settlement date, not the trade date.

Bond and settlement terms

The underlying is a default-free, US dollar-denominated fixed-rate bond. Prices and cash flows below are expressed per $100 face value.

The bond remains outstanding after forward delivery. Its only cash flow between cash settlement and forward delivery is the 15 September coupon. Bond and forward quotations are clean prices; accrued interest is paid in addition at cash settlement and forward delivery.

Funding and execution

A unit of cash invested at the beginning of an interval grows to the factor shown at its end. The same factors apply to borrowing and lending.

Funding rates are deterministic. Coupons can be reinvested at the applicable factor. Short selling is unrestricted, short-sale proceeds are available for investment, and short sellers must pay equivalent coupons to the bond lender. Ignore taxes, transaction costs, margins, and counterparty risk.

A dealer offers either side of the November forward at a clean delivery price of 101.70, with no initial payment.

Draft calculation

The worksheet under review follows these steps:

1. Add accrued interest through 14 June to the clean spot price.
2. Carry that amount from 15 June to 15 November using 1.025150.
3. Subtract the September coupon at its face amount, without reinvestment.
4. Record the remainder as the clean forward price.

Question 53

The full spot purchase cost payable on 15 June, per $100 face value, is closest to:

• A. 102.200
• B. 102.700
• C. 102.683

Best answer: B

Explanation

The cash buyer pays the full, or dirty, price: the clean quotation plus accrued interest as of cash settlement. Under 30/360, 15 March to 15 June is 90 days of the 180-day coupon period. The semiannual coupon is 3.00 per $100 face value.

\[ P_{\mathrm{full}}=101.20+3.00\left(\frac{90}{180}\right)=102.70. \]

The worksheet uses the trade date, producing only 89 days of accrual. The funding period also starts at settlement, when the purchase payment is made. November accrued interest belongs to the later forward-delivery invoice.

Why each answer fits or falls short

• A. This amount adds November delivery-date accrued interest of 1.00 instead of June settlement-date accrued interest of 1.50.
• B. Settlement-date accrued interest is \(3.00(90/180)=1.50\), making the full purchase cost \(101.20+1.50=102.70\).
• C. This amount uses 89 days of accrued interest through the trade date rather than 90 days through the cash settlement date.

Related terms: Clean price; Dirty price; Accrued interest; Settlement date.

Question 54

The no-arbitrage clean forward delivery price for 15 November, per $100 face value, is closest to:

• A. 102.253
• B. 99.715
• C. 101.253

Best answer: C

Explanation

A cash-and-carry hedge finances the full spot purchase cost. The September coupon is received before delivery, so its reinvested value reduces the amount the forward seller must recover at delivery. That net amount is a full delivery price; delivery-date accrued interest must then be subtracted to obtain a clean quotation.

June settlement accrued interest is 1.50. November delivery accrued interest covers 60 of 180 days and equals 1.00. Therefore:

\[ F_{\mathrm{clean}}=(101.20+1.50)(1.025150)-3.00(1.010000)-1.00=101.252905. \]

The coupon is carried only from September to November because it is unavailable for investment before its payment date.

Why each answer fits or falls short

• A. This is the fair full delivery price; obtaining the clean forward quote requires subtracting November accrued interest of 1.00.
• B. This result funds only the clean spot price, omitting the 1.50 of accrued interest that must also be financed at settlement.
• C. The clean forward price is \((101.20+1.50)(1.025150)-3.00(1.010000)-1.00=101.252905\).

Related terms: Bond forward pricing; Cost of carry; Coupon reinvestment; Accrued interest.

Question 55

Assume every worksheet line other than the coupon deduction has been corrected. What adjustment to the calculated clean forward price is required solely to correct the coupon line, per $100 face value?

• A. Decrease by 0.075.
• B. Decrease by 0.030.
• C. Decrease by 0.045.

Best answer: B

Explanation

The cash bond holder receives the September coupon before delivering the bond in November. Its delivery-date benefit includes both the coupon and the interest earned after receipt. The relevant accumulation factor is therefore the September-to-November factor, not either factor beginning in June.

\[ \text{Additional coupon benefit}=3.00(1.010000)-3.00=0.030. \]

Because coupon benefits are deducted from financed purchase costs, recognizing this additional benefit decreases the clean forward price by 0.030. The correction changes neither the amount originally financed nor the accrued interest payable at forward delivery.

Why each answer fits or falls short

• A. This approximately applies the entire June-to-November funding increment to the coupon, overstating its reinvestment period.
• B. The September coupon produces 3.030 by November, so subtracting only 3.000 understates the coupon benefit by 0.030.
• C. The 0.045 adjustment applies the June-to-September funding increment to a coupon that is not received until September.

Related terms: Coupon reinvestment; Cash flow timing; Accumulation factor.

Question 56

After comparing prices on a consistent quotation basis, which conclusion about an arbitrage trade at the dealer’s quote is most accurate?

• A. Buy the forward and short the bond; reverse cash-and-carry locks in a profit.
• B. Take no position in either market; the quote is consistent with no-arbitrage pricing.
• C. Sell the forward and finance a bond purchase; cash-and-carry locks in a profit.

Best answer: C

Explanation

Arbitrage comparisons must use either clean prices on both sides or full prices on both sides. The dealer’s clean delivery price is 101.70. Adding November accrued interest gives a delivery invoice of 102.70. The financed full spot cost, net of the reinvested coupon, is lower.

Borrow to buy the bond, reinvest the September coupon, and deliver the bond into a short forward. The delivery-date surplus is:

\[ (101.70+1.00)+3.00(1.010000)-102.70(1.025150)=0.447095. \]

Under the stated assumptions, this surplus requires no initial net investment. A new forward has zero value only when its contractual delivery price is fair; zero initial payment alone does not establish fair pricing.

Why each answer fits or falls short

• A. The dealer’s clean quote is below the fair full forward price but above the fair clean forward price, so reverse cash-and-carry loses money.
• B. The clean quote of 101.70 exceeds the fair clean price of approximately 101.253, so the dealer’s zero-payment contract is mispriced.
• C. The dealer’s clean quote exceeds the no-arbitrage clean price, so a financed spot purchase and a short forward lock in a positive surplus.

Related terms: Cash-and-carry arbitrage; Reverse cash-and-carry; Forward contract value; Clean price.

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Practice Vignette 15

Topic: Alternative Investments

Larchgate Property Trust

Nadia Sen is reviewing Larchgate Property Trust, a listed equity REIT holding retail and logistics properties. She is assessing its recurring earnings and asset backing at 31 December 2026. Larchgate reports under IFRS and uses the cost model for investment property.

All dollar amounts are US dollars. Exhibit amounts and share counts are in millions. Larchgate has no preferred shares, noncontrolling interests, or dilutive securities.

Annual operating results

The following figures cover the year ended 31 December 2026. Net income includes the depreciation, property-sale gain, and straight-line rental revenue shown below.

For adjusted funds from operations (AFFO), Sen deducts recurring maintenance capital spending and straight-line rental revenue exceeding cash rent from funds from operations (FFO). She does not deduct expansion capital spending. No other AFFO adjustments apply.

Year-end asset values and claims

Asset values do not overlap, and the year-end figures reflect all completed 2026 property sales. There are no unlisted assets or claims. Ignore income taxes and transaction costs throughout the analysis.

Question 57

Larchgate’s 2026 FFO per common share is closest to:

• A. $4.62
• B. $5.92
• C. $4.80

Best answer: C

Explanation

FFO adjusts reported earnings by adding back real estate depreciation and removing gains on sales of depreciable real estate. Depreciation reflects historical-cost allocation rather than necessarily measuring economic property deterioration, while disposal gains do not represent ongoing property operations.

Using amounts in millions:

\[ \mathrm{FFO} = 62 + 86 - 28 = 120. \]

Annual FFO per share uses the weighted-average common share count for the earnings period:

\[ \text{FFO per share} = \frac{120}{25} = 4.80. \]

The 26 million shares outstanding at year-end are appropriate for a valuation measured on that date, not for allocating earnings generated throughout 2026.

Why each answer fits or falls short

• A. Dividing $120 million of FFO by 26 million year-end shares incorrectly uses a point-in-time denominator for an annual earnings measure.
• B. Adding depreciation but retaining the $28 million property-sale gain produces $148 million, or $5.92 per share, rather than FFO.
• C. Net income plus real estate depreciation minus property-sale gains equals $120 million, which divided by 25 million weighted-average shares gives $4.80.

