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Free FRM Risk Management & Investment Management Practice Questions & Answers
400 exam-style Risk Management & Investment Management questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 211
What is the Arbitrage Pricing Theory (APT)?
Select an option first.
Correct answer: B — A multi-factor model where expected return is a linear combination of sensitivities to multiple systematic risk factors, each with its own risk premium
Explanation: B is correct. APT (Ross, 1976): E(R) = Rf + β₁λ₁ + β₂λ₂ + ... + βₖλₖ, where β = factor loading, λ = factor risk premium. It is more flexible than CAPM (one factor) and does not require market portfolio identification. A is options pricing. C is a naive equilibrium. D is arbitrage trading.
Question 212
What is 'alpha decay' in the context of active investing?
Select an option first.
Correct answer: B — The tendency for return anomalies (like momentum) to weaken over time as more capital exploits them, or for a manager's alpha edge to erode as their strategy becomes more widely known
Explanation: B is correct. Alpha decay occurs because: (1) As more investors exploit an anomaly, it gets arbitraged away; (2) A manager's unique insights may become embedded in prices as others learn the strategy; (3) Growing AUM forces the manager into less attractive positions. A is a capacity constraint. C is market risk. D is fee drag.
Question 213
What is 'return on equity' (ROE)?
Select an option first.
Correct answer: B — Net income divided by shareholders' equity, measuring profitability from equity capital
Explanation: B is correct. ROE = Net Income / Shareholders' Equity. It measures how efficiently a company generates profit from shareholder capital. A higher ROE generally indicates better management efficiency. It can be decomposed via DuPont analysis. A uses revenue (not net income). C is the equity multiplier. D is a market-based measure.
Question 214
What is the DuPont decomposition of ROE?
Select an option first.
Correct answer: B — ROE = Net Profit Margin × Asset Turnover × Financial Leverage (equity multiplier)
Explanation: B is correct. DuPont: ROE = (Net Income/Revenue) × (Revenue/Total Assets) × (Total Assets/Equity) = Profit Margin × Asset Turnover × Equity Multiplier. This decomposes ROE into profitability, efficiency, and leverage components. A is incomplete. C rearranges the formula incorrectly. D is just the stock price.
Question 215
What is 'Return on Invested Capital' (ROIC)?
Select an option first.
Correct answer: B — After-tax operating profit (NOPAT) divided by invested capital (debt + equity), measuring how efficiently a company generates profit from all sources of capital
Explanation: B is correct. ROIC = NOPAT / Invested Capital. It measures return generated on all capital employed, including both debt and equity, making it capital-structure neutral. ROIC > WACC creates value; ROIC < WACC destroys value. A is ROA. C is an asset turnover variant. D uses gross profit (not NOPAT).
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Question 216
What is 'net asset value' (NAV) and how is it calculated for a fund?
Select an option first.
Correct answer: B — Total assets of the fund minus total liabilities, divided by the number of shares outstanding — the per-share price at which investors buy and sell fund shares
Explanation: B is correct. NAV = (Total Assets − Liabilities) / Shares Outstanding. Mutual funds price NAV once daily after market close. Hedge funds may calculate NAV monthly. A is market cap. C is performance, not NAV. D is the asset manager's own market cap.
Question 217
What is 'return attribution' and what are its three components?
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Correct answer: B — Decomposing active portfolio returns into: allocation effect (sector overweights), selection effect (stock picking within sectors), and interaction effect (combined impact of allocation and selection decisions)
Explanation: B is correct. Brinson-Hood-Beebower attribution: Allocation effect = (w_p − w_b) × (R_b,sector − R_b); Selection effect = w_b × (R_p,sector − R_b,sector); Interaction = (w_p − w_b) × (R_p,sector − R_b,sector). Together they sum to total active return. A is P&L reporting. C is team allocation. D is time-series comparison.
Question 218
What is 'beta' in the CAPM and how is it estimated?
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Correct answer: B — The slope coefficient from regressing security returns on market returns — measures systematic risk. Beta > 1: more volatile than market; Beta < 1: less volatile; Beta = 0: no market sensitivity (risk-free asset)
Explanation: B is correct. Beta = Cov(R_i, R_m) / Var(R_m). Estimated by OLS regression of security returns against market returns (characteristic line). The slope = beta; intercept = alpha. A describes expected return. C is Jensen's alpha (the intercept). D: the risk-free rate has zero correlation with risky assets, giving beta = 0.
