IMT Exam 1 — CSI Investment Management Techniques (IMT®) Exam 1 Quick Reference

Last revised: June 29, 2026

Compact formulas, decision rules, and exam traps for Canadian Securities Institute IMT Exam 1 preparation.

Exam Identity and Use

This Quick Reference is independent review support for the Canadian Securities Institute CSI Investment Management Techniques (IMT®) Exam 1, exam code IMT Exam 1. Use it to consolidate formulas, portfolio-management logic, and applied decision rules. Always align final study with the current CSI materials and learning objectives.

High-Yield Exam 1 Map

Area	What to know cold	Typical exam decision point
Portfolio process	Objectives, constraints, policy, implementation, monitoring	Identify the correct next step in the investment management process
Client profile / IPS	Return, risk, liquidity, time horizon, tax, legal/regulatory, unique constraints	Distinguish a true constraint from an objective
Risk and return	Arithmetic/geometric return, standard deviation, beta, covariance, correlation	Select the right risk measure for the situation
Diversification	Correlation, systematic vs unsystematic risk, efficient frontier	Explain why adding a security may reduce portfolio risk
Asset allocation	Strategic, tactical, rebalancing, core-satellite	Choose policy mix versus short-term deviation
CAPM / market models	Beta, expected return, alpha, SML	Decide if a security is underpriced or overpriced
Performance measurement	TWR, MWR, Sharpe, Treynor, Jensen alpha, information ratio	Match the measure to the manager/client situation
Security analysis	Top-down, bottom-up, fundamental, technical, passive/active	Identify which analysis method is being used
Fixed-income basics	Price-yield relationship, duration, convexity, credit spread	Estimate bond price effect from rate changes
Equity valuation basics	P/E, dividend yield, DDM, ROE, DuPont	Interpret whether a stock looks cheap, expensive, or risky

Investment Management Process

Step	Purpose	Exam trap
1. Define client situation	Gather facts, goals, constraints, risk tolerance, time horizon	Do not recommend products before the client profile is understood
2. Set objectives	Translate goals into required return and acceptable risk	“Wants high return” is not enough; required return must be feasible
3. Build IPS	Document objectives, constraints, asset mix, benchmarks, review rules	IPS is a control document, not just a sales summary
4. Develop strategy	Strategic asset allocation, permitted securities, diversification	Asset allocation usually drives most portfolio risk/return
5. Implement	Select securities/managers, trade, control costs and taxes	Implementation must remain consistent with the IPS
6. Monitor and rebalance	Compare to benchmarks, client changes, drift, performance	Rebalancing is discipline, not market timing by default

IPS Objectives and Constraints

IPS component	Meaning	High-yield distinction
Return objective	Return needed to meet goals after costs, tax, inflation	Required return may exceed risk capacity; then goals must change
Risk tolerance	Willingness and ability to accept volatility/loss	Ability is financial; willingness is psychological
Liquidity	Need for cash or near-cash assets	High liquidity need reduces ability to hold volatile/illiquid assets
Time horizon	When funds are needed; may be multi-stage	Longer horizon usually increases risk capacity, but not always
Tax circumstances	Account type, tax sensitivity, income/capital gains preference	After-tax return matters in taxable accounts
Legal/regulatory	Trust, mandate, policy, contractual, regulatory constraints	A legal constraint can override return preferences
Unique circumstances	ESG preference, concentrated holdings, family needs, restrictions	Must be specific and investment-relevant

Return Formula Sheet

Holding Period Return

\[ R = \frac{P_1 - P_0 + I}{P_0} \]

Where \(P_0\) is beginning price, \(P_1\) is ending price, and \(I\) is income received.

Arithmetic Mean

\[ \bar{R} = \frac{R_1 + R_2 + \cdots + R_n}{n} \]

Use for expected single-period return when each period is equally likely.

Geometric Mean

\[ R_G = \left[(1+R_1)(1+R_2)\cdots(1+R_n)\right]^{1/n} - 1 \]

Use for compound multi-period performance.