Related terms: Funds from operations; Real estate depreciation; Property disposal gains; Weighted-average shares.

Question 58

Under Sen’s stated convention, Larchgate’s 2026 AFFO per common share is closest to:

• A. $3.60
• B. $3.90
• C. $2.20

Best answer: A

Explanation

AFFO refines FFO to estimate recurring cash capacity after maintaining the existing property portfolio. Because AFFO conventions vary, the specified adjustments control the calculation. Sen deducts both recurring maintenance spending and rental revenue recognized ahead of cash collection.

Using amounts in millions:

\[ \mathrm{AFFO} = 62 + 86 - 28 - 22.5 - 7.5 = 90. \]\[ \text{AFFO per share} = \frac{90}{25} = 3.60. \]

The positive straight-line rental adjustment is subtracted because recognized revenue exceeds cash rent. Expansion spending is excluded under the stated convention because it represents growth investment rather than recurring maintenance. Its exclusion does not mean that expansion requires no financing.

Why each answer fits or falls short

• A. Applying the maintenance and straight-line rent deductions yields AFFO of $90 million, or $3.60 per weighted-average common share.
• B. This deducts maintenance capital spending but omits the $7.5 million noncash rent adjustment, overstating AFFO by $0.30 per share.
• C. This additionally deducts $35 million of expansion spending, which the stated AFFO convention excludes, understating AFFO by $1.40 per share.

Related terms: Adjusted funds from operations; Straight-line rent; Maintenance capital expenditures; Growth capital expenditures.

Question 59

At 31 December 2026, Larchgate’s NAV per common share is closest to:

• A. $40.38
• B. $38.00
• C. $39.52

Best answer: B

Explanation

Common-shareholder NAV equals the current value of assets less all claims senior to common equity. Property appraisals replace historical carrying amounts, while cash and marketable securities are added separately because their values are not included in the appraisals.

Using amounts in millions:

\[ \text{Common NAV} = 1{,}600 + 60 + 40 - 650 - 62 = 988. \]\[ \text{NAV per share} = \frac{988}{26} = 38.00. \]

Both debt and other liabilities reduce the value available to common shareholders. Because NAV is measured at a particular date, the denominator is the common shares outstanding on that date, rather than the weighted-average shares used for annual per-share earnings measures.

Why each answer fits or falls short

• A. Deducting debt but omitting $62 million of other liabilities produces $1,050 million of equity value, or approximately $40.38 per share.
• B. Asset value of $1,700 million less $712 million of liabilities leaves $988 million for 26 million year-end common shares.
• C. This divides $988 million of common NAV by 25 million weighted-average shares instead of the 26 million shares outstanding at the valuation date.

Related terms: Net asset value; Property valuation; Debt fair value; Shares outstanding.

Question 60

Assume Larchgate sells a retained property on 1 January 2027 for its $150 million appraised value. Its IFRS carrying amount is $110 million, and its appraisal is included in the year-end property value. All proceeds remain in cash. Considering only the sale and excluding subsequent operating changes, which statement best describes its effects on 2027 net income, 2027 AFFO, and total NAV at closing?

• A. Net income increases by $40 million, AFFO is unchanged, and total NAV is unchanged.
• B. Net income increases by $40 million, AFFO is unchanged, and total NAV increases by $40 million.
• C. Net income and AFFO each increase by $40 million, and total NAV is unchanged.

Best answer: A

Explanation

Accounting income, recurring cash capacity, and NAV respond differently to a property disposal. The recognized gain equals sale proceeds less the IFRS carrying amount:

\[ \text{Disposal gain} = 150 - 110 = 40 \text{ million}. \]

This gain increases net income. It is removed when calculating FFO, so it does not increase AFFO under Sen’s convention. The sale proceeds are investing cash inflows, not recurring operating cash capacity.

NAV already includes the property at its $150 million appraised value. Selling it at that value reduces property assets by $150 million and increases cash by the same amount, leaving total NAV unchanged. Subsequent effects from lost rent, reinvestment, or distributions are outside this question’s assumptions.

Why each answer fits or falls short

• A. The sale recognizes a $40 million accounting gain excluded from AFFO and exchanges $150 million of appraised property value for equal cash.
• B. The appraisal already incorporates the property’s $150 million value, so recognizing a gain over carrying amount creates no additional NAV.
• C. The $40 million disposal gain increases net income but is excluded from FFO and therefore does not increase AFFO.

Related terms: Disposal gains; Investing cash flows; Adjusted funds from operations; Net asset value.

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Practice Vignette 16

Topic: Alternative Investments

Clearwater’s Pending Acquisition Position

Elena Rao, a risk analyst at Clearwater Opportunities Fund, reviews a position established after Harrow Industries announced its acquisition of Vale Components. Rao must distinguish the position’s transaction-specific risks from ordinary equity-market exposure. All prices and amounts are in US dollars.

Transaction terms and holdings

For each Vale share, Harrow will pay $20 cash plus 0.80 Harrow shares. Both components are fixed, with no collar or price adjustment. Closing is scheduled four months after the fund establishes its position.

At entry, the indicated consideration is $52 per Vale share, giving a $4 spread over Vale’s market price. The fund shorts 0.80 Harrow shares for each Vale share held.

Financing review

Shareholder and regulatory approvals have been obtained. The cash consideration depends on new acquisition debt. The merger agreement permits Harrow to terminate if it cannot obtain that debt at an annual coupon of 8.0% or less. Harrow has no committed alternative funding source.

Initial lender indications were 7.0%. Following a credit-market sell-off, nonbinding indications have increased to 9.0%. Broad equity-index levels have remained approximately unchanged. Clearwater has sufficient liquidity for all stated scenarios, and its committed term stock borrow extends two months beyond the scheduled closing date.

Committee stress assumptions

If the transaction terminates, the committee assumes Vale immediately trades at its standalone value of $34 and Harrow rebounds to $45. These are conditional stress estimates, not observed prices; the broad equity market is assumed unchanged in this scenario.

For all calculations, ignore dividends, interest, stock-borrow charges, transaction costs, and taxes. Measure profit or loss from the original entry prices.

Question 61

Which source of return best characterizes Clearwater’s rationale for establishing the position?

• A. Convergence of Vale’s price to the agreed consideration if the acquisition closes.
• B. Appreciation of the firms’ equity values as the broad stock market rises.
• C. Convergence of the firms’ standalone valuations as their operating performance becomes more similar.

Best answer: A

Explanation

The position is merger arbitrage, an event-driven strategy seeking to capture the difference between a target’s trading price and the consideration payable upon completion. Clearwater’s short position matches the Harrow shares deliverable for its Vale holding. If the transaction closes, those delivered shares can cover the short, leaving the cash component as the remaining proceeds. This differs from an equity relative-value trade based on converging standalone valuations or a directional investment based on rising equity markets. The spread compensates the fund for uncertainty surrounding a contingent corporate event; it is not a risk-free pricing discrepancy.

Why each answer fits or falls short

• A. The fund purchases Vale below the indicated acquisition consideration and shorts the Harrow shares it would receive upon completion.
• B. A broad market rally is not the position’s central return mechanism because the Harrow short offsets the acquisition’s stock-consideration exposure.
• C. The position follows the contractual exchange ratio rather than evidence that the firms’ standalone valuations or operating performance will converge.

Related terms: Merger arbitrage; Event-driven strategies; Deal spread; Exchange ratio.

Question 62

In an independent successful-closing scenario, assume the financing condition is satisfied and Harrow trades at $36 immediately before completion. Clearwater uses the Harrow shares received in the acquisition to cover its short. The position’s total gross profit is closest to:

• A. $80,000
• B. $400,000
• C. $720,000

Best answer: B

Explanation

At completion, Vale’s consideration reflects Harrow’s actual share price, not its price when the position was established. The value received per Vale share is:

\[ 20+0.80(36)=48.80. \]

Let \(\Pi\) denote the position’s gross dollar profit. The long position gains the increase in Vale’s value, while the short gains from Harrow’s price decline:

\[ \Pi=100{,}000(48.80-48.00)+80{,}000(40.00-36.00)=400{,}000. \]

The fund receives 80,000 Harrow shares, exactly enough to cover its short, plus $2,000,000 cash. Relative to its initial net cash outlay of $1,600,000, this also produces a $400,000 profit. The exchange-ratio hedge offsets changes in the stock component when the transaction completes on its stated terms.