Question 219
What is 'idiosyncratic volatility' and what drives it?
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Correct answer: B — Volatility specific to an individual stock or asset that is uncorrelated with market movements — driven by firm-specific events such as earnings surprises, management changes, product launches, or litigation outcomes
Explanation: B is correct. Idiosyncratic (specific) volatility = total volatility − systematic volatility. It is diversified away in large portfolios. Factors: earnings surprises, management quality, competitive dynamics, regulatory events specific to the firm. A conflates the two. C is systematic volatility. D is market volatility.
Question 220
What is 'alpha generation' in portfolio management?
Select an option first.
Correct answer: B — Generating returns above what is explained by systematic risk factors — true skill-based excess return not attributable to beta, factor exposures, or luck. True alpha is rare and tends to decay over time
Explanation: B is correct. True alpha: after controlling for all risk factors (market beta, size, value, momentum), a positive residual return indicates genuine manager skill. Most empirical studies find that few managers generate persistent alpha after fees. A is absolute return. C is benchmark matching. D is real return.
Question 221
What is 'portfolio rebalancing' and why is it necessary?
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Correct answer: B — Periodically restoring a portfolio to its target asset allocation after market movements cause weights to drift — ensures the risk profile remains aligned with the investor's objectives
Explanation: B is correct. Rebalancing: over time, outperforming assets grow to a larger share, increasing risk concentration. Rebalancing (calendar-based or threshold-based) restores the target allocation. Cost: transaction costs and taxes. Benefit: systematic buy-low/sell-high effect and maintenance of intended risk. A is a crisis response. C is performance-based selling. D is active management.
Question 222
What is 'factor exposure' or 'factor loading' in a multi-factor model?
Select an option first.
Correct answer: B — The sensitivity of a security's return to a specific risk factor — how much the security's return changes for a unit change in the factor. Higher loading means greater sensitivity to that factor
Explanation: B is correct. Factor loading (β_i): in a multi-factor model R_i = α + β_1F_1 + β_2F_2 + ... + ε, each β measures the exposure to the corresponding factor. A stock with high value loading benefits when value stocks outperform. A is sector allocation. C is index composition. D is factor return.
Question 223
What is 'benchmark-relative risk' vs 'absolute risk'?
Select an option first.
Correct answer: B — Benchmark-relative risk measures how much a portfolio deviates from its benchmark (tracking error, active risk); absolute risk measures total portfolio volatility (standard deviation) regardless of any benchmark — the appropriate measure depends on the investor's mandate
Explanation: B is correct. Benchmark-relative: tracking error, active beta. Used for mandates where performance is measured against a benchmark. Absolute: standard deviation, VaR. Used for absolute return mandates (hedge funds, balanced funds). Neither is inherently 'better' — it depends on the mandate. A is incorrect. C is wrong. D: tracking error can be higher or lower than absolute vol.
Question 224
What is 'ex-ante' vs 'ex-post' risk?
Select an option first.
Correct answer: B — Ex-ante risk is the forward-looking, predicted risk (based on current factor exposures, covariance matrices) used in portfolio construction; ex-post risk is the realised historical risk observed after the fact — both are important but often differ
Explanation: B is correct. Ex-ante (prospective): estimated future volatility and correlations from current data — used to manage risk now. Ex-post (realised): actual historical volatility and returns — used to evaluate manager skill. They differ because market conditions change. A is not the distinction. C and D are different risk dimensions.
Question 225
What is 'currency overlay' in international portfolio management?
Select an option first.
Correct answer: B — A strategy that separates currency management from underlying asset management — a specialist overlay manager hedges currency exposure from international assets, allowing the asset manager to focus purely on security selection
Explanation: B is correct. Currency overlay: a pension fund holds international equities and appoints a separate currency overlay manager who systematically manages FX exposure (hedging some or all, or actively taking currency views). Separates two different sources of return/risk. A is speculative FX trading. C is a passive full-hedge approach. D is a static approach.
Question 226
What is 'alpha and beta separation'?
Select an option first.