Annualized Return

\[ R_{\text{annual}} = (1+R_{\text{period}})^m - 1 \]

Where \(m\) is the number of periods per year.

Real Return Approximation

\[ R_{\text{real}} \approx R_{\text{nominal}} - \text{inflation} \]

Exact Real Return

\[ R_{\text{real}} = \frac{1+R_{\text{nominal}}}{1+\text{inflation}} - 1 \]

Risk Formula Sheet

Variance and Standard Deviation

\[ \sigma^2 = \frac{\sum (R_i - \bar{R})^2}{n} \]\[ \sigma = \sqrt{\sigma^2} \]

Standard deviation measures total volatility around the mean.

Annualized Standard Deviation

\[ \sigma_{\text{annual}} = \sigma_{\text{period}} \sqrt{m} \]

Use only when periodic returns are assumed independent and similarly distributed.

Coefficient of Variation

\[ CV = \frac{\sigma}{E(R)} \]

Lower CV means less risk per unit of expected return.

Covariance and Correlation

\[ \rho_{A,B} = \frac{\text{Cov}_{A,B}}{\sigma_A \sigma_B} \]

Correlation ranges from \(-1\) to \(+1\).

Correlation	Meaning	Portfolio effect
+1.00	Perfect positive movement	No diversification benefit
0	No linear relationship	Diversification benefit
-1.00	Perfect inverse movement	Maximum diversification benefit
Less than +1	Not perfectly correlated	Some risk reduction possible

Two-Asset Portfolio Return

\[ E(R_p) = w_A E(R_A) + w_B E(R_B) \]

Two-Asset Portfolio Risk

\[ \sigma_p^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B\rho_{A,B}\sigma_A\sigma_B \]

Beta

\[ \beta_i = \frac{\text{Cov}_{i,m}}{\sigma_m^2} \]

Beta measures sensitivity to market movements, not total risk.

CAPM, Alpha, and Security Market Line

CAPM Expected Return

\[ E(R_i) = R_f + \beta_i [E(R_m)-R_f] \]

Input	Meaning	Trap
\(R_f\)	Risk-free rate	Base return for bearing no market risk
\(E(R_m)-R_f\)	Market risk premium	Compensation for market risk
\(\beta_i\)	Systematic risk	Beta does not measure unsystematic risk
\(E(R_i)\)	Required return	Compare with expected/forecast return

Alpha

\[ \alpha_i = R_i - [R_f + \beta_i(R_m - R_f)] \]

Result	Interpretation
Positive alpha	Return exceeded CAPM-required return
Negative alpha	Return fell short of CAPM-required return
Zero alpha	Return matched required return for beta risk

SML Decision Rule

Forecast return vs CAPM required return	Security implication
Forecast return > required return	Undervalued / attractive, all else equal
Forecast return < required return	Overvalued / unattractive, all else equal
Forecast return = required return	Fairly valued under CAPM assumptions

Risk Measures: Match the Measure to the Question

Measure	Captures	Best used for	Common trap
Standard deviation	Total volatility	Stand-alone portfolio risk	Penalizes upside and downside volatility
Variance	Squared volatility	Formula work	Harder to interpret directly
Beta	Systematic market risk	Diversified portfolios / CAPM	Not useful for undiversified total risk alone
Correlation	Co-movement	Diversification decisions	Low correlation does not guarantee positive return
Tracking error	Volatility of active return vs benchmark	Active manager consistency	Low tracking error can still mean poor return
Downside risk	Negative-return volatility	Loss-sensitive investors	Not always the same as standard deviation
Duration	Bond price sensitivity to rates	Interest-rate risk	Longer duration means higher rate sensitivity
Credit spread	Extra yield over safer benchmark	Credit/default risk	Wider spread may signal higher risk, not just value
Liquidity risk	Difficulty selling near fair value	Thin markets, private assets	High quoted return may hide exit risk