Why each answer fits or falls short

• A. This includes only Vale’s increase from $48.00 to $48.80 and omits the $320,000 gain on the Harrow short.
• B. Vale contributes $80,000 and the Harrow short contributes $320,000, producing a combined gross profit of $400,000.
• C. This incorrectly values Vale at the initial $52 indicated consideration and then adds the short gain despite Harrow’s lower closing price.

Related terms: Stock-for-stock merger; Hedge ratio; Short-sale profit; Merger consideration.

Question 63

Which risk to Clearwater’s position is most directly increased by the credit-market update?

• A. Deal-break risk arising from Harrow’s acquisition-financing condition.
• B. Funding-liquidity risk arising from Clearwater’s collateral requirements.
• C. Short-squeeze risk arising from Clearwater’s stock-borrow availability.

Best answer: A

Explanation

Merger-arbitrage positions are exposed to failure of the conditions required for completion. Here, the relevant condition is acquisition financing: Harrow can terminate if debt at an annual coupon of 8.0% or less is unavailable. Lender indications have risen from 7.0% to 9.0%, and no alternative funding is committed. This increases the probability of termination, although a nonbinding indication does not establish that failure is certain. Financing risk at the acquirer must be distinguished from funding-liquidity risk at the hedge fund. Clearwater’s liquidity and stock-borrow arrangements remain sufficient under the stated assumptions, so those mechanisms do not explain the incremental risk from the credit-market change.

Why each answer fits or falls short

• A. The 9.0% financing indication exceeds the contractual 8.0% limit, increasing the likelihood that Harrow cannot satisfy the financing condition.
• B. The financing deterioration concerns Harrow’s acquisition debt, while Clearwater has sufficient liquidity for the stated scenarios.
• C. Clearwater’s term stock borrow remains committed beyond scheduled closing, and the update provides no evidence of deteriorating share-borrow availability.

Related terms: Deal-break risk; Financing condition; Funding liquidity risk; Stock-borrow risk.

Question 64

Compared with an unhedged holding of the same 100,000 Vale shares, how would Clearwater’s position perform in the committee’s deal-break scenario?

• A. It would incur the same dollar loss because the exchange-ratio hedge removes Harrow’s contribution to profit or loss.
• B. It would incur a larger dollar loss because the Harrow short also loses when Harrow shares rebound.
• C. It would incur a smaller dollar loss because the exchange-ratio hedge offsets Vale’s decline after termination.

Best answer: B

Explanation

A hedge matched to merger consideration is not a general hedge against losses following deal failure. In the committee’s stress scenario, Vale falls from $48 to $34, producing a $1,400,000 loss on 100,000 shares. Harrow rises from $40 to $45, so Clearwater’s 80,000-share short loses another $400,000. Clearwater therefore loses $1,800,000, compared with $1,400,000 for the unhedged Vale holding. Once the transaction terminates, the contractual exchange ratio no longer links the securities’ values. This illustrates the asymmetric downside of merger arbitrage: reduced market exposure during normal conditions can coexist with losses on both legs when a deal breaks, even without a broad equity-market decline.

Why each answer fits or falls short

• A. The hedge removes Harrow-price exposure conditional on completion, not after termination when no Harrow shares are delivered to cover the short.
• B. Both positions lose $1,400,000 on Vale, but Clearwater additionally loses $400,000 on the Harrow short as its price rises to $45.
• C. After termination, the contractual exchange relationship no longer applies, and Harrow’s assumed rebound creates a loss on the short.

Related terms: Event risk; Negative skewness; Basis risk; Stress testing.

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Practice Vignette 17

Topic: Portfolio Construction

Brookmere’s Portfolio Arbitrage Review

Mira Shah, CFA, an analyst at Brookmere Asset Management, reviews diversified portfolios for a one-year arbitrage pricing theory (APT) strategy. She models common return risk using unexpected economic growth and unexpected inflation. For the initial screen, she assumes that residual returns are fully diversified away.

Prices and return forecasts

North and South are correctly priced benchmark portfolios. Cedar and Vale are candidate trades whose current prices may depart from APT pricing. All amounts are in US dollars. Prices are per portfolio unit, and forecasts are one-year total returns, including distributions.

Factor exposures

Each sensitivity measures the percentage-point change in portfolio return for a one-percentage-point factor surprise. Factor scaling is identical across portfolios.

Trading assumptions

One-year borrowing and lending are available at the risk-free rate of 3.0%. Cash has zero exposure to both factors. Fractional portfolio units may be traded, short selling is unrestricted, and all short-sale proceeds are available for reinvestment. Ignore taxes, transaction costs, short-sale fees, and margin requirements.

Question 65

Cedar’s annual required return under the two-factor APT is closest to:

• A. 11.0%.
• B. 10.6%.
• C. 7.6%.

Best answer: B

Explanation

APT required return equals the risk-free rate plus compensation for exposure to each priced factor. Because North and South are correctly priced, their expected excess returns identify the annual growth and inflation premiums, denoted by \(\lambda_G\) and \(\lambda_I\):

\[ \lambda_G+0.5\lambda_I=5.0\%,\qquad 0.5\lambda_G+\lambda_I=4.0\%. \]

Solving gives a growth premium of 4.0% and an inflation premium of 2.0%. Applying Cedar’s sensitivities gives:

\[ E[R_{\mathrm{Cedar}}]_{\mathrm{APT}}=3.0\%+1.4(4.0\%)+1.0(2.0\%)=10.6\%. \]

The required return is determined by Cedar’s systematic exposures, not by its separate 11.0% return forecast.

Why each answer fits or falls short

• A. Cedar’s 11.0% forecast is its expected return at the current price, not the return required by its factor exposures.
• B. The benchmark-implied factor premiums give Cedar a required return of \(3.0\%+1.4(4.0\%)+1.0(2.0\%)=10.6\%\).
• C. This includes Cedar’s factor compensation of \(1.4(4.0\%)+1.0(2.0\%)=7.6\%\) but omits the 3.0% risk-free return.

Related terms: Arbitrage pricing theory; Factor risk premium; Factor sensitivity.

Question 66

Using the APT required return as the pricing benchmark, which assessment of Vale is most appropriate?

• A. Overpriced, with an expected return 0.2 percentage points below its required return.
• B. Underpriced, with an expected return 4.2 percentage points above its required return.
• C. Underpriced, with an expected return 1.2 percentage points above its required return.

Best answer: C

Explanation

Mispricing is assessed by comparing expected return at the quoted price with the return required for the portfolio’s factor exposures. North and South imply annual growth and inflation premiums of 4.0% and 2.0%, respectively. Vale therefore requires:

\[ E[R_{\mathrm{Vale}}]_{\mathrm{APT}}=3.0\%+0.6(4.0\%)+1.3(2.0\%)=8.0\%. \]

Its forecast exceeds this requirement by 1.2 percentage points. A higher expected return than that of a properly financed, factor-matched benchmark indicates a price below the APT-consistent level. Under the initial residual-diversification and frictionless-trading assumptions, buying Vale and taking the opposite position in its factor-matched alternative would isolate this pricing discrepancy.

Why each answer fits or falls short

• A. Reversing the growth and inflation premiums produces a mistaken 9.4% required return, whereas their correct assignment gives 8.0%.
• B. The 4.2-percentage-point gap omits the risk-free rate by comparing Vale’s 9.2% expected return with factor compensation of only 5.0%.
• C. Vale’s required return is \(3.0\%+0.6(4.0\%)+1.3(2.0\%)=8.0\%\), so its 9.2% forecast exceeds that return by 1.2 percentage points.

Related terms: APT mispricing; Required return; Expected return; Factor-matched portfolio.

Question 67

Shah purchases 10,000 units of Cedar. Which accompanying positions produce zero initial net investment and zero exposure to both reported factors?

• A. Short 8,000 North units and 15,000 South units; lend $600,000.
• B. Short 24,000 North units and 5,000 South units; lend $600,000.
• C. Short 28,000 North units and 12,500 South units; lend $1,400,000.

