Apply investment analysis through 20 original multiple-choice questions and 60 worked concepts covering the ten supplied 2026 curriculum domains. Practice links regression evidence, currency hedging, accounting adjustments, valuation, portfolio risk, and professional conduct to concrete decisions. The questions form ten shared-vignette pairs, presented as abbreviated item-set excerpts; each repeats the facts needed for independent use. They sample the supplied allocation rather than reproduce a full examination or complete four-question item sets. Financial reporting uses IFRS unless stated otherwise. Calculations specify their conventions, and explanations distinguish model assumptions from market outcomes. This guide addresses the 2026 curriculum; the separate 2027 version is excluded.
What this guide covers
Study 60 investment-analysis concepts and solve 20 original vignette questions for CFA Level II 2026.
Quantitative Methods
1. Partial regression coefficients and joint F-tests
A multiple-regression coefficient measures the conditional change in the dependent variable associated with a one-unit increase in one regressor, holding the others fixed. Its interpretation depends on units, transformations, and indicator reference groups. Individual t-tests address single coefficient restrictions; a joint F-test addresses several restrictions together. For nested ordinary least squares models, compare the increase in residual sum of squares from imposing restrictions with unrestricted residual variance. A high overall R-squared does not establish that every coefficient contributes independently or that the relationship is causal.
Worked example: An unrestricted model has residual sum of squares 80, while removing two predictors raises it to 100. With 100 observations and four unrestricted slopes, F = [(100 − 80)/2]/[80/95] = 11.875. Compare this with the appropriate supplied critical value.
Common mistake: A significant overall model does not imply that each individual predictor is significant after controlling for the remaining regressors.
Official syllabus reference: [1]
2. Heteroskedasticity, serial correlation, and multicollinearity
Heteroskedasticity means conditional error variance differs across observations; serial correlation means errors are related across ordered observations. Under suitable exogeneity conditions, either can leave ordinary least squares coefficients unbiased while making conventional standard errors unreliable. Heteroskedasticity-consistent or autocorrelation-consistent covariance estimators target inference, with the choice matching the error process. Multicollinearity instead concerns related regressors: imperfect collinearity inflates coefficient uncertainty, while perfect collinearity prevents unique estimation. Robust standard errors do not repair an omitted variable correlated with included regressors or establish a correct conditional mean.
Worked example: A monthly return model has residuals clustered in consecutive positive runs and volatility that rises during crises. An analyst uses an autocorrelation- and heteroskedasticity-consistent covariance estimate for inference, while separately investigating whether a missing crisis variable changes the conditional mean.
Common mistake: Changing the standard-error estimator does not automatically remove coefficient bias caused by an endogenous regressor or omitted explanatory variable.
Official syllabus reference: [1]
3. Logistic probabilities and odds ratios
Logistic regression models the log odds of a binary outcome as a linear combination of predictors. If the linear index is z, probability is 1/(1 + exp(−z)), which stays between zero and one. A coefficient changes log odds; its exponential is the multiplicative change in odds for a one-unit predictor increase. Probability effects depend on the starting probability and other covariates, so a coefficient is not a constant percentage-point effect. Classification cutoffs reflect decision costs and objectives rather than a universal statistical threshold.
Worked example: A default model produces z = −2 for one borrower and z = −1 after leverage increases by one unit. Default probability rises from approximately 11.9% to 26.9%; the associated coefficient of one multiplies the odds by approximately 2.718.
Common mistake: An odds ratio of two doubles the odds, not necessarily the event probability, because odds and probabilities use different denominators.
Official syllabus reference: [1]
4. Stationarity, unit roots, and cointegration
A covariance-stationary series has a stable mean, finite constant variance, and autocovariances that depend on lag rather than calendar time. A random walk has a unit root, so shocks persist and level regressions can appear significant without an economic relationship. Differencing can remove a unit root, whereas a deterministic trend may require detrending. Two nonstationary series are cointegrated when an appropriate linear combination is stationary. An error-correction model then combines short-run changes with adjustment toward a long-run equilibrium; unit-root and cointegration tests require their specific critical values.
Worked example: Two price indices individually behave like random walks, but P − 1.5Q fluctuates around a stable mean. A model of changes in P can include the lagged equilibrium gap, allowing deviations to influence the next period's price adjustment.
Common mistake: A high R-squared between trending levels does not establish a stable predictive relationship; shared nonstationarity can generate spurious significance.
Official syllabus reference: [1]
5. ARCH volatility and mean-reverting forecasts
Conditional heteroskedasticity models describe changing forecast variance rather than necessarily changing expected returns. In a simple ARCH(1) specification, next-period variance equals a positive constant plus a coefficient times the most recent squared innovation. A large surprise raises forecast risk regardless of its sign. For a stationary ARCH(1) model with coefficient below one, unconditional variance equals the constant divided by one minus that coefficient. Volatility clustering therefore permits persistent risk forecasts without implying predictable return direction. Forecast standard deviation is the square root of forecast variance.
Worked example: Suppose h-next = 0.0001 + 0.60ε² and the latest return innovation is −0.03. Forecast variance is 0.00064, giving volatility of approximately 2.53%. The unconditional variance is 0.00025, so this forecast lies above the long-run level.
Common mistake: A negative return shock raises variance through its square in basic ARCH; it does not mechanically produce a negative expected return.
Official syllabus reference: [1]
6. Regularization, text features, and leakage
Machine-learning performance must be evaluated on observations excluded from model selection and preprocessing estimates. Ridge regression shrinks coefficients through a squared-coefficient penalty; lasso uses an absolute-value penalty and can set coefficients to zero. Text applications convert documents into features such as term frequencies or TF-IDF weights, but vocabulary selection and scaling must respect training boundaries. Chronological financial forecasts require information available at each prediction date. Low training error can reflect overfitting, while validation guides model complexity and a separate test sample estimates subsequent generalization.
Worked example: An analyst predicts next-quarter earnings from filings. She builds the vocabulary and TF-IDF weights using training-period documents, selects lasso strength on a later validation window, and evaluates once on subsequent filings released before the relevant prediction dates.
Common mistake: A test set stops being an independent performance check when repeated model changes are chosen because they improve its results.
Official syllabus reference: [1]
Economics
7. Covered parity and forward-contract value
Covered interest parity links spot exchange rates, forward rates, and two currency interest rates through a hedged borrowing-and-investing trade. For domestic currency per foreign currency, F = S(1 + rdT)/(1 + rfT) when both rates use compatible simple-interest conventions. Effective-rate conventions require corresponding accumulation factors. An existing forward's delivery price stays fixed, while its value changes with replacement forward rates. A long foreign-currency contract is worth foreign notional times the replacement-rate advantage, discounted in domestic currency. Transaction costs and cross-currency basis can affect executable market relationships.
Worked example: Spot is CAD 1.50 per foreign unit, with one-year effective rates of 5% in CAD and 2% abroad. The fair forward is 1.544118. A contract to buy one million foreign units at 1.52 is worth approximately CAD 22,969 today.
Common mistake: The quoted forward exchange rate is not the contract's current monetary value; a newly initiated fair forward generally starts at zero value.