Time-Weighted vs Money-Weighted Return

Measure	Also known as	Cash-flow treatment	Best for	Exam clue
Time-weighted return	TWR	Neutralizes external cash-flow timing	Evaluating portfolio manager skill	Manager does not control deposits/withdrawals
Money-weighted return	MWR / IRR	Sensitive to cash-flow size and timing	Client’s actual experience	Client controls contribution/withdrawal timing

TWR Chain-Linking

\[ TWR = [(1+R_1)(1+R_2)\cdots(1+R_n)] - 1 \]

Money-Weighted Return Concept

MWR is the discount rate that equates the present value of cash inflows and outflows with ending value. In exam scenarios, choose MWR when the question emphasizes the investor’s actual dollar-weighted result.

Portfolio Theory Quick Reference

Concept	Meaning	Exam use
Efficient frontier	Portfolios with highest expected return for each risk level	Identify efficient vs inefficient portfolios
Minimum-variance portfolio	Lowest-risk portfolio on the frontier	Not necessarily the highest return
Optimal risky portfolio	Best risk-return mix before adding risk-free asset	Depends on risk/return/correlation assumptions
Capital market line	Efficient combinations of risk-free asset and market portfolio	Uses total portfolio standard deviation
Security market line	CAPM required return for beta	Uses beta, not standard deviation
Systematic risk	Marketwide risk	Cannot be diversified away
Unsystematic risk	Company/industry-specific risk	Can be reduced through diversification
Market portfolio	Theoretical portfolio of all risky assets	CAPM benchmark concept

CML vs SML

Feature	Capital Market Line	Security Market Line
Risk measure	Standard deviation	Beta
Applies to	Efficient portfolios	Individual securities and portfolios
Based on	Total risk	Systematic risk
Slope	Sharpe ratio of market portfolio	Market risk premium
Main use	Choose efficient portfolio mix	Judge required return / alpha

Asset Allocation Decision Matrix

Approach	Description	When to choose	Trap
Strategic asset allocation	Long-term policy weights	Core portfolio design	Not a short-term forecast tool
Tactical asset allocation	Short-term deviations from policy	Manager has active market view	Must define limits and risk controls
Dynamic allocation	Adjusts exposure as conditions change	Rules-based risk or market response	Can increase trading and tax costs
Core-satellite	Passive/low-cost core plus active satellites	Control cost while seeking alpha	Satellites must not unintentionally dominate risk
Rebalancing	Restore target weights after drift	Maintain risk profile	Selling winners/buying laggards can feel counterintuitive
Liability-driven allocation	Assets matched to future obligations	Retirement, foundations, specific liabilities	Return target alone is insufficient

Rebalancing Rules

Method	How it works	Advantage	Weakness
Calendar	Rebalance at set intervals	Simple discipline	Ignores size of drift
Percentage-of-portfolio	Rebalance when weights breach bands	Responds to material drift	Requires monitoring
Constant-mix	Sell assets that rise, buy those that fall	Maintains stable risk exposure	Can underperform in strong trends
Buy-and-hold	Let weights drift	Low trading cost	Risk profile can change materially
CPPI-style	Increase risky asset exposure as cushion grows	Downside-risk control concept	Assumptions may fail in gaps/fast markets

Asset Class Characteristics

Asset class	Return source	Key risks	Portfolio role
Cash / money market	Interest income	Inflation, reinvestment risk	Liquidity and capital preservation
Government bonds	Coupon, price change	Interest-rate, inflation risk	Income, stability, duration management
Corporate bonds	Coupon plus credit spread	Credit, spread, liquidity risk	Higher income than government bonds
Preferred shares	Dividends, rate sensitivity	Credit, rate, call risk	Income, hybrid equity/fixed-income exposure
Common equity	Dividends, earnings growth, valuation change	Market, business, liquidity risk	Long-term growth
Real assets	Income, inflation linkage, appreciation	Liquidity, valuation, sector risk	Diversification and inflation sensitivity
Alternatives	Strategy-specific	Liquidity, leverage, complexity	Diversification/absolute-return potential if understood