Correct answer: B — The investment strategy of separating passive market exposure (beta, accessed cheaply via index funds or futures) from active return-generating (alpha, accessed through skilled managers) to optimise costs and performance
Explanation: B is correct. Alpha-beta separation: obtain cheap beta via passive funds (low cost, liquid). Allocate active risk budget only to managers with demonstrated alpha-generating ability (portable alpha). This optimises fee spending — don't pay active fees for beta that can be acquired cheaply. A has the mandates backwards. C is a statistical approach. D is not a regulatory requirement.
Question 227
What is 'equal-weighted portfolio' vs 'market-cap-weighted portfolio'?
Select an option first.
Correct answer: B — Equal-weighted: each stock receives 1/N weight regardless of size — overweights small caps, requires frequent rebalancing; market-cap-weighted: weights proportional to market capitalisation — naturally self-rebalancing, tends to overweight the most expensive/overvalued stocks
Explanation: B is correct. Equal weight: intuitive diversification, small-cap tilt (size premium), higher rebalancing costs. Cap weight: self-rebalancing (no need to trade as prices change), lower costs, but momentum tilt and concentration in large/expensive stocks. Research shows equal-weighting has historically outperformed but with higher turnover. A ignores structural differences. C is not always true. D is incorrect.
Question 228
What is 'min-variance portfolio'?
Select an option first.
Correct answer: B — The portfolio on the efficient frontier with the lowest possible standard deviation — found by minimising portfolio variance subject to weights summing to 1. Does not require expected return inputs (only covariance matrix), making it more robust to estimation error
Explanation: B is correct. Minimum variance portfolio (MVP): the leftmost point on the efficient frontier. Advantage: only requires the covariance matrix (not expected returns), which is more reliably estimated. Research shows MVP portfolios often have competitive risk-adjusted returns. A is the maximum return portfolio. C is equal-weight. D is a minimum tracking error portfolio.
Question 229
What is 'Omega ratio' and what advantage does it have over Sharpe ratio?
Select an option first.
Correct answer: B — Omega = E[max(R−L, 0)] / E[max(L−R, 0)]. It incorporates all moments of the return distribution (not just mean and variance), making it preferable when returns are non-normal — particularly for hedge fund and alternative investment strategies with skewed distributions
Explanation: B is correct. Omega advantage: Sharpe only uses the first two moments (mean and standard deviation), assuming normality. Omega uses all moments — captures skewness, kurtosis, fat tails. More accurate for non-normal distributions (hedge funds, options strategies). Sharpe overestimates performance for positively skewed strategies and underestimates for negatively skewed ones. A is wrong. C is too restrictive. D is debatable.
Question 230
What is the Sharpe ratio for a portfolio with 0% return, 0% risk-free rate, and 5% standard deviation?
Select an option first.
Correct answer: B — 0.00
Explanation: B is correct. Sharpe = (0% − 0%) / 5% = 0/5 = 0.00. A zero Sharpe means the portfolio earned the risk-free rate (or equal to it when rf = 0). It is defined (not undefined). A is wrong — the calculation is valid. C would require infinite returns. D would require negative returns.
Question 231
What is 'active share'?
Select an option first.
Correct answer: B — The proportion of a portfolio's holdings that differs from the benchmark — a portfolio with 100% active share has no overlap with the benchmark; 0% means it perfectly replicates the benchmark. High active share funds have more opportunity for differentiated returns but also higher idiosyncratic risk
Explanation: B is correct. Active share = 0.5 × Σ|w_p,i − w_b,i|. Research (Cremers & Petajisto, 2009) showed that high active share funds had higher before-fee alpha than closet indexers. Closet indexers: high fee but low active share. True active management requires high active share. A is manager allocation. C is turnover rate. D is a different ratio.
Question 232
What is the 'transfer coefficient' (TC) in the Fundamental Law of Active Management?
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Correct answer: B — A measure of how effectively a manager can implement their views — when portfolio construction is unconstrained TC = 1; when there are no short-selling or other constraints, information can be fully expressed. With constraints, TC < 1, reducing the full potential IR
Explanation: B is correct. Full Law: IR = TC × IC × √N. Constraints (no shorting, turnover limits, tracking error limits) prevent full expression of investment views → TC < 1. A manager with IC = 0.1 and N = 100 but TC = 0.5 has IR = 0.5 × 0.1 × 10 = 0.5 (half the unconstrained potential). A is fee transfer. C is alpha decay. D is correlation.