Official syllabus reference: [1]
8. Executable triangular currency arbitrage
Triangular arbitrage compares an executable sequence of three currency trades with the starting currency amount. Dealer bids apply when selling the base currency, while offers apply when buying it; every quote must first be read in its stated units. Midpoint comparisons can suggest opportunities that disappear once spreads are included. A valid calculation follows actual cash conversions around the triangle and returns to the original currency. It also assumes sufficient quoted liquidity and consistent settlement, because indicative rates or asynchronous prices may not support an executable profit.
Worked example: EUR/JPY is 166.00 bid and 166.20 offer; USD/JPY is 150.00 bid and 150.10 offer; EUR/USD is 1.1000 bid and 1.1010 offer. Selling EUR 1 million through JPY and USD returns approximately EUR 1,004,477.18, before costs.
Common mistake: Choosing whichever side of each quote produces the largest number ignores whether the trade buys or sells that quote's base currency.
Official syllabus reference: [1]
9. Uncovered parity and carry-trade crash risk
Uncovered interest parity proposes that an interest-rate advantage is offset by expected currency depreciation when investors leave exchange risk unhedged. With domestic currency per foreign currency, the parity-implied expected future spot resembles the covered forward relationship, but it is an expectations hypothesis rather than an arbitrage identity. A carry trade borrows in a low-yield currency and invests in a higher-yield currency without fully hedging exchange exposure. Returns depend jointly on interest and currency movements. Persistent carry profits can coexist with infrequent large losses, funding stress, and time-varying risk premiums.
Worked example: An investor borrows 100 funding-currency units at 1% and converts them into 100 investment-currency units earning 6%. If the investment currency falls to 0.94 funding units, proceeds are 99.64 versus repayment of 101, producing a 1.36 loss.
Common mistake: A positive interest differential is not a locked-in carry profit when the investment currency's future conversion rate remains uncertain.
Official syllabus reference: [1]
10. Purchasing power parity and real exchange rates
Relative purchasing power parity links expected exchange-rate changes to inflation differences. For domestic currency per foreign currency, higher domestic inflation implies a rise in the quoted exchange rate over time, other things equal. The real exchange rate adjusts the nominal rate for relative price levels and helps distinguish nominal depreciation from changes in international purchasing power. PPP is more useful as a long-horizon anchor than a precise short-run trading rule. Nontraded goods, transport costs, productivity differences, and changing equilibrium real exchange rates limit literal application.
Worked example: Spot is 1.20 domestic units per foreign unit. Expected inflation is 5% domestically and 2% abroad. Relative PPP implies a one-year rate of 1.20(1.05)/(1.02) = approximately 1.2353, meaning domestic-currency depreciation under this quotation.
Common mistake: Higher domestic inflation does not imply domestic appreciation merely because the numerical domestic-per-foreign exchange-rate quote is expected to increase.
Official syllabus reference: [1]
11. Growth accounting and capital deepening
Growth accounting decomposes potential output growth into total factor productivity growth and factor-input contributions. For Cobb-Douglas production with capital share α, output growth is approximately TFP growth + α times capital growth + (1 − α) times labor growth. Output per worker growth depends on TFP and capital per worker, distinguishing technological progress from capital deepening. Diminishing marginal returns limit growth from accumulating capital alone. The framework describes contributions under production-function assumptions; measured TFP is a residual that can also reflect measurement error, utilization, and omitted input quality.
Worked example: Assume a capital share of 0.4, capital growth of 5%, labor growth of 1%, and TFP growth of 1.5%. Potential output growth is approximately 1.5% + 0.4(5%) + 0.6(1%) = 4.1%; output per worker grows approximately 3.1%.
Common mistake: Capital deepening raises output per worker, but without continuing productivity improvements it need not sustain permanently higher per-worker growth.
Official syllabus reference: [1]
12. Growth theories and conditional convergence
Classical growth theory emphasizes population responses that can erode gains in income per person. Neoclassical theory emphasizes diminishing capital returns and a steady state, with sustained per-capita growth driven by exogenous technological progress. Endogenous growth models explain how knowledge creation, human capital, and innovation incentives can sustain growth internally, often through spillovers. Conditional convergence predicts faster growth for poorer economies only after accounting for differences in steady-state determinants. Saving, institutions, education, population growth, and technology access therefore matter when comparing countries rather than assuming universal catch-up.
Worked example: Two countries share similar institutions, saving rates, population growth, and technology access, but one has much less capital per worker. Neoclassical reasoning predicts faster transitional growth there. A third country with weak property rights need not converge to their income level.
Common mistake: A low starting income alone does not establish convergence; countries may be moving toward substantially different steady-state income levels.
Official syllabus reference: [1]
Financial Statement Analysis
13. Equity method versus acquisition accounting
Significant influence generally leads to equity-method accounting, while control leads to consolidation; percentage ownership is evidence rather than the sole determinant. The equity method records one investment asset and a share of adjusted earnings, with dividends reducing the carrying amount. Acquisition accounting consolidates controlled assets, liabilities, revenues, and expenses, recognizes acquisition-date fair-value adjustments and goodwill, and presents noncontrolling interests where applicable. Additional depreciation or amortization from acquisition-date adjustments affects subsequent earnings. Reporting methods can change sales, margins, and leverage ratios even when underlying economic exposure is similar.
Worked example: An investor pays 90 for a 30% associate interest. Its share of annual profit is 12, extra depreciation on purchase adjustments is 2, and dividends received are 3. The investment closes at 97, with equity-method income of 10.
Common mistake: Recognizing dividends from an equity-method associate as additional income double counts value already included through the investor's share of earnings.
Official syllabus reference: [1]
14. IFRS pension net interest and remeasurement
For an IFRS defined-benefit plan, service cost and net interest generally enter profit or loss, while remeasurements enter other comprehensive income. Net interest applies the discount rate to the opening net defined-benefit liability or asset, subject to relevant adjustments. Asset returns beyond the interest-income component belong to remeasurement, alongside actuarial obligation changes. Contributions affect plan funding rather than directly defining pension expense. Analysis should distinguish operating compensation cost, financing effects, and assumption-driven remeasurement; changes in discount rates can materially alter obligations without representing current employee service.
Worked example: Opening obligations are 200 and assets are 180, with a 5% discount rate and service cost of 8. Net interest is 1, so expense is 9. Actual asset return of 6 falls below interest income of 9, creating a 3 OCI loss.
Common mistake: Using actual plan-asset return directly in IFRS profit-or-loss expense incorrectly moves the asset-return remeasurement out of other comprehensive income.
Official syllabus reference: [1]
15. Share-based compensation and dilution
Equity-settled employee awards generally create compensation expense over the service period using grant-date measurement, with treatment depending on vesting conditions and applicable standards. They are economically costly even when operating cash flow adds back the noncash expense. Valuation must also address dilution from outstanding and future awards without counting the same burden twice. A share forecast should separate grants, vesting, exercises, forfeitures, and repurchases. Cash-settled awards differ because the liability is remeasured, potentially creating earnings volatility as the underlying share price changes.