Fixed-Income Quick Rules

Topic	Rule	Exam trap
Price and yield	Bond prices move inversely to yields	Price change is not linear for large rate moves
Coupon rate vs yield	Coupon is contractual; yield is market-required return	Premium/discount depends on coupon vs market yield
Premium bond	Coupon rate > market yield	Price above par, tends toward par at maturity
Discount bond	Coupon rate < market yield	Price below par, tends toward par at maturity
Longer maturity	Usually more interest-rate sensitivity	Coupon level also matters
Lower coupon	More duration, all else equal	Zero-coupon bonds have high duration sensitivity
Callable bond	Issuer may redeem early	Investor faces reinvestment risk when rates fall
Putable bond	Investor may sell back to issuer	Benefits investor; usually lower yield than comparable non-putable
Credit spread widening	Credit risk perception rises	Bond price generally falls
Yield curve steepening	Long yields rise vs short yields, or short yields fall vs long	Identify which segment changes

Approximate Bond Price Change

\[ \%\Delta P \approx -D_{\text{mod}} \times \Delta y \]

Modified Duration

\[ D_{\text{mod}} = \frac{D_{\text{Mac}}}{1 + y/m} \]

Duration Plus Convexity Approximation

\[ \%\Delta P \approx -D_{\text{mod}}\Delta y + \frac{1}{2}C(\Delta y)^2 \]

Where \(C\) is convexity and \(\Delta y\) is the yield change in decimal form.

Equity Analysis and Valuation

Metric	Plain formula	Interpretation	Trap
EPS	Net income available to common / weighted avg common shares	Profit per common share	EPS growth can be affected by buybacks
P/E ratio	Price / EPS	Price paid per unit of earnings	Low P/E can signal value or distress
Earnings yield	EPS / Price	Earnings relative to price	Inverse of P/E
Dividend yield	Annual dividend / price	Cash income yield	High yield may signal falling price or dividend risk
Payout ratio	Dividends / earnings	Share of earnings paid out	High payout may limit reinvestment
Retention ratio	1 - payout ratio	Share of earnings retained	Supports growth if reinvested well
P/B ratio	Price / book value per share	Market value vs accounting equity	Less useful for asset-light firms
ROE	Net income / average equity	Return on shareholder capital	Can rise from leverage, not just better operations
ROA	Net income / average assets	Profitability of assets	Affected by business model and leverage
Debt-to-equity	Total debt / equity	Financial leverage	Higher leverage magnifies gains and losses

Dividend Discount Model

\[ P_0 = \frac{D_1}{k - g} \]

Use when dividends are meaningful and expected to grow at a stable rate. \(k\) must be greater than \(g\).

Sustainable Growth Rate

\[ g = ROE \times \text{retention ratio} \]

DuPont Analysis

\[ ROE = \frac{\text{Net income}}{\text{Sales}} \times \frac{\text{Sales}}{\text{Assets}} \times \frac{\text{Assets}}{\text{Equity}} \]

Component	Meaning	Interpretation
Net profit margin	Net income / sales	Operating profitability
Asset turnover	Sales / assets	Efficiency of asset use
Equity multiplier	Assets / equity	Financial leverage

High ROE is strongest when driven by margins and efficiency, not only leverage.

Active, Passive, and Style Distinctions

Strategy	Core idea	Best fit	Trap
Passive indexing	Replicate benchmark exposure	Low cost, broad market exposure	Tracking error still exists
Enhanced indexing	Small active bets around index	Seek modest alpha with controlled risk	May underperform after costs
Active management	Security selection / market timing / factor tilts	Belief in manager skill or market inefficiency	Alpha must be evaluated net of fees and risk
Growth investing	Buy firms with high expected growth	Expanding earnings/revenues	Overpaying for growth is a risk
Value investing	Buy securities below estimated intrinsic value	Mispricing / mean reversion	Value traps exist
Momentum	Follow price/earnings trends	Persistent trends	Reversals can be sharp
Quality	Strong balance sheets, stable earnings	Defensive growth	Valuation can become expensive
Small-cap tilt	Smaller companies	Higher growth potential	Higher volatility and liquidity risk