Best answer: B

Explanation

Factor neutrality requires matching position values times sensitivities, rather than treating North and South as pure-factor portfolios. The Cedar purchase costs $1 million. Let \(x\) and \(y\) be the North and South short positions, respectively, measured in millions of dollars. Neutralizing both factors requires:

\[ x+0.5y=1.4,\qquad 0.5x+y=1.0. \]

These equations give \(x=1.2\) and \(y=0.4\). At the quoted prices, Shah must short 24,000 North units and 5,000 South units. The shorts generate $1.6 million; after paying $1 million for Cedar, she lends the remaining $600,000. Cash adds no factor exposure, and the complete position requires no initial net investment.

Why each answer fits or falls short

• A. The $400,000 North short and $1.2 million South short balance initial financing but leave nonzero exposure to both factors.
• B. The $1.2 million and $400,000 shorts offset Cedar’s factor exposures, while the $600,000 deposit makes initial net investment zero.
• C. Shorting $1.4 million of North and $1.0 million of South mistakes the benchmarks for pure-factor portfolios and overhedges both exposures.

Related terms: Factor neutrality; Self-financing portfolio; Short selling; Replicating portfolio.

Question 68

In a separate robustness test, Cedar’s constituent returns are found to share a material, zero-mean liquidity shock with identical positive loadings. The shock is independent of growth and inflation; North, South, and cash have zero exposure to it. This finding replaces the initial residual-diversification assumption for this test. How should Shah interpret a zero-cost position that is long Cedar and uses only North, South, and cash to neutralize the two reported factors?

• A. The position retains systematic liquidity risk that the benchmark hedges cannot eliminate.
• B. The position retains only diversifiable risk that disappears as Cedar adds more issuers.
• C. The position is riskless because the remaining liquidity shock has zero expected value.

Best answer: A

Explanation

Neutralizing the reported factors establishes riskless arbitrage only if no material uncertain return component remains. A shock shared by Cedar’s constituents is systematic within that portfolio, even though the original two-factor model labels it residual return. Identical positive loadings do not disappear as the number of holdings increases. Because the permitted hedge instruments have no liquidity exposure, the position retains this source of uncertainty. A zero-mean shock can still have substantial variance and produce losses. The apparent two-factor return spread could therefore reflect compensation for omitted risk rather than arbitrage; that risk must be modeled or offset before a riskless-arbitrage conclusion is justified.

Why each answer fits or falls short

• A. Cedar retains exposure to an independent common shock, while North, South, and cash provide no offsetting liquidity exposure.
• B. The identical liquidity loading is common across constituents, so adding more issuers does not diversify away this residual component.
• C. Zero expected value does not imply zero variance, so the remaining liquidity shock can generate losses despite its zero mean.

Related terms: Systematic risk; Idiosyncratic risk; Omitted factor risk; Riskless arbitrage.

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Practice Vignette 18

Topic: Portfolio Construction

Alder ETF Trading Review

Mira Shah, a portfolio analyst at Vale Asset Management, reviews trading conditions in the Alder Small-Cap Equity ETF. She obtains synchronized fund data and executable quotes from Northbridge Securities, an authorized participant in the ETF.

10:00 a.m. snapshot

All amounts are in US dollars. NAV reflects current underlying-security prices rather than the previous closing prices.

Execution assumptions

The ETF uses pro rata, in-kind creations and redemptions with no cash component. For the baseline analysis, Northbridge can purchase or sell the designated basket at its stated value.

The additional AP costs include processing, brokerage, and financing charges beyond the stated purchase and sale prices. They apply equally to creation and redemption transactions and are borne entirely by Northbridge, not the fund.

Northbridge can lock all transaction prices simultaneously for the required quantities, and settlement creates no delivery or funding mismatch. Ignore taxes. Underlying-security prices remain unchanged during the modeled transactions, and the fund has no other flows, distributions, or expenses.

Question 69

Which transaction and net profit correctly describe how Northbridge can capture the snapshot mispricing for one creation-unit equivalent?

• A. Buy the basket, create one unit, and sell the ETF shares for a $13,000 net profit.
• B. Buy ETF shares, redeem one unit, and sell the basket for a $19,000 net profit.
• C. Buy the basket, create one unit, and sell the ETF shares for a $9,000 net profit.

Best answer: C

Explanation

When ETF shares trade sufficiently above the cost of obtaining the creation basket, an authorized participant can buy the basket, exchange it for newly issued ETF shares, and sell those shares. The executable ETF sale price is the bid, not the ask or midpoint. Northbridge’s net profit is:

\[ \Pi = 50,000(40.26) - 2,000,000 - 4,000 = 9,000. \]

The synchronized execution assumptions allow Northbridge to lock this spread rather than speculate on future convergence. Redemption runs in the opposite direction: purchasing the relatively expensive ETF shares and selling the received basket would generate a loss under these quotes.

Why each answer fits or falls short

• A. The $13,000 amount is the gross spread and omits the additional $4,000 of AP costs.
• B. Buying ETF shares at the ask and redeeming them produces a $19,000 loss after costs, not a profit.
• C. Selling 50,000 ETF shares at $40.26 generates $2,013,000, exceeding the $2,000,000 basket cost and $4,000 additional costs by $9,000.

Related terms: Authorized participant; Creation arbitrage; Primary market; Bid-ask spread.

Question 70

Using the midpoint of the ETF bid and ask prices, the ETF’s premium relative to NAV at the snapshot is closest to:

• A. 0.65%.
• B. 0.75%.
• C. 0.70%.

Best answer: C

Explanation

An ETF premium measures the amount by which its secondary-market price exceeds NAV, expressed as a percentage of NAV. The requested price convention is the midpoint:

\[ P_{\mathrm{mid}} = \frac{40.26 + 40.30}{2} = 40.28. \]

The premium is therefore:

\[ \text{Premium} = \frac{40.28 - 40.00}{40.00} \times 100\% = 0.70\%. \]

The denominator is NAV, not the ETF market price. Because both NAV and the quotes reflect the same observation time, this comparison does not mix current ETF prices with a previous closing NAV. The midpoint premium is a valuation measure, not an executable arbitrage return after costs.

Why each answer fits or falls short

• A. A 0.65% premium uses the $40.26 bid price rather than the requested bid-ask midpoint.
• B. A 0.75% premium uses the $40.30 ask price rather than the requested bid-ask midpoint.
• C. The midpoint is $40.28, giving a premium of \(40.28/40.00 - 1 = 0.70\%\).

Related terms: ETF premium; Net asset value; Midquote.

Question 71

If three creation units settle on the snapshot terms, what are the fund’s shares outstanding and NAV per share immediately afterward?

• A. 12,150,000 shares outstanding and NAV per share of $39.51.
• B. 12,000,000 shares outstanding and NAV per share of $40.50.
• C. 12,150,000 shares outstanding and NAV per share of $40.00.

Best answer: C

Explanation

An in-kind creation increases both the ETF’s assets and its shares outstanding. When the contributed basket equals the NAV of the shares issued, creation does not dilute existing shareholders. Three units add \(3 \times 50,000 = 150,000\) shares and \(3 \times 2,000,000 = 6,000,000\) dollars of assets. The resulting NAV per share is:

\[ \mathrm{NAV}_{\mathrm{new}} = \frac{480,000,000 + 6,000,000}{12,000,000 + 150,000} = 40.00. \]

Northbridge bears the transaction costs, so those costs do not reduce fund assets. The ETF’s secondary-market premium also does not increase fund NAV: investors trading ETF shares above NAV do not transfer that premium into the fund’s portfolio.

Why each answer fits or falls short

• A. The $39.51 amount divides existing net assets by the expanded share count while omitting the contributed baskets.
• B. The $40.50 amount includes the contributed assets but omits the 150,000 newly issued ETF shares.
• C. Creation adds 150,000 shares and $6,000,000 of assets, leaving NAV at $486,000,000 divided by 12,150,000 shares, or $40.00.

Related terms: Creation unit; In-kind creation; Shares outstanding; NAV dilution.

Question 72

For this question only, the ETF quotes change to a $40.14 bid and $40.18 ask while NAV remains $40.00. Limited basket liquidity increases the executable basket purchase cost to $2,004,000, and the additional $4,000 of AP costs is unchanged. What is the implication for one-unit creation arbitrage?