Worked example: A company grants 300,000 equity-settled awards worth 12 each for three years of service. With all awards expected to vest and straight-line recognition appropriate, annual expense is 1.2 million. The analyst separately models when vesting increases outstanding shares.
Common mistake: Adding back noncash compensation in cash-flow analysis does not make employee awards economically free or eliminate their potential dilution.
Official syllabus reference: [1]
16. Foreign-currency translation and functional currency
Functional currency reflects the primary economic environment in which an entity operates and determines the relevant foreign-currency accounting approach. Translating a foreign operation whose functional currency differs from the presentation currency generally uses closing rates for assets and liabilities, with resulting translation differences in other comprehensive income. Remeasuring records into functional currency instead distinguishes monetary items from nonmonetary items measured at historical cost, with exchange effects generally affecting earnings. Analysts should identify rate exposures and balance-sheet composition before predicting the sign of translation gains or losses; revenue translation alone is insufficient.
Worked example: A subsidiary has functional-currency assets of 500 and liabilities of 300, creating net assets of 200. If its currency strengthens from 0.80 to 0.90 presentation units, the simplified opening-net-asset translation effect is a gain of 20 before current-period flow effects.
Common mistake: A foreign subsidiary's currency appreciation does not automatically increase reported profit through the translation adjustment; that adjustment may enter OCI.
Official syllabus reference: [1]
17. Bank credit quality and loss allowances
Bank analysis requires connecting asset quality, allowance adequacy, earnings, and capital rather than relying on ordinary industrial-company leverage measures. Loan-loss provisions reduce earnings and build allowances, while charge-offs use the allowance against identified credit losses. Under IFRS expected-credit-loss accounting, deterioration in credit risk can shift measurement from twelve-month to lifetime expected losses, subject to the applicable classification. Compare allowance coverage, delinquency, loan growth, collateral quality, and concentration together. A low provision may indicate improving credit conditions or optimistic estimates; its interpretation requires the portfolio's underlying risk trends.
Worked example: A bank begins with an allowance of 40, records provision expense of 15, and charges off loans of 10 with no recoveries. Closing allowance is 45. If troubled loans rise from 50 to 90, allowance coverage falls despite the larger reserve.
Common mistake: An increasing allowance balance alone does not demonstrate stronger credit protection when problem loans or risk concentrations are increasing faster.
Official syllabus reference: [1]
18. Earnings normalization and cash-flow reconciliation
Normalized earnings aim to represent sustainable operating performance by adjusting unusual items, accounting differences, and nonrecurring financing or tax effects. Each adjustment should have an economic rationale and consistent tax treatment. Cash-flow analysis then examines whether earnings are supported by collections rather than temporary working-capital changes or aggressive recognition. Receivable growth exceeding sales, repeated restructuring charges, and capitalization changes can weaken comparability. A recurring cash cost should not disappear merely because management labels it exceptional. Adjusting both profit and invested capital may be necessary when changing capitalization policies.
Worked example: Reported pretax profit is 50, including a one-time property gain of 12 and a genuinely unusual closure cost of 4. Normalized pretax profit is 42. The analyst then checks whether rising receivables explain weak operating cash conversion.
Common mistake: Removing every expense labeled exceptional can overstate sustainable earnings when similar charges recur as part of the company's normal business.
Official syllabus reference: [1]
Corporate Issuers
19. Payout irrelevance, signaling, and agency costs
Under frictionless assumptions with a fixed investment policy, distributing cash through dividends or fair-value repurchases does not itself create shareholder wealth. Real-world payout choices can matter through taxes, transaction costs, information asymmetry, and agency conflicts. A dividend increase may signal management's confidence in sustainable cash generation, while a repurchase can distribute temporary excess cash more flexibly. Reduced free cash flow may constrain managerial overinvestment. These mechanisms are conditional: borrowing to maintain an unsustainable dividend can weaken financial flexibility, and a payout announcement is not proof of improved operating prospects.
Worked example: A company worth 500 distributes 50 in cash without changing investment opportunities. Its ex-distribution equity is worth 450, and shareholders collectively receive 50. If the announcement also reveals unexpectedly strong sustainable earnings, the observed price response can differ.
Common mistake: A dividend payment does not create value merely by moving corporate cash into shareholders' accounts; additional frictions or information effects are needed.
Official syllabus reference: [1]
20. Dividend taxation and imputation
Under classical double taxation, corporate earnings are taxed first at the company level and distributed after-tax earnings are taxed again to shareholders. The combined effective rate is tc + (1 − tc)tp, not simply the sum of the two rates. Imputation systems may credit some corporate tax against shareholder liability, with outcomes depending on the specified credit and investor eligibility. Split-rate systems apply different corporate rates to retained and distributed profits. Calculations must state the relevant tax assumptions; no single effective rate applies universally across jurisdictions or investor types.
Worked example: Assume corporate tax is 25% and dividend tax is 20%, with no credits. One unit of pretax profit leaves 0.75 for distribution and 0.60 after shareholder tax. The combined effective tax rate is therefore 40%, rather than 45%.
Common mistake: Adding corporate and shareholder tax percentages ignores that shareholder tax is usually applied to the smaller, after-corporate-tax dividend base.
Official syllabus reference: [1]
21. Repurchase accretion and financing opportunity cost
A repurchase reduces shares outstanding, but its EPS effect also depends on how funding changes earnings. Cash funding sacrifices after-tax investment income; debt funding adds after-tax interest expense. Repurchases tend to increase EPS when the shares' earnings yield exceeds the relevant after-tax financing cost, holding operating performance constant. EPS accretion is an accounting outcome, not sufficient evidence of value creation. Paying more than intrinsic value can transfer wealth from continuing shareholders to selling shareholders even when reported EPS rises. Timing and weighted-average share counts also affect reported EPS.
Worked example: A firm earns 20 on 10 million shares and buys back 1 million shares for 15 million. Forgone after-tax interest is 0.3 million. EPS becomes 19.7/9 = approximately 2.19, above the original 2.00, without proving the purchase price was attractive.
Common mistake: A higher post-repurchase EPS does not establish that management purchased undervalued shares or increased the intrinsic wealth of continuing shareholders.
Official syllabus reference: [1]
22. Stable dividends versus constant payout ratios
A constant payout-ratio policy distributes a fixed proportion of earnings, making dividends fluctuate with profitability. A stable-dividend policy instead smooths payments and adjusts them toward a target associated with sustainable earnings. Partial-adjustment models increase or decrease the previous dividend by a specified fraction of the gap to the target. Stability can reduce unwanted dividend volatility but may require financial reserves when earnings weaken. Neither policy determines the optimal investment program by itself; liquidity, covenants, capital needs, and shareholder preferences constrain feasible distributions.
Worked example: Previous dividends were 2 per share. Sustainable EPS is estimated at 8, the target payout is 40%, and the adjustment factor is 25%. The target dividend is 3.20, so the new smoothed dividend is 2 + 0.25(1.20) = 2.30.
Common mistake: A target payout ratio within a smoothing model does not require the current dividend to equal that ratio times current earnings.