Top-Down vs Bottom-Up

Method	Starts with	Then analyzes	Exam clue
Top-down	Economy and market cycle	Sectors, industries, securities	GDP, rates, inflation, sector rotation
Bottom-up	Individual companies	Industry and macro context later	Financial statements, management, valuation
Fundamental	Intrinsic value	Earnings, cash flow, balance sheet	“Undervalued relative to fundamentals”
Technical	Price/volume patterns	Trends, support/resistance	“Chart signal” or trading pattern

Economic and Market Indicators

Indicator	Generally positive for	Generally negative for	Key nuance
Falling interest rates	Existing bonds, rate-sensitive sectors	New income reinvestment	May signal weaker economy
Rising interest rates	New bond investors, lenders	Existing bond prices, leveraged firms	Rate reason matters: growth vs inflation
Higher inflation	Real assets, inflation-linked cash flows	Fixed coupons, cash purchasing power	Nominal returns can look high while real returns fall
Strong GDP growth	Cyclical equities, credit quality	Defensive relative performance	Too strong may trigger rate hikes
Widening credit spreads	Future credit opportunity if compensated	Existing risky bonds	Usually signals rising credit concern
Currency appreciation	Foreign purchasing power	Export competitiveness	Portfolio effect depends on hedge status
Yield curve inversion	Short yields above long yields	Bank margins, cyclical sentiment	Often read as slowdown/recession signal

Performance Measurement Ratios

Sharpe Ratio

\[ \text{Sharpe} = \frac{R_p - R_f}{\sigma_p} \]

Uses total risk. Best for portfolios that may not be fully diversified.

Treynor Ratio

\[ \text{Treynor} = \frac{R_p - R_f}{\beta_p} \]

Uses systematic risk. Best when the portfolio is well diversified.

Jensen Alpha

\[ \alpha_p = R_p - [R_f + \beta_p(R_m - R_f)] \]

Measures return above or below CAPM-required return.

Information Ratio

\[ IR = \frac{R_p - R_b}{\text{tracking error}} \]

Measures active return per unit of active risk.

Ratio	Numerator	Risk denominator	Best comparison
Sharpe	Portfolio excess return over risk-free rate	Standard deviation	Total-risk efficiency
Treynor	Portfolio excess return over risk-free rate	Beta	Systematic-risk efficiency
Jensen alpha	Actual return minus CAPM required return	Built into CAPM beta adjustment	Value added vs required return
Information ratio	Active return over benchmark	Tracking error	Active manager skill vs benchmark

Performance Attribution

Attribution type	Question answered	Example
Asset allocation effect	Did the manager overweight/underweight the right asset classes or sectors?	Overweight equities when equities beat bonds
Security selection effect	Did the manager choose better securities within a category?	Selected banks that beat the bank sector
Interaction effect	Combined allocation and selection effect	Overweight a sector and selected winners there
Currency effect	Did exchange-rate movement help or hurt?	Unhedged foreign assets gained from weaker Canadian dollar
Fee/tax effect	How much return was lost to costs or taxes?	High turnover reduced after-tax return

Tax-Aware Portfolio Logic

Item	General Canadian exam-prep logic	Portfolio implication
Interest income	Generally fully taxable in non-registered accounts	Often less tax-efficient than capital gains/dividends
Dividends	Canadian eligible dividends may receive preferential tax treatment	Tax status of account and investor matters
Capital gains	Usually taxed when realized; only part is taxable under current rules	Deferral can have value
Registered accounts	Tax treatment differs from taxable accounts	Asset location matters
Turnover	More trading can accelerate taxable events and costs	High-turnover strategies need after-tax evaluation
Tax-loss selling	Realize losses to offset gains where permitted	Must respect applicable tax rules and timing constraints

Do not memorize tax rates unless provided in current materials. Focus on after-tax return, account type, and suitability.