• A. A $1,000 loss means creation provides no positive arbitrage incentive.
• B. A $3,000 profit means creation provides a positive arbitrage incentive.
• C. A zero profit means creation is exactly at the arbitrage break-even point.

Best answer: A

Explanation

A positive ETF premium does not necessarily create an executable arbitrage opportunity. The authorized participant must compare ETF sale proceeds at the bid with the actual basket acquisition cost and all additional charges. Under the revised conditions:

\[ \Pi = 50,000(40.14) - 2,004,000 - 4,000 = -1,000. \]

The break-even ETF bid is \((2,004,000 + 4,000)/50,000 = 40.16\), above the available $40.14 bid. Reduced basket liquidity has therefore eliminated Northbridge’s incentive to create at these prices. Transaction costs and basket execution frictions establish arbitrage bounds within which an ETF premium can persist, even when the published NAV is current.

Why each answer fits or falls short

• A. ETF sale proceeds of $2,007,000 are $1,000 below the combined $2,004,000 basket purchase cost and $4,000 additional costs.
• B. The $3,000 profit incorrectly uses the basket’s $2,000,000 NAV value instead of its revised $2,004,000 executable purchase cost.
• C. The break-even result incorrectly assumes Northbridge can sell ETF shares at the $40.16 midpoint rather than the $40.14 bid.

Related terms: Arbitrage bounds; Basket liquidity; Transaction costs; Creation arbitrage.

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Practice Vignette 19

Topic: Portfolio Construction

Alder Quay’s Equity Risk Review

Leena Rao, a risk analyst at Alder Quay Asset Management, reviews a parametric value at risk (VaR) report for a long-only equity portfolio. The risk committee wants to understand the reported threshold, evaluate the model assumptions, and assess sensitivity to higher volatility.

Baseline report inputs

All returns and portfolio values are measured in USD.

The baseline model assumes independent, identically distributed normal daily returns. It approximates the holding-period return by adding daily simple returns rather than compounding them and applies that return to the current portfolio value. The report includes expected return and expresses VaR as a positive loss relative to current value, not relative to expected future value.

The portfolio is treated as a fixed linear exposure over the holding period. There are no external cash flows, trading costs, or rebalancing.

Historical return diagnostics

Rao separately examines 2,000 daily portfolio returns to evaluate whether the baseline model remains suitable.

The review also identifies persistent clusters of unusually large absolute daily returns. These patterns recur across subsamples and are not attributable to changes in portfolio composition. The committee continues to use the stated baseline inputs for its calculations while considering a replacement model.

Question 73

Using the baseline model, the portfolio’s 10-trading-day 99% VaR is closest to:

• A. $22.90 million.
• B. $6.97 million.
• C. $7.37 million.

Best answer: B

Explanation

Parametric VaR converts a lower-tail return quantile into a positive monetary loss. Under independent daily normal returns, expected return scales with the holding period, while standard deviation scales with its square root. Let \(V_0\) be current portfolio value, \(h\) the number of trading days, and \(\mu_d\) and \(\sigma_d\) the daily mean and standard deviation.

\[ \mathrm{VaR}=V_0\left(z\sigma_d\sqrt{h}-h\mu_d\right). \]

Using the supplied inputs and expressing dollar amounts in millions:

\[ \mathrm{VaR}=100\left[2.33(0.01)\sqrt{10}-10(0.0004)\right]=6.9681. \]

The result is approximately $6.97 million. Because VaR is measured relative to current portfolio value, the positive expected holding-period return reduces the reported loss threshold.

Why each answer fits or falls short

• A. This amount multiplies one-day VaR by ten, incorrectly scaling the volatility component linearly rather than by the square root of time.
• B. Including expected return gives a loss threshold of \(100[2.33(0.01)\sqrt{10}-10(0.0004)]=6.9681\) million.
• C. This amount includes the ten-day volatility adjustment but omits the expected ten-day gain, which reduces the loss threshold by $0.40 million.

Related terms: Parametric VaR; Square-root-of-time rule; Normal quantile; Holding period.

Question 74

Under the baseline model, which statement best interprets the report’s 10-trading-day 99% VaR?

• A. The probability that the portfolio’s loss on the next trading day exceeds the reported VaR is 1%.
• B. The mean portfolio loss among the worst 1% of 10-trading-day outcomes equals the reported VaR.
• C. The probability that the portfolio’s loss over the next 10 trading days exceeds the reported VaR is 1%.

Best answer: C

Explanation

VaR is a quantile of a loss distribution for a specified confidence level and holding period. Alder Quay’s 99% ten-trading-day VaR identifies a loss threshold that the model assigns a 1% probability of exceeding over the next ten trading days. Equivalently, the model assigns a 99% probability to an outcome no worse than that threshold, including outcomes with gains.

VaR is neither a maximum possible loss nor an average of extreme losses. Expected shortfall measures the average loss beyond the VaR threshold. The horizon is also essential: a ten-day threshold cannot be interpreted using a one-day exceedance probability. These probabilities are model-based, not guarantees about realized outcomes.

Why each answer fits or falls short

• A. The report’s threshold applies to the ten-trading-day loss distribution, so its 1% exceedance probability does not apply to a one-day loss.
• B. The mean loss conditional on being in the worst 1% describes expected shortfall, not the quantile reported as VaR.
• C. The reported VaR is the 99th percentile of the model’s ten-trading-day loss distribution, leaving 1% probability beyond that threshold.

Related terms: Value at risk; Quantile; Expected shortfall; Tail probability.

Question 75

The committee wants a replacement return specification that addresses both the historical tail-shape evidence and volatility clustering. Which specification best meets that objective?

• A. A symmetric normal return distribution with time-varying conditional volatility.
• B. An asymmetric, fat-tailed return distribution with constant conditional volatility.
• C. An asymmetric, fat-tailed return distribution with time-varying conditional volatility.

Best answer: C

Explanation

A normal distribution is symmetric and has zero excess kurtosis. The observed skewness of -0.85 and excess kurtosis of 4.20 therefore challenge the baseline normal-return assumption. An asymmetric, fat-tailed specification can represent a longer downside tail and greater tail weight.

The positive autocorrelation of squared returns and recurring clusters of large absolute returns provide separate evidence that volatility changes through time. A model with time-varying conditional volatility can distinguish high-risk periods from quieter periods. Combining flexible tail shape with changing conditional volatility addresses both sets of diagnostics. Such a specification still requires estimation and validation; these observations alone do not establish a precise revised VaR amount.

Why each answer fits or falls short

• A. Time-varying volatility addresses clustering, but the symmetric normal specification does not directly capture the observed negative skewness.
• B. An asymmetric, fat-tailed distribution addresses the tail-shape evidence, but constant conditional volatility does not capture persistent volatility clustering.
• C. Asymmetric heavy tails address the observed skewness and excess kurtosis, while time-varying conditional volatility addresses clustering in large absolute returns.

Related terms: Negative skewness; Excess kurtosis; Volatility clustering; Conditional volatility.

Question 76

In a local sensitivity test, daily volatility increases from 1.00% to 1.50%. The expected daily return and all other baseline assumptions remain unchanged. The percentage increase in 10-trading-day 99% VaR is closest to:

• A. 50.0%.
• B. 52.9%.
• C. 125.0%.

Best answer: B

Explanation

With portfolio value, confidence level, and horizon unchanged, the volatility component of VaR rises in proportion to daily standard deviation. However, the positive expected-return deduction remains fixed. Consequently, the complete VaR measure does not increase by exactly the same percentage as volatility.

Portfolio value cancels when comparing the shocked and baseline thresholds:

\[ \frac{2.33(0.015)\sqrt{10}-10(0.0004)}{2.33(0.010)\sqrt{10}-10(0.0004)}-1=0.5287. \]

Thus, VaR increases by approximately 52.9%. If expected return were zero, the increase would equal the 50% volatility increase. Here, subtracting the same positive expected gain from both thresholds makes the percentage increase slightly larger.

Why each answer fits or falls short

• A. This result scales the entire baseline VaR by the volatility ratio, although the expected-return deduction remains unchanged.
• B. Recalculating both thresholds gives a ratio of approximately 1.5287, so the positive fixed expected-return deduction makes VaR rise by more than 50%.
• C. This result applies the 2.25 variance multiplier to VaR, although the risk component depends on standard deviation rather than variance.