Official syllabus reference: [1]
23. Capital structure, tax shields, and distress costs
Debt can create value through interest tax shields when deductions are usable, but expected distress costs and financing constraints can offset that benefit. Trade-off reasoning balances marginal tax advantages against marginal expected distress and agency costs. Pecking-order reasoning instead emphasizes information asymmetry and a preference for internal funds, then debt, then equity. These theories explain different financing patterns rather than prescribe one universal debt ratio. Valuation must keep operating cash flows, financing assumptions, and discount rates consistent, especially when leverage changes materially over the forecast horizon.
Worked example: A recapitalization is estimated to add 18 of present-value tax shields but create 7 of expected distress costs and 3 of issuance costs. Its estimated net value contribution is 8, assuming operating investment and other effects remain unchanged.
Common mistake: A lower debt coupon than the cost of equity does not mean unlimited borrowing continually reduces the company's overall financing cost.
Official syllabus reference: [1]
24. Restructuring value and acquisition premiums
Corporate restructuring creates value when the combined present value of improved cash flows, financing benefits, or released assets exceeds implementation costs and value transferred to other parties. Acquisition analysis separates standalone target value, synergy value, purchase price, and integration costs. A buyer can acquire an attractive business yet destroy value by paying an excessive premium. Divestitures and spin-offs can improve focus or reveal segment values, but conglomerate discounts do not disappear automatically. Forecasts should specify operational sources of gains rather than treat EPS accretion as a substitute for discounted-cash-flow analysis.
Worked example: A target is worth 120 independently. The buyer expects synergies worth 30 and integration costs worth 8, but offers 150. Buyer net value is 120 + 30 − 8 − 150 = −8, despite positive gross synergies.
Common mistake: Positive synergy estimates do not guarantee buyer gains because the acquisition premium and implementation costs may absorb more than those synergies.
Official syllabus reference: [1]
Equity Valuation
25. Gordon growth, sustainable growth, and PVGO
The Gordon model values a stable dividend stream as next-period dividend divided by required return minus perpetual growth, requiring required return to exceed growth. Sustainable growth can be estimated as retention multiplied by ROE when leverage and profitability assumptions are stable. Present value of growth opportunities separates equity value into a no-growth earnings component and value from future investment. Growth creates value only when reinvestment earns sufficiently attractive returns relative to the cost of equity. A high growth rate is therefore not automatically beneficial, and terminal assumptions must remain economically sustainable.
Worked example: Next-year EPS is 5, retention is 40%, and sustainable ROE is 15%, giving growth of 6%. With a 10% required return and dividend of 3, value is 75. The no-growth earnings value is 50, so PVGO is 25.
Common mistake: Increasing retention does not necessarily raise value; reinvesting at returns below the required equity return can make growth value destructive.
Official syllabus reference: [1]
26. FCFF and enterprise-to-equity reconciliation
Free cash flow to the firm is cash available to debt and equity capital providers after operating taxes and reinvestment. A common formulation is EBIT(1 − tax rate) + depreciation − capital expenditure − working-capital investment. Discount FCFF at WACC under consistent leverage assumptions to obtain operating enterprise value. Add separately valued nonoperating assets and subtract debt and other senior claims to reach common equity value. Interest expense is excluded from FCFF because financing costs enter WACC. Terminal growth must be supported by reinvestment rather than imposed independently of operating economics.
Worked example: EBIT is 100, tax is 25%, depreciation is 20, capital expenditure is 35, and working-capital investment is 10. FCFF equals 50. If operating value is 600, excess cash is 40, and debt is 180, equity value is 460.
Common mistake: Subtracting interest in FCFF and then discounting at WACC counts financing costs twice rather than maintaining a firm-wide cash-flow perspective.
Official syllabus reference: [1]
27. FCFE and net borrowing
Free cash flow to equity measures cash potentially distributable to common shareholders after operating needs, investment, and net debt financing. Starting with net income, add noncash charges, subtract capital expenditure and working-capital investment, and add net borrowing. Discount FCFE at the cost of equity rather than WACC. Actual dividends can differ from FCFE because boards retain surplus cash or distribute accumulated balances. Debt-financing assumptions are especially important: temporary borrowing can inflate current FCFE without supporting a sustainable perpetual distribution. Changing leverage may require changing equity risk and discount rates.
Worked example: Net income is 60, depreciation is 15, capital expenditure is 30, working-capital investment is 8, and net borrowing is 5. FCFE is 42. If dividends are 20, the remaining 22 is retained rather than evidence of a calculation error.
Common mistake: Net borrowing belongs in FCFE, but treating a temporary debt increase as permanent recurring cash generation can materially overstate equity value.
Official syllabus reference: [1]
28. Residual income and clean-surplus adjustments
Residual income subtracts an equity capital charge from accounting earnings: RIt = NIt − reBt−1. Equity value equals current book value plus the present value of future residual income under consistent clean-surplus assumptions. Clean surplus links ending book value to beginning book value, earnings, and owner distributions or contributions. Items bypassing net income may require adjustments to avoid omitting economic gains and losses. Residual-income models are useful when dividends are unrepresentative or free cash flow is temporarily negative, but they remain sensitive to accounting quality and continuing abnormal profitability.
Worked example: Beginning book value is 40 per share, forecast EPS is 6, and the required return is 12%. The equity charge is 4.80, leaving residual income of 1.20. If that occurs once and then disappears, value is 40 + 1.20/1.12 = 41.07.
Common mistake: Residual income is not the same as accounting profit; positive earnings can coexist with negative residual income when the capital charge is larger.
Official syllabus reference: [1]
29. Comparable multiples and denominator consistency
Relative valuation compares market prices with appropriately matched operating or equity measures. Equity multiples such as P/E use earnings available to equity; enterprise multiples such as EV/EBITDA pair firm-wide value with pre-financing operating measures. Comparability requires examining growth, profitability, risk, leverage, accounting policies, and forward versus historical periods. A low multiple may reflect weaker prospects rather than mispricing. Normalize unusual earnings and align lease, pension, and nonoperating adjustments across numerator and denominator. Multiples embed assumptions about future cash generation even when no explicit discounted-cash-flow model is shown.
Worked example: A company has market equity of 300, debt of 100, excess cash of 20, and EBITDA of 50. Enterprise value is 380 and EV/EBITDA is 7.6. Dividing equity value alone by EBITDA gives 6.0 but mismatches the capital-provider perspectives.
Common mistake: A peer's lower P/E does not prove undervaluation when its growth, earnings quality, risk, or capital structure differs materially.
Official syllabus reference: [1]
30. Private-company control and marketability adjustments
Private-company valuation first defines the ownership interest and valuation basis, then normalizes cash flows and selects a consistent income, market, or asset approach. Owner compensation, related-party transactions, and discretionary expenses may require adjustment. Control and marketability affect value through different mechanisms: control changes decision rights, while marketability concerns the ability to sell an interest. Apply discounts or premiums only when the starting valuation lacks the relevant characteristic. Sequential percentage adjustments multiply rather than add, and unsupported blanket discounts can double count risks already incorporated in cash flows or required returns.