Portfolio Suitability Decision Table

Client fact pattern	Likely implication	Avoid
Short time horizon and high liquidity need	Higher cash/short-term fixed income allocation	Illiquid or highly volatile strategy
Long horizon, stable income, high risk capacity	More growth assets may be suitable	Assuming willingness equals ability
Low willingness but high ability	Education and conservative implementation may be needed	Forcing high-risk allocation
High required return but low risk capacity	Goals, savings, or horizon must be adjusted	Chasing unsuitable return
Concentrated employer stock	Diversification and risk control priority	Adding correlated sector exposure
Taxable investor in high marginal bracket	After-tax return and asset location matter	Ranking investments only by pre-tax yield
Income need with inflation concern	Balance current income and real purchasing power	Overconcentration in nominal fixed income
Ethical/ESG restriction	Reflect in IPS and security universe	Treating preference as informal if material

Common Exam Traps

Trap	Correct approach
Confusing risk tolerance with risk capacity	Willingness is psychological; capacity is financial
Using arithmetic mean for compound long-term performance	Use geometric mean for multi-period compounded return
Treating beta as total risk	Beta is systematic risk only
Assuming diversification eliminates all risk	It reduces unsystematic risk, not systematic risk
Comparing Sharpe ratios when beta is requested	Sharpe uses standard deviation; Treynor uses beta
Ignoring cash-flow timing in returns	TWR for manager skill; MWR for investor experience
Calling a low P/E stock automatically cheap	Check earnings quality, growth, leverage, and sector context
Assuming higher yield means better bond	Higher yield may reflect credit, liquidity, call, or duration risk
Forgetting bond price-yield inverse relationship	Rates up, existing bond prices down
Ignoring IPS constraints during implementation	Product choice must fit objectives and constraints

Calculation Checklist

Before solving, identify:

Return type: holding period, arithmetic, geometric, annualized, real, after-tax.
Risk type: standard deviation, beta, duration, tracking error, downside risk.
Perspective: client actual experience or manager performance.
Benchmark: market index, risk-free rate, policy benchmark, liability target.
Time period: monthly, quarterly, annual; convert consistently.
Weights: ensure portfolio weights sum to 100%.
Signs: bond price change is negative when yields rise.
Units: basis points vs percentages; 100 bps = 1.00%.
Tax/costs: confirm whether returns are gross, net, pre-tax, or after-tax.
Decision rule: know what result means, not just the calculation.

Mini Decision Flow: Performance Question

    flowchart TD
	    A[Performance question] --> B{External cash flows?}
	    B -->|Yes, manager evaluation| C[Use time-weighted return]
	    B -->|Yes, client actual result| D[Use money-weighted return / IRR]
	    B -->|No or already return data| E{Risk-adjusted measure?}
	    E -->|Total risk| F[Sharpe ratio]
	    E -->|Systematic risk / beta| G[Treynor or Jensen alpha]
	    E -->|Benchmark active risk| H[Information ratio]
	    E -->|No| I[Compare raw or benchmark-relative return]

Last-Week Review Priorities

Priority	Drill
Formulas	Recreate return, risk, CAPM, duration, and performance formulas from memory
Interpretation	For every formula, write what a high/low/positive/negative result means
IPS scenarios	Classify facts into objective, constraint, or irrelevant detail
Risk measure selection	Match standard deviation, beta, duration, and tracking error to scenarios
Bond questions	Practice yield-change price estimates and premium/discount logic
Equity questions	Interpret P/E, dividend yield, ROE, DuPont, and DDM assumptions
Performance questions	Decide TWR vs MWR; Sharpe vs Treynor vs information ratio
Suitability	Check time horizon, liquidity, tax, risk, and concentration before recommending

Practical Next Step

Work a timed mixed set of IMT Exam 1-style questions, then review every miss by category: formula error, concept confusion, suitability error, or misread wording. Re-drill the category that caused the most lost marks before moving to full practice exams.

Scenario Guide

Investment Policy and Understanding Risk Profile