Related terms: Parametric VaR; Volatility; Expected return.

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Practice Vignette 20

Topic: Ethical and Professional Standards

Hospitality and Client Gifts at Pinecrest

Nadia Shah, CFA, manages several institutional and private-client portfolios at Pinecrest Asset Management. She directs trades and votes on the firm’s approved-broker list. Felix Mora, CFA, is her supervisor and oversees the compliance officer’s hospitality reviews. Mora also has authority to consent to personal compensation arrangements on Pinecrest’s behalf.

Applicable law imposes no additional restrictions relevant to the benefits described.

Pinecrest’s review process

Pinecrest’s policy distinguishes two categories:

• Trading-counterparty entertainment: Benefits exceeding $250 require written compliance approval. An $8,000 annual allowance applies to each employee.
• Unexpected client appreciation gifts: Unconditional gifts recognizing completed service may be retained if the employee reports the donor, nature, estimated value, and circumstances by the next business day.

For counterparty entertainment, the compliance checklist verifies the available annual allowance and obtains the counterparty’s written statement that no transactions are promised. Mora receives quarterly approval totals. The process does not examine recipients’ investment authority or connect hospitality records with subsequent broker-selection decisions.

Aspen Securities’ invitation

During Pinecrest’s annual broker review, Aspen Securities asks to increase its current 10% share of Pinecrest’s trading business. Aspen then offers Shah and a companion a three-night destination music-festival package, including business-class flights, resort accommodation, and premium concert access. The package is worth $6,800 and has no business program.

Shah has received no other counterparty entertainment that year. Aspen provides the required no-commitment statement, and compliance approves the entire package in writing. Shah accepts and attends.

A subsequent review finds that Aspen’s order share remains 10% and its transactions meet Pinecrest’s documented best-execution criteria.

A client’s recognition

Later that month, long-standing private client Tessa Lorne unexpectedly presents Shah with two bottles of wine worth $450 at the end of a Friday-evening meeting. Shah had no advance notice of the gift. Lorne’s accompanying note thanks Shah for service during the completed investment year. The gift involves no future performance condition or agreement to provide additional services.

Shah accepts the gift and emails Mora on the next business morning, identifying Lorne, describing the wine, estimating its value, and explaining the occasion. Mora acknowledges receipt.

Question 77

Which conclusion about Shah’s acceptance of Aspen’s package is most accurate?

• A. Her acceptance complied with Standard I(B) because written employer approval covered every element of the package.
• B. Her acceptance complied with Standard I(B) because Aspen’s order share remained unchanged and its transactions met execution criteria.
• C. Her acceptance violated Standard I(B) because the package could reasonably be expected to compromise her broker-selection judgment.

Best answer: C

Explanation

Standard I(B), Independence and Objectivity, prohibits accepting benefits that reasonably could be expected to compromise investment judgment. The assessment concerns the benefit’s potential influence, not merely whether subsequent records demonstrate biased decisions.

Aspen is seeking more business during a broker review in which Shah has both voting and trading authority. Its $6,800 package includes companion travel and substantial leisure benefits, with no business program. These circumstances create a material threat to her objectivity. Compliance approval establishes that Pinecrest’s internal checklist was followed; it does not establish compliance with the Standards. Neither employer permission nor the absence of an explicit trading commitment makes this package acceptable.

Why each answer fits or falls short

• A. Employer approval does not authorize acceptance of lavish counterparty entertainment that could reasonably be expected to compromise investment judgment.
• B. Unchanged trading outcomes do not eliminate the reasonably foreseeable threat to objectivity created when Shah accepted the package.
• C. Aspen’s substantial leisure package benefits Shah and a companion while she influences a broker review in which Aspen seeks additional business.

Related terms: Independence and Objectivity; Broker entertainment; Conflicts of interest.

Question 78

Holding Pinecrest’s dollar limits fixed, which replacement for the approval checklist and related monitoring best supports Mora’s duty to make reasonable efforts to prevent and detect violations?

• A. Review donor relationships, package terms, and recipients’ decision-making authority, then independently test approvals and related broker-selection decisions.
• B. Review employee declarations of impartiality and broker assurances of no promised trades, then independently compare the broker’s execution prices with benchmarks.
• C. Review package costs and signed no-obligation statements, then independently reconcile accepted benefits with approved values and annual allowances.

Best answer: A

Explanation

Standard IV(C), Responsibilities of Supervisors, requires reasonable efforts to ensure that supervised personnel comply with applicable requirements, including the Code and Standards. Delegating individual reviews to compliance does not eliminate Mora’s supervisory responsibility for an adequate process.

Pinecrest’s existing checks emphasize spending capacity and explicit commitments. Neither directly evaluates how entertainment might influence someone who selects brokers and directs trades. A stronger framework examines the donor’s commercial interests, the package’s substance and timing, and the recipient’s authority before acceptance. Independent testing of approvals and related broker decisions then helps detect failures in application. Cost reconciliation and execution-price comparisons remain useful supporting controls, but they do not substitute for assessing the underlying threat to objectivity.

Why each answer fits or falls short

• A. This framework assesses potential influence before acceptance and tests whether approvals and subsequent decisions comply with appropriate independence safeguards.
• B. Declarations and execution-price testing do not adequately address implicit influence over broker approval or order allocation.
• C. Financial reconciliation and no-obligation statements can confirm procedural compliance while overlooking influence arising from a recipient’s authority and donor relationship.

Related terms: Responsibilities of Supervisors; Compliance procedures; Gift preclearance; Broker selection.

Question 79

Considering only Lorne’s appreciation gift, which conclusion about Shah’s conduct is most accurate?

• A. She failed to meet the applicable requirements because she had not secured written employer approval before accepting the gift.
• B. She met the applicable requirements by promptly reporting the unexpected gift and its circumstances to Mora.
• C. She failed to meet the applicable requirements because she had not disclosed the gift to her other managed clients.

Best answer: B

Explanation

Under Standard I(B), gifts from existing clients must be disclosed to the employer so that potential effects on impartial treatment can be evaluated. When advance notification is not possible, prompt disclosure after acceptance is appropriate.

Lorne’s gift was unexpected and recognized completed service without imposing future conditions. Shah’s next-business-morning email supplied the information Mora needed, and it satisfied Pinecrest’s stated policy. The employer can use that information to assess whether oversight of account service or trade allocations is warranted. Pinecrest’s separate preapproval threshold concerns trading-counterparty entertainment, not this client appreciation gift. The facts also do not establish a requirement to circulate the gift details to all other clients.

Why each answer fits or falls short

• A. The unexpected client gift could be reported promptly afterward, and Pinecrest’s $250 preapproval rule applies to trading-counterparty entertainment.
• B. Shah disclosed the donor, nature, value, and retrospective purpose of the unexpected gift at the next business opportunity.
• C. This unconditional appreciation gift requires employer disclosure, not routine notification to every other client whose account Shah manages.

Related terms: Client gifts; Employer disclosure; Preferential treatment.

Question 80

Replace only the client appreciation gift with the following facts: Before the next investment year begins, Lorne sends Shah a signed proposal to pay her personally $12,000 if Lorne’s account outperforms its agreed benchmark during that year. Shah forwards the complete proposal to Mora, who gives oral approval. Shah has not yet accepted, and no written employer consent exists. Which statement about employer consent is most accurate?

• A. Mora’s written consent becomes necessary only when the bonus is earned because Shah has not yet received compensation.
• B. Mora’s oral approval is sufficient because Lorne’s offer and Shah’s disclosure to him are both written.
• C. Mora must give written consent before Shah accepts; his email agreeing to the disclosed terms would suffice.

Best answer: C

Explanation

Standard IV(B), Additional Compensation Arrangements, requires written consent from all parties involved before accepting compensation that could reasonably create a conflict with the employer’s interests. A personal bonus contingent on future account performance can encourage preferential attention to that account, making employer consent necessary.

Lorne has documented her proposed terms, and Shah has fully disclosed them. However, Mora’s oral approval does not satisfy Pinecrest’s written-consent requirement under the Standard. As the firm’s authorized representative, he can provide that consent by email; a paper signature is not essential. Shah must obtain the written consent before agreeing to the arrangement. Deferring payment until performance is measured does not defer the consent obligation.