Worked example: A marketable minority interest is valued at 80. Assume a justified 25% control premium and then a 20% marketability discount for the interest being valued. The result is 80(1.25)(0.80) = 80, with each adjustment tied to its valuation basis.
Common mistake: Control premiums and marketability discounts cannot be applied mechanically without identifying which rights and liquidity characteristics the starting value already reflects.
Official syllabus reference: [1]
Fixed Income
31. Bootstrapped discount factors and forward rates
Bootstrapping extracts discount factors sequentially from instruments whose earlier cash-flow discount factors are already known. Each new maturity supplies an equation for its remaining unknown discount factor. Spot rates convert those factors into maturity-specific annualized yields, while forward rates describe implied borrowing or lending between future dates. With annual compounding, a one-year forward from year one to year two satisfies 1 + f1,1 = (1 + s2)²/(1 + s1). Implied forwards are no-arbitrage relationships, not guaranteed forecasts of realized future short rates.
Worked example: A one-year spot rate of 3% and a two-year 4% annual-coupon par bond imply D2 = [100 − 4/1.03]/104 = 0.924197. The two-year spot rate is approximately 4.02%, and the implied second-year forward is approximately 5.05%.
Common mistake: A coupon bond's yield to maturity is not automatically the spot rate for its final maturity because its earlier coupons also carry value.
Official syllabus reference: [1]
32. Roll-down return and term-structure assumptions
Rolling down the yield curve describes a bond's movement to a shorter remaining maturity as time passes. On an unchanged upward-sloping curve, its yield may decline and its price may rise, contributing return beyond coupon income. This outcome depends on how the curve actually evolves, not merely its initial slope. Realized holding-period return also reflects coupon reinvestment, default effects, spread changes, and sale price. A strategy based on unchanged spot curves differs from one assuming future spot rates realize today's forwards; confusing those assumptions can exaggerate expected excess return.
Worked example: A four-year bond yields 4.5%, while comparable three-year bonds yield 4.0%. If the curve is unchanged one year later, the bond is valued near the three-year yield, producing a price gain in addition to its coupon, before spread and reinvestment effects.
Common mistake: An upward-sloping curve does not guarantee a profitable roll-down trade because future rate increases or spread widening can offset the anticipated gain.
Official syllabus reference: [1]
33. Arbitrage-free interest-rate trees
An arbitrage-free short-rate tree is calibrated so discounted model cash flows reproduce benchmark bond prices, while its branching structure reflects an assumed rate-volatility process. Value a security backward by discounting risk-neutral expected next-node values and adding applicable cash flows. Embedded options alter node decisions: an issuer call can cap investor value at the exercise price, while an investor put can establish a floor. Calibration prevents inconsistencies with today's curve but does not guarantee future rate predictions. Exercise timing and coupon conventions must match the instrument's contractual terms.
Worked example: At a node, next-period values are 102 and 98 with equal risk-neutral weights and a 4% one-period rate. Before other cash flows, continuation value is 100/1.04 = 96.15. An immediately exercisable investor put at 99 raises node value to 99.
Common mistake: Using historical up-move probabilities instead of the calibrated pricing probabilities breaks the replication logic underlying an arbitrage-free valuation tree.
Official syllabus reference: [1]
34. OAS, effective duration, and negative convexity
Option-adjusted spread is the spread added within a specified interest-rate model to reproduce an option-embedded bond's market price. Its estimate depends on the benchmark curve, volatility assumptions, and exercise modeling. Effective duration and convexity revalue the security under curve shifts while allowing option-driven cash flows to change. Callable bonds can exhibit negative convexity when falling rates increase call likelihood and limit price appreciation. Modified duration based on fixed cash flows can misrepresent this exposure. Spread duration separately evaluates sensitivity to changes in the credit or valuation spread.
Worked example: A callable bond is worth 100 initially, 101 after a downward curve shift, and 97 after an equal upward shift. Its asymmetric response reflects limited upside and larger downside; effective convexity computed from those values is negative.
Common mistake: A callable bond's OAS is not independent of the assumed rate volatility, even when its observed price and initial yield curve are unchanged.
Official syllabus reference: [1]
35. Hazard rates, recovery, and expected credit loss
Credit valuation separates default likelihood, loss severity, timing, and compensation for bearing systematic and liquidity risks. Expected loss for a simple horizon is exposure times default probability times loss given default. A constant hazard rate implies survival probability exp(−λT), so cumulative default probability differs from simply multiplying hazard by time except as an approximation. A rough spread relationship is spread ≈ hazard × loss given default under restrictive assumptions. Observed spreads also contain risk and liquidity premiums, so using them as literal physical default probabilities requires caution.
Worked example: A one-year exposure of 10 million has a 2% default probability and 40% recovery. Expected credit loss is 10 million × 0.02 × 0.60 = 120,000. A market spread larger than 120 basis points can also compensate investors for priced risk and illiquidity.
Common mistake: A credit spread is not a direct, model-free estimate of real-world default probability because recovery assumptions and nondefault premiums also matter.
Official syllabus reference: [1]
36. Credit default swap protection and basis
A credit default swap transfers specified reference-entity credit risk through premium payments in exchange for contingent protection following a contractual credit event. Protection value rises when credit quality deteriorates, all else equal. Premium-leg and protection-leg present values determine fair pricing, with conventions governing accrued premiums and settlement. The CDS-bond basis compares CDS spreads with comparable cash-bond credit spreads, but financing, liquidity, deliverability, and counterparty effects can prevent easy arbitrage. Buying protection does not hedge every bond risk, particularly interest-rate movements or differences between the bond and covered reference obligation.
Worked example: An investor owns 5 million of reference debt and buys matching protection. If a covered credit event settles at 35% recovery, the simplified protection payment is 5 million × 65% = 3.25 million, offsetting the modeled credit loss before premiums and basis differences.
Common mistake: Matching CDS notional to bond face value does not remove interest-rate risk, liquidity risk, or every possible mismatch in credit-event coverage.
Official syllabus reference: [1]
Derivatives
37. Carry arbitrage and forward repricing
A forward delivery price is set so a new contract has zero value under no-arbitrage assumptions. For an asset with known cash income, finance spot ownership and subtract the present value of income before carrying the net amount to maturity. A convenient form is F0 = [S0 − PV(income)]/D(0,T). An existing long forward with delivery price K has value [Ft − K]D(t,T), adjusted for the relevant underlying structure. Dividends, storage costs, convenience yield, and borrowing constraints can change the appropriate carry relationship and arbitrage feasibility.
Worked example: A stock costs 100, will pay a dividend with present value 2, and has a one-year discount factor of 0.95. Its fair forward is 98/0.95 = 103.16. An existing long contract at 101 is worth approximately 2.05 at that date.
Common mistake: The fair delivery price of a new forward and the current value of an existing forward are different quantities with different units.
Official syllabus reference: [1]
38. Swap fixed rates and remaining-leg valuation
A plain interest-rate swap exchanges fixed and floating payments on a common notional without generally exchanging that notional. At initiation, choose the fixed rate so the legs have equal present values. Under a simple single-curve framework with unit notional, the par fixed rate is [1 − D(T)] divided by the discounted accrual-factor sum. Existing swaps are valued using remaining contractual payments and current curves. A receive-fixed swap generally gains when relevant rates decline, but valuation also depends on reset timing, accrued payments, and any separate projection and discount curves.
Worked example: Annual discount factors are 0.97 and 0.93. The two-year par swap rate is (1 − 0.93)/(0.97 + 0.93) = 3.6842%. With the same curve, receiving 4% instead has value approximately 0.006 per unit notional at initiation of that comparison.
Common mistake: A swap's originally agreed fixed rate does not reset to the new market par rate whenever market interest rates change.
Official syllabus reference: [1]
39. Risk-neutral binomial valuation and exercise
The binomial model values a contingent claim through replication or equivalent risk-neutral probabilities. For up factor u, down factor d, and risk-free accumulation R, the up weight is (R − d)/(u − d), requiring d < R < u for the standard no-arbitrage setup. Discount expected next-node payoffs at the risk-free rate. American options additionally require comparing continuation with immediate exercise at every eligible node. A European option omits that intermediate exercise choice. Risk-neutral probabilities are valuation devices and need not match actual expected stock-price movements.
Worked example: A stock at 50 moves to 60 or 40, and the risk-free factor is 1.05. For a strike-50 call, p = 0.625 and value is [0.625(10) + 0.375(0)]/1.05 = 5.95. No forecast probability is required.
Common mistake: An American option's value cannot be obtained by discounting terminal payoffs alone when early exercise is economically preferable at an intermediate node.
Official syllabus reference: [1]
40. Black futures-option valuation
Black's model values a European option using a forward or futures price under an appropriate lognormal pricing framework. A call is D[F N(d1) − K N(d2)], where d1 = [ln(F/K) + 0.5σ²T]/(σ√T), d2 = d1 − σ√T, and D is the discount factor. Unlike a spot-stock formula, both payoff terms are discounted together. Inputs must use the option expiry, relevant underlying contract, and consistent volatility units. Related applications include certain interest-rate options and swaptions with instrument-specific payoff and annuity scaling.
Worked example: Let F = K = 100, annual volatility = 20%, expiry = one year, and D = 0.95. Then d1 = 0.10 and d2 = −0.10. Using N(0.10) = 0.53983 and N(−0.10) = 0.46017, call value is approximately 7.57.
Common mistake: Using a futures price as though it were an undiscounted spot asset in the stock-option formula can apply discounting inconsistently.
Official syllabus reference: [1]
41. Black–Scholes–Merton and implied volatility
The Black–Scholes–Merton framework values European equity options using stock price, strike, time, interest rate, volatility, and any modeled dividend yield. Its basic assumptions include continuous trading, frictionless markets, and a specified lognormal diffusion with constant parameters. Implied volatility is the volatility input that matches an observed option price; it is not a directly observed future realized volatility. Different strikes and expiries often imply different volatilities, revealing limitations of the constant-volatility model. For currencies, the foreign risk-free rate plays a role analogous to a continuous dividend yield.
Worked example: Two otherwise comparable calls trade at 8 and 10. Holding stock price, strike, expiry, rates, and dividend assumptions fixed, the more expensive call has higher implied volatility because call value increases with volatility in the standard model.
Common mistake: Implied volatility is a price-derived model input, not a promise that the underlying will subsequently realize exactly that volatility.
Official syllabus reference: [1]
42. Delta hedging, gamma, and vega
Delta measures the option-value sensitivity to a small underlying-price change. Gamma measures how delta changes as the underlying moves, so a delta-neutral position generally needs rebalancing. Vega measures sensitivity to a change in the model's volatility input; its quoted unit must be checked. A local option-value approximation combines delta times the price move, half gamma times the squared move, and vega times the volatility change. Hedging one sensitivity does not neutralize the others, and discrete trading, transaction costs, and large movements create residual hedge risk.
Worked example: A portfolio has delta 500, gamma 80, and vega 1,200 per one-percentage-point volatility change. Shorting 500 shares neutralizes current delta. A one-unit price rise still creates approximately 40 of gamma-related gain before rebalancing, with volatility exposure remaining.
Common mistake: A delta-neutral portfolio is not risk-free because changing delta, volatility, time decay, and discrete hedge adjustments still affect its value.
Official syllabus reference: [1]
Alternative Investments
43. Commodity storage, convenience yield, and roll return
Commodity futures pricing reflects financing, storage, and the convenience benefit of holding physical inventory. A simplified continuous-carry relationship is F = S exp[(r + storage − convenience yield)T]. High convenience yield can support backwardation, while financing and storage can contribute to contango. A collateralized futures investor's return combines futures-price changes and collateral income; spot movement and convergence or roll effects help explain those changes. Curve shape alone does not fix future total return because spot prices and the curve can move. Physical scarcity can change convenience yield rapidly.
Worked example: Spot is 100, annual financing plus storage is 6%, convenience yield is 2%, and maturity is one year. The simplified forward is 100 exp(0.04) = 104.08. If purchased there and later settled at unchanged spot of 100, the long futures position loses.
Common mistake: Contango does not guarantee a negative total commodity return; sufficiently strong spot-price increases or collateral income can offset negative convergence effects.
Official syllabus reference: [1]
44. Real-estate NOI, capitalization rates, and leverage
Direct capitalization values stabilized real estate as net operating income divided by an appropriate capitalization rate. NOI excludes financing costs and is distinct from cash flow available to equity after debt service and capital needs. A capitalization rate embeds growth and risk assumptions, so comparable transactions require adjustments for location, leases, property condition, and income quality. Discounted-cash-flow analysis is preferable when occupancy or rents are changing materially. Leverage magnifies equity exposure to property-value changes, while appraised values can lag market conditions and smooth measured return volatility.
Worked example: A stabilized property earns annual NOI of 1.2 million. At a 6% capitalization rate, value is 20 million. If the required cap rate rises to 6.5% with unchanged NOI, value falls to 18.46 million, reducing equity by 1.54 million before costs.
Common mistake: Capitalizing cash flow after mortgage interest with an unlevered property capitalization rate mixes equity financing effects with asset-level valuation.
Official syllabus reference: [1]
45. Private-equity cash flows and performance multiples
Private-equity performance combines irregular capital calls, distributions, and residual asset values. Internal rate of return is sensitive to timing, while multiples show value relative to contributed capital without fully capturing time. DPI measures distributions divided by paid-in capital; RVPI measures remaining value divided by paid-in capital; TVPI equals their sum. Interim multiples depend on the quality of residual valuations, and subscription financing can affect reported timing-based returns. Comparing funds requires consistent vintage, strategy, fee treatment, and valuation assumptions rather than ranking them using one headline statistic.
Worked example: Investors contribute 100, receive cumulative distributions of 70, and retain estimated fund value of 60. DPI is 0.70, RVPI is 0.60, and TVPI is 1.30. These figures do not reveal whether the gains occurred over three years or ten.