Why each answer fits or falls short

• A. The consent requirement applies before acceptance of the compensation arrangement, not merely when the contingent payment is earned or received.
• B. A written client offer and written employee disclosure do not substitute for the employer’s own written consent.
• C. The prospective personal performance bonus requires prior written employer consent, and an email can satisfy the writing requirement.

Related terms: Additional Compensation Arrangements; Written consent; Performance-based compensation.

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Practice Vignette 21

Topic: Ethical and Professional Standards

Cedarbridge and Bayhaven’s Referral Program

Maya Chen, CFA, is a private wealth adviser employed by Cedarbridge Asset Management. Owen Malik, CFA, is a financial planner employed by Bayhaven Planning. Bayhaven refers clients seeking discretionary investment management to Cedarbridge while continuing to provide their financial planning services.

Local law permits the arrangement described below. Statutory referral-fee disclosure requirements cover cash payments but do not cover noncash benefits.

Program terms

For each referred client who funds a Cedarbridge account, Cedarbridge provides Bayhaven with a one-time credit toward third-party financial planning software. The credit equals 20% of the client’s estimated management fee for the first full year and is issued at the end of the quarter in which funding occurs.

Bayhaven can use every credit against software it already purchases, dollar for dollar, but cannot exchange credits for cash. Neither Maya nor Owen receives any personal payment from the program.

Park’s prospective account

Elena Park, an existing Bayhaven planning client, is considering Cedarbridge. Owen has not yet recommended Cedarbridge to her, and she has not signed an investment-management agreement.

The firms use the following assumptions to estimate the benefit associated with her potential referral:

Approvals and reporting

Both employers require written approval before employees participate in referral arrangements. Maya and Owen obtained that approval after fully describing the program, including the credit formula and its noncash form.

Their employers currently receive quarterly referral-payment reports drawn from cash receipt and disbursement records. Software credits appear only in separate vendor ledgers and are excluded from those reports. The ledgers identify each referred client, recipient, credit value, and issue date.

The firms are reviewing the benefit estimate, ongoing employer reporting, and prospective-client disclosure process before Owen proceeds with Park’s referral.

Question 81

Based on the stated assumptions, what estimated dollar value should Owen disclose for Bayhaven’s noncash benefit associated with Park’s referral?

• A. $0
• B. $22,500
• C. $4,500

Best answer: C

Explanation

Standard VI(C), Referral Fees, covers compensation and benefits received in cash or in kind. The disclosure should describe the benefit’s nature and estimated dollar value. Because Bayhaven can apply every credit against an expense it already incurs, the credit’s economic value equals its face amount.

Park’s estimated annual management fee is \(3{,}000{,}000 \times 0.0075 = 22{,}500\), and the referral benefit is \(22{,}500 \times 0.20 = 4{,}500\), both in dollars. Owen should describe a one-time software credit with an estimated value of $4,500, rather than reporting either zero cash receipts or Cedarbridge’s entire management fee.

Why each answer fits or falls short

• A. The software credit has economic value because it reduces Bayhaven’s existing expenses, even though it cannot be redeemed for cash.
• B. This amount is Cedarbridge’s estimated first-year management fee, not the 20% portion provided to Bayhaven as referral compensation.
• C. Bayhaven’s estimated benefit is 20% of Park’s $22,500 estimated first-year management fee, or $4,500.

Related terms: Referral fees; Noncash compensation; Estimated dollar value.

Question 82

Which procedure should Owen recommend for ongoing employer monitoring to align most closely with the recommended compliance procedures for Standard VI(C)?

• A. Report all referral benefits to Bayhaven management annually, supported by quarterly reconciliations of the cash records and vendor ledgers.
• B. Report the nature and value of cash and noncash referral benefits to Bayhaven management at least quarterly.
• C. Notify Bayhaven management whenever the benefit terms change, relying on its initial approval for credits issued under unchanged terms.

Best answer: B

Explanation

Recommended compliance procedures for Standard VI(C) include regular, at least quarterly, employer updates describing the nature and value of referral compensation. Initial approval establishes employer awareness of the arrangement but does not replace ongoing monitoring of the benefits it generates.

Bayhaven’s cash-based reporting process excludes the program’s actual compensation. Owen should incorporate the vendor-ledger information into employer updates so management receives a complete account of cash and noncash benefits. Annual reporting or notification only when contractual terms change provides less timely oversight. The quarterly frequency is a recommended compliance procedure; it should not be confused with a separate mandatory reporting deadline imposed by the facts of this case.

Why each answer fits or falls short

• A. Annual reporting is less frequent than the recommended employer updates, even if Owen reconciles complete records each quarter.
• B. Regular employer updates should include the nature and value of referral compensation, including software credits, at least quarterly.
• C. Reporting only changes in terms omits regular updates about benefits received under the approved arrangement.

Related terms: Referral fees; Employer disclosure; Compliance procedures.

Question 83

Under the Code and Standards, which statement about disclosure responsibilities to referred prospective investment-management clients such as Park is most accurate?

• A. Only Owen has disclosure responsibilities because Bayhaven receives the benefit and Maya receives no personal compensation.
• B. Both Maya and Owen have disclosure responsibilities because the arrangement involves compensation paid and received for referrals.
• C. Neither Maya nor Owen has disclosure responsibilities because local statutory requirements exclude noncash referral benefits.

Best answer: B

Explanation

Standard VI(C) addresses referral compensation both paid to others and received from others. Maya’s responsibility arises from Cedarbridge paying the referral benefit; Owen’s arises from Bayhaven receiving it. Neither the noncash form nor the absence of personal compensation removes these responsibilities.

Local law requires less disclosure than the Code and Standards. Under Standard I(A), Knowledge of the Law, members must follow the stricter applicable requirement, which here includes disclosure of noncash referral benefits. The firms may coordinate delivery of appropriate disclosures, but neither professional can treat the paying or receiving side as categorically exempt. Employer approval also does not substitute for appropriate disclosure to affected clients and prospects.

Why each answer fits or falls short

• A. Cedarbridge’s payment creates a disclosure responsibility for Maya even though she receives no personal portion of the benefit.
• B. Standard VI(C) covers referral benefits paid and received, including firm-level noncash benefits, despite the narrower local statutory requirement.
• C. The Code and Standards impose broader disclosure duties than local law, so the statutory exclusion does not eliminate their responsibilities.

Related terms: Referral fees; Knowledge of the Law; Conflicts of interest.

Question 84

For this question only, assume neither professional discloses the arrangement to Park before she signs a binding Cedarbridge investment-management agreement on 8 June. Both provide complete disclosures on 10 June. Park funds her account on 15 June, and Bayhaven receives its credit at quarter-end. Which assessment of Maya’s disclosure timing is most accurate?

• A. It complies because complete disclosure occurred before Park funded her account.
• B. It complies because complete disclosure occurred before Bayhaven received its software credit.
• C. It violates the standard because complete disclosure first occurred after Park entered the advisory agreement.

Best answer: C

Explanation

Referral-benefit disclosure must allow a prospective client to evaluate the arrangement before entering a formal agreement for services. Complete content delivered later does not satisfy that timing requirement.

Park became contractually committed to Cedarbridge on 8 June without receiving any referral-benefit disclosure. Maya’s first disclosure on 10 June was therefore untimely under Standard VI(C). The later account-funding date and quarter-end credit issuance do not extend the deadline: those events concern implementation and compensation, rather than Park’s initial decision to engage the adviser. Subsequent disclosure informs Park but does not erase the original timing violation.

Why each answer fits or falls short

• A. Account funding is not the disclosure deadline; Park had already entered the binding investment-management agreement when disclosure occurred.
• B. The benefit’s payment date does not postpone the obligation to disclose before Park enters the formal services agreement.
• C. Standard VI(C) requires appropriate disclosure before entry into a formal services agreement, making the 10 June disclosure untimely.

Related terms: Referral fees; Prospective clients; Disclosure timing.

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Practice Vignette 22

Topic: Ethical and Professional Standards

Vega’s investment account

Elena Ward, CFA, advises Tomas Vega on a $4,000,000 nondiscretionary account at Bellmere Investments. The account represents all his investable financial assets.