Common mistake: A higher private-equity IRR does not necessarily mean a larger wealth multiple because cash-flow timing can strongly influence the IRR.
Official syllabus reference: [1]
46. Merger arbitrage and event-driven downside
Merger arbitrage seeks to earn the spread between a target's trading price and the expected value received if a transaction closes. Cash deals often involve buying the target; stock deals may also require shorting the acquirer in the exchange ratio. Returns depend on completion probability, timing, financing terms, and break-price downside. A narrow spread can conceal severe asymmetric losses if the transaction fails. Event-driven strategies can become correlated with broader markets during stress because financing conditions, regulatory concerns, and investor deleveraging affect multiple deals simultaneously.
Worked example: A target trades at 48 against a cash offer of 50 and is expected to fall to 35 if the deal fails. Ignoring time and costs, break-even completion probability solves 48 = p(50) + (1 − p)35, giving approximately 86.7%.
Common mistake: The quoted merger spread is not a guaranteed return because failure can create a loss far larger than the successful-deal gain.
Official syllabus reference: [1]
47. Convertible arbitrage and relative-value exposures
Convertible arbitrage commonly combines a long convertible security with a short position in the issuer's equity to reduce immediate stock-price exposure. The position can retain gamma, volatility, credit, interest-rate, and liquidity risks. Rebalancing a long-gamma exposure can benefit from realized stock movement, but financing costs, borrow availability, credit deterioration, and conversion terms can offset gains. Relative-value positions are therefore not automatically market neutral in every dimension. Factor analysis should examine nonlinear and stress exposures rather than rely only on a low historical equity beta.
Worked example: A convertible position has equity delta equivalent to 6,000 shares, so the manager shorts 6,000 shares initially. If credit spreads widen sharply while the stock barely moves, the convertible can lose value despite the apparently balanced equity hedge.
Common mistake: Offsetting equity delta does not eliminate the convertible's credit exposure, financing risk, embedded-option sensitivity, or need for future hedge adjustments.
Official syllabus reference: [1]
48. Hedge-fund factors, liquidity, and portfolio fit
Hedge-fund strategy labels do not fully describe economic risk. Factor models can reveal exposure to equity markets, credit spreads, rates, trend following, volatility selling, or liquidity conditions. Nonlinear payoffs and changing leverage may require richer analysis than a static linear regression. Portfolio fit also depends on redemption terms, gates, capital lockups, fee structures, and operational risk. Appraisal or stale pricing can understate measured volatility and correlation. An allocation that improves average variance may still worsen drawdowns if the fund's losses concentrate in the same adverse states as existing holdings.
Worked example: A fund reports low equity beta but earns steady small gains and loses heavily when volatility spikes. Adding it to an equity portfolio may increase shared crash exposure, even if a full-sample correlation calculation suggests modest diversification.
Common mistake: A low average historical correlation does not establish reliable crisis diversification when leverage, illiquidity, or nonlinear exposures change during market stress.
Official syllabus reference: [1]
Portfolio Management
49. Economic surprises and consumption risk premiums
Economic news changes asset values by altering expected cash flows, discount rates, or risk premiums relative to prior expectations. Strong reported growth can coincide with falling prices if investors expected even stronger growth or anticipate tighter policy. Consumption-based reasoning links required returns to an asset's performance in economically painful states: assets that pay poorly when consumption is low require greater compensation. Business-cycle analysis also connects policy rates, credit spreads, earnings expectations, and valuation multiples, but relationships depend on the shock driving the cycle and what markets have already priced.
Worked example: Earnings grow 8%, but investors had priced 12% growth. Equity prices can fall despite positive reported growth. A company whose sales collapse during recessions may also require a higher risk premium than a company providing resilient essential services.
Common mistake: Positive economic growth is not automatically bullish because market prices respond to surprises and discount-rate changes, rather than the reported number alone.
Official syllabus reference: [1]
50. Multifactor risk and active-return attribution
A multifactor model separates returns into exposures to common factors and a residual component. Portfolio factor exposure is the weighted sum of security exposures, while active exposure is the difference from the benchmark. Expected active return can arise from intentional factor tilts or security-selection effects. Risk depends on factor covariances and residual covariance assumptions, so several apparently distinct positions may share one dominant risk driver. Attribution should use exposures and factor definitions consistent with the investment process, rather than calling every benchmark-relative gain security-selection skill.
Worked example: A portfolio has value-factor exposure 0.6 and its benchmark has exposure 0.2. If the value factor returns 3%, the active factor contribution is approximately (0.6 − 0.2)3% = 1.2%, before residual and other factor contributions.
Common mistake: Outperforming a benchmark through a rewarded factor tilt is not necessarily evidence of superior individual-security selection after factor exposures are controlled.
Official syllabus reference: [1]
51. Information ratio and the fundamental law
The information ratio divides expected active return by active risk, measuring benchmark-relative efficiency. The fundamental law relates achievable information ratio to forecasting skill, the square root of independent breadth, and the ability to translate forecasts into positions. Constraints and transaction costs can reduce that transfer. Breadth counts effectively independent decisions rather than raw trade volume; correlated forecasts add less diversification. Increasing leverage scales expected active return and active risk together under ideal conditions, leaving the ratio unchanged. Estimated skill and dependence are uncertain, making mechanical forecasts of attainable performance fragile.
Worked example: Assume information coefficient 0.05, independent breadth 100, and transfer coefficient 0.8. The implied information ratio is 0.05√100(0.8) = 0.40. At 4% active risk, expected active return is approximately 1.6%, before any costs excluded from the inputs.
Common mistake: Executing more correlated trades does not increase effective breadth proportionally, and adding leverage alone does not improve an unchanged strategy's information ratio.
Official syllabus reference: [1]
52. ETF premiums, creation, and trading frictions
An exchange-traded fund's market price can differ from its net asset value because shares trade continuously while underlying valuations, liquidity, and trading hours may differ. Authorized participants can create or redeem shares using specified baskets, helping connect ETF prices with underlying asset values. The mechanism is not costless: spreads, financing, taxes, market closures, and basket differences can limit arbitrage. Investors should distinguish management expenses from trading costs and tracking difference. During stress, an apparent premium or discount may partly reflect stale underlying marks rather than a clear arbitrage opportunity.
Worked example: An international ETF trades at 101 while its last published NAV is 100, but the underlying market closed hours earlier. New information may justify the ETF price; comparing it with updated fair-value estimates is more informative than assuming a one-unit mispricing.
Common mistake: An ETF premium over a stale NAV does not automatically create a risk-free arbitrage because underlying securities may be unavailable at those marks.
Official syllabus reference: [1]
53. VaR, expected shortfall, and scenario limits
Value at risk is a loss quantile for a specified horizon and confidence level. It identifies a threshold but does not describe the average severity beyond that threshold. Expected shortfall summarizes the tail beyond the quantile under suitable distributional definitions. Sensitivity measures describe local responses to individual risk factors, while scenarios evaluate specified joint movements and nonlinear effects. These measures complement one another because historical distributions may omit relevant stresses and local approximations can fail for options. Risk limits should specify horizon, confidence, valuation method, and treatment of diversification.
Worked example: Two portfolios each have a one-day 95% VaR of 2 million. In the worst 5% of modeled outcomes, one loses an average of 3 million and the other 8 million. Their equal VaR conceals materially different tail severity.
Common mistake: A 95% VaR is neither the maximum possible loss nor a statement that losses beyond the threshold will be small.
Official syllabus reference: [1]
54. Historical simulation, Monte Carlo, and backtest integrity
Historical simulation reuses observed risk-factor changes, retaining relationships represented in the selected sample but missing events absent from it. Monte Carlo simulation generates scenarios from specified distributions and dependence assumptions, offering flexibility at the cost of model risk. Both require appropriate instrument revaluation, especially for nonlinear exposures. Strategy backtests additionally need point-in-time universes, publication-date information, realistic costs, and chronological out-of-sample evaluation. Repeated strategy searches introduce selection bias even when each individual calculation is accurate. Sensitivity analysis tests how conclusions change when consequential modeling assumptions are varied.
Worked example: A researcher fits a strategy on 2015–2020 data, selects settings on 2021–2022, and evaluates on 2023–2025. Delisted securities remain in historical universes, filings enter after release, and trading costs are charged. Monte Carlo then tests stresses beyond observed history.
Common mistake: Generating more Monte Carlo paths reduces sampling noise but does not correct a poorly chosen return distribution or unrealistic dependence structure.
Official syllabus reference: [1]
Ethical and Professional Standards
55. Knowledge of the law and dissociation
Standard I(A), Knowledge of the Law, requires understanding and complying with applicable laws, regulations, and professional requirements governing one's activities. When requirements conflict, members and candidates must follow the stricter applicable requirement. They must not knowingly participate in violations and must dissociate from unlawful or unethical conduct. Appropriate action can include internal escalation, legal consultation, refusing a task, or leaving an engagement, depending on the circumstances. Reporting to authorities is not universally required by the Standard itself, although applicable law may impose specific reporting obligations.
Worked example: A local rule permits a disclosure practice that the CFA Standards require to be more complete. The analyst follows the stricter professional requirement and asks the firm to correct the disclosure. If ordered to participate in the violation, she dissociates.
Common mistake: A supervisor's approval does not excuse participation in conduct that violates applicable law or a stricter requirement of the Standards.
Official syllabus reference: [1]
56. Independence, gifts, and additional compensation
Standard I(B) protects independent judgment from gifts, benefits, or pressures that could reasonably compromise objectivity. Evaluate the source, size, purpose, and timing of a benefit rather than applying an invented universal monetary limit. Standard IV(B) separately addresses additional compensation arrangements that may conflict with employer interests, requiring written consent from all parties involved. A disclosed benefit can still be inappropriate if it compromises independence. Modest ordinary hospitality differs from lavish issuer-sponsored travel, while client rewards and third-party inducements require analysis of their particular conflicts and disclosure requirements.
Worked example: An issuer offers an analyst a luxury holiday immediately before a recommendation update. Declining protects independence. Separately, a client proposes a performance bonus; before accepting, the analyst obtains the written consent required for the additional compensation arrangement.
Common mistake: Disclosure alone does not make every gift acceptable; a benefit can remain improper when it reasonably threatens independent professional judgment.
Official syllabus reference: [1]
57. Material nonpublic information and mosaic analysis
Standard II(A) prohibits acting or causing others to act on material nonpublic information. Materiality concerns whether information would likely affect price or matter to a reasonable investor, assessed in the circumstances rather than by a universal percentage rule. Mosaic analysis permits conclusions assembled from public information and nonmaterial nonpublic information. It does not permit using a material confidential fact merely because the analyst also performed extensive legitimate research. Selective disclosure to clients does not make information public. Firms should restrict affected activity and encourage appropriate broad dissemination.
Worked example: An analyst combines public capacity data with routine, nonmaterial supplier comments to infer stronger demand; that can be permissible mosaic research. A private CFO statement that a major acquisition is agreed adds material nonpublic information and changes the trading restriction.
Common mistake: Calling research a mosaic does not neutralize a material confidential fact embedded within it, regardless of how many public sources were also consulted.
Official syllabus reference: [1]
58. Suitability at the total-portfolio level
Standard III(C), Suitability, requires reasonable inquiry into a client's investment experience, risk and return objectives, and financial constraints before making recommendations or taking investment action within an advisory relationship. Assess suitability in the context of the total portfolio and update information as circumstances change. For mandate-based management, investment decisions must remain consistent with the stated mandate. A security with high standalone volatility may be suitable as a limited diversifier, while a seemingly conservative asset may be unsuitable if it creates excessive concentration or conflicts with liquidity needs.
Worked example: A client needs a large tuition payment in nine months. Even if a long-lockup fund has attractive expected returns, committing the required cash would conflict with the liquidity constraint. A small allocation funded from genuinely long-term assets requires a separate portfolio assessment.
Common mistake: A client's willingness to buy an investment does not by itself establish suitability when the recommendation conflicts with documented financial needs.
Official syllabus reference: [1]
59. Fair dealing, performance presentation, and records
Fair dealing requires equitable treatment when disseminating recommendations and taking investment action, rather than identical outcomes for every client. Allocation policies should be appropriate, disclosed, and consistently applied without favoring selected accounts. Performance presentation must be fair, accurate, and complete, with relevant limitations and calculation methods communicated. Supporting records should substantiate analyses, recommendations, and performance claims under the applicable requirements. Selectively presenting successful accounts or excluding terminated portfolios can mislead. Different service levels may be permissible when properly disclosed and not used to disadvantage other clients unfairly.
Worked example: A manager receives half the shares requested for two equally eligible orders of 200 and 800. Under a disclosed proportional policy, allocations are 100 and 400. The performance report then includes relevant unsuccessful and terminated accounts rather than highlighting only winners.
Common mistake: Fair dealing does not require equal share quantities, and an accurate calculation can still mislead when the presented sample is selectively chosen.
Official syllabus reference: [1]
60. Conflicts, transaction priority, and referral fees
Standard VI requires clear disclosure of matters that could reasonably impair independence or interfere with duties to clients, prospective clients, and employers. Beneficial ownership, compensation arrangements, and relationships can create conflicts even when no improper trade has occurred. Client and employer transactions must receive priority over transactions in which the member or candidate is a beneficial owner. Referral compensation must be disclosed as required so relevant parties can assess incentives and service costs. Effective controls combine timely, prominent disclosure with restrictions where disclosure alone does not resolve the conflict.
Worked example: An adviser receives a referral payment from an outside manager and also wants to buy shares recommended to clients. She discloses the referral arrangement appropriately before the service agreement and follows transaction-priority procedures before making her personal investment.
Common mistake: Disclosing personal ownership does not permit trading ahead of clients, and a referral payment can require disclosure even without an explicit recommendation fee.
Official syllabus reference: [1]
Official syllabus sources
- 2026 Level II Topic Outlines combined (link opens in new window)
- CFA® Program Level II exam | CFA Institute