January communications

Vega’s existing investment policy statement (IPS) seeks moderate long-term growth, requires at least 5% in cash, and permits up to 20% in illiquid investments.

On 14 January, Vega tells Ward that he has unexpectedly retired without a pension and must pay an $800,000 divorce settlement in nine months. He has no resources outside the account available for that payment. He says his willingness to take investment risk remains high.

On 16 January, Ward recommends investing $600,000 of the account’s $1,000,000 cash balance in a private fund that prohibits withdrawals for ten years. She checks compliance with the existing IPS percentage limits but does not reassess Vega’s financial circumstances or investment objectives. She tells him that a broader review can wait until the scheduled annual meeting. Vega declines the recommendation, and no investment occurs.

Revised IPS and unsolicited requests

On 1 February, Ward completes a comprehensive reassessment with Vega. They sign a revised IPS emphasizing capital preservation and moderate total-portfolio risk. It requires $800,000 to remain in cash or short-term government bills for the settlement. It does not categorically prohibit speculative securities.

The account’s holdings are:

On 5 February, Vega proposes two alternative unsolicited purchases of the same highly speculative listed common stock: $12,000 or $1,200,000. Each proposal is evaluated separately against the unchanged portfolio. Either purchase would be funded by selling diversified listed equities, leaving the settlement reserve untouched.

Ward explains why she would not recommend the stock for Vega and that its entire purchase price could be lost. Vega demonstrates that he understands the risks and remains interested in proceeding. Documented risk analysis concludes that the $12,000 purchase would not materially affect total-portfolio risk, whereas the $1,200,000 purchase would create a concentration materially inconsistent with his current risk objectives.

Applicable local law permits either otherwise lawful unsolicited purchase after informed written client consent. Bellmere requires documentation of the discussion and written client instructions but imposes no additional restriction beyond applicable professional duties.

Execution-only inquiry

Vega also shows his revised IPS and the larger proposed order to Daniel Moss, CFA, at Harbor Brokerage. Harbor offers a separate execution-only account. Moss would execute Vega’s precise instructions, provide no investment advice, exercise no discretion, and manage no portfolio mandate. All applicable legal disclosures and order-handling requirements would be satisfied.

Question 85

Which statement best evaluates Ward’s 16 January recommendation under Standard III(C), Suitability?

• A. She fulfilled her duty because the recommendation complied with the existing IPS percentage limits.
• B. She fulfilled her duty because Vega reaffirmed his willingness to accept substantial investment risk.
• C. She failed her duty because the material changes required reassessment before making the recommendation.

Best answer: C

Explanation

Suitability in an advisory relationship requires reasonable inquiry into the client’s current financial circumstances, investment experience, objectives, and constraints before recommending an investment. Material changes require timely reassessment rather than waiting automatically for the next annual review. Ward knew that Vega’s employment income had ended and that he faced an $800,000 payment within nine months. Those facts could change his liquidity requirements and capacity to bear losses, even if his willingness to take risk remained high. The private fund’s compliance with the old IPS percentage limits did not establish its suitability under the changed circumstances. Ward’s failure occurred when she made the recommendation; an executed trade or realized loss was not necessary.

Why each answer fits or falls short

• A. Compliance with legacy allocation limits does not replace reassessment after Ward learns of material changes in Vega’s income and liquidity requirements.
• B. Vega’s stated willingness to take risk does not establish his financial ability to bear risk after retirement and a substantial settlement obligation.
• C. Ward knew about Vega’s retirement and settlement obligation but recommended an investment without reassessing his current circumstances and objectives.

Related terms: Suitability; Risk capacity; Liquidity requirements; Investment policy statement.

Question 86

Under Standard III(C), which statement about the $12,000 unsolicited order is most accurate?

• A. Execution is permitted after documenting the discussion and obtaining Vega’s informed written instruction.
• B. Execution requires an IPS amendment naming the stock as an authorized investment.
• C. Execution is prohibited because Ward would not recommend the stock for Vega.

Best answer: A

Explanation

An unsolicited request should not be executed merely because the client initiated it. The adviser should discuss a request that does not align with the recommended strategy, explain its implications, and follow applicable firm procedures. Portfolio-level materiality then matters. Here, the $12,000 position represents only 0.3% of Vega’s portfolio, does not affect the settlement reserve, and has been assessed as immaterial to overall risk. Vega understands the potential loss and still wants the purchase. Because neither the IPS nor firm policy categorically prohibits the security, Ward may execute after obtaining and documenting his informed written instruction. His acknowledgment permits acceptance in these circumstances; it is not a general waiver of suitability duties.

Why each answer fits or falls short

• A. The order has an immaterial portfolio effect, Vega understands its risks, and documented written instructions satisfy the stated acceptance requirements.
• B. The IPS need not name every security, and this purchase has an immaterial portfolio effect without breaching a categorical investment prohibition.
• C. Ward’s unwillingness to recommend the stock does not automatically prohibit an informed unsolicited order with an immaterial total-portfolio effect.

Related terms: Unsolicited orders; Total-portfolio context; Materiality; Informed client consent.

Question 87

For the $1,200,000 order only, assume Vega refuses any further IPS review and insists on execution within his existing advisory account. He offers to sign a comprehensive risk acknowledgment and waiver. What is Ward’s most appropriate response?

• A. Execute through a client-directed sleeve while leaving the advisory agreement and IPS unchanged.
• B. Withhold execution and reassess whether the advisory relationship can continue.
• C. Execute after obtaining the signed acknowledgment and retaining the current IPS.

Best answer: B

Explanation

A materially consequential unsolicited request requires more than documenting that the client accepts investment risk. The adviser should revisit the IPS and determine whether the requested exposure can be reconciled with the client’s circumstances and a suitable advisory framework. An IPS revision must reflect a genuine reassessment, not merely authorize an otherwise unsuitable transaction. Here, the proposed position represents 30% of Vega’s assets and is materially inconsistent with his current risk objectives. Because he refuses further review and insists on using the existing advisory account, Ward should withhold execution and reconsider whether that relationship can continue. Neither a comprehensive waiver nor an internal client-directed label removes her professional responsibility.

Why each answer fits or falls short

• A. Relabeling a holding within the same advisory account does not remove Ward’s responsibility for its material effect on the total portfolio.
• B. The materially inconsistent order and Vega’s refusal to review the IPS require Ward to reconsider the relationship rather than rely on a waiver.
• C. Written acknowledgment does not cure a materially unsuitable transaction within an ongoing advisory relationship when the client refuses the necessary reassessment.

Related terms: Material unsolicited orders; Advisory relationship; IPS revision; Suitability.

Question 88

With respect only to Standard III(C), which statement best describes Moss’s responsibility if Harbor executes the larger order under the stated arrangement?

• A. Moss must apply Ward’s IPS because it governs every investment account Vega owns.
• B. Moss need not perform an advisory suitability assessment in the stated execution-only relationship.
• C. Moss must assess total-portfolio suitability because he knows the proposed investment is material.

Best answer: B

Explanation

Standard III(C) distinguishes an advisory relationship from execution-only brokerage. An adviser must evaluate client suitability, while a portfolio manager must remain consistent with the mandate being managed. Moss occupies neither role: he would execute precise instructions in a separate account without recommending investments, exercising discretion, or managing a strategy. His receipt of Vega’s IPS and knowledge of the proposed concentration do not independently create an advisory relationship. Consequently, Standard III(C) does not require him to perform Ward’s suitability assessment. This conclusion is limited to suitability under that standard; Moss remains responsible for applicable law, order handling, and other relevant professional obligations.

Why each answer fits or falls short

• A. Receiving a copy of another adviser’s IPS does not make Moss responsible for implementing that policy in a separate execution-only account.
• B. Moss provides no advice, exercises no discretion, and manages no mandate, so Standard III(C)’s advisory suitability assessment does not apply.
• C. Knowledge of the order’s size does not itself transform Moss’s execution-only service into an advisory relationship or portfolio-management mandate.

Related terms: Execution-only brokerage; Advisory relationship; Investment mandate; Standard III(C).

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Continue Level II practice

Use the explanations to identify a missed fact, an unsupported assumption or a calculation step. This public set is fixed, so repeated attempts may reflect remembered answers. Continue with further case practice in Finance Prep after targeted study.