Question 233
What is 'skewness' in the context of return distributions and why does it matter for risk management?
Select an option first.
Correct answer: B — A measure of the asymmetry of a return distribution — negative skewness (long left tail) means occasional large losses occur more frequently than a normal distribution would predict; positive skewness means occasional large gains. Risk models assuming normality underestimate tail losses for negatively skewed strategies
Explanation: B is correct. Negative skewness: common in option-selling strategies, credit strategies, carry trades. Strategies look good most of the time (small positive returns) but suffer occasional large losses. Sharpe ratio overstates risk-adjusted performance for negatively skewed strategies. Positive skew: long options strategies. A is time-variation. C is autocorrelation. D is kurtosis.
Question 234
What is 'excess kurtosis' (leptokurtosis) and its implications for risk management?
Select an option first.
Correct answer: B — Fat tails — a return distribution with more mass in the tails (extreme observations) than a normal distribution (which has kurtosis of 3). Excess kurtosis > 0 means fat tails, implying that extreme events (market crashes, large gains) occur more frequently than normal models predict
Explanation: B is correct. Excess kurtosis = kurtosis − 3. Fat tails (positive excess kurtosis) mean: VaR models assuming normality underestimate loss probabilities at high confidence levels. Financial returns typically have excess kurtosis of 2-8. This motivated Expected Shortfall and fat-tailed distributions (Student's t) in risk models. A and D describe normal/mesokurtic distributions. C is normality.
Question 235
What is 'efficient market hypothesis' (EMH) and its three forms?
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Correct answer: B — Weak form: prices reflect all historical price data; Semi-strong form: prices reflect all publicly available information; Strong form: prices reflect all information (public and private). Each form has different implications for the usefulness of technical and fundamental analysis
Explanation: B is correct. EMH (Fama, 1970): Weak: technical analysis cannot generate excess returns (past prices already embedded). Semi-strong: fundamental analysis cannot generate excess returns (public info embedded). Strong: even insider trading cannot generate excess returns (private info embedded). Empirical evidence supports weak and semi-strong but refutes strong form. A is the strong form claim only. C and D are unjustified restrictions.
Question 236
What is 'home country bias' as a portfolio anomaly?
Select an option first.
Correct answer: B — The tendency of investors to hold a disproportionately large share of their portfolio in domestic equities, despite the diversification benefits available from international investing
Explanation: B is correct. Home country bias: US investors hold far more US equities than the ~55% US share of global market cap. UK investors hold mostly UK equities (10% of world). This leads to under-diversification and concentration in domestic economic risks. Causes: familiarity bias, perceived information advantage, currency risk aversion, regulatory constraints. A is a different bias. C is large-cap bias. D is brand familiarity.
Question 237
What is 'disposition effect' as a behavioural finance concept?
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Correct answer: B — The tendency of investors to sell winning positions too early (to lock in gains) and hold losing positions too long (avoiding realising losses) — contrary to optimal tax and performance management
Explanation: B is correct. Disposition effect (Shefrin and Statman, 1985): based on prospect theory — investors are more sensitive to losses than gains. Winning stocks are sold to 'bank' the gain; losing stocks are held hoping for recovery. This is suboptimal: taxes are more efficient if gains are deferred; fundamental analysis should drive selling decisions. A is loss-chasing. C is liquidity preference. D is herding.
Question 238
What is 'anchoring bias' in investment decision-making?
Select an option first.
Correct answer: B — Over-reliance on an initial piece of information (the 'anchor') when making subsequent decisions — e.g., investors anchoring on a stock's 52-week high and using it as a reference point for valuation, even if circumstances have fundamentally changed
Explanation: B is correct. Anchoring: the first number seen (historical price, analyst target, book value) disproportionately influences subsequent judgment. Example: a stock fell from $100 to $50 — investors anchor on $100, seeing it as 'cheap' at $50 even if fundamentals justify a lower price. A is not anchoring. C is herding/momentum. D is complacency bias.
Question 239
What is 'overconfidence bias' in portfolio management?
Select an option first.
Correct answer: B — The tendency of investors and managers to overestimate their skill, the precision of their forecasts, and their ability to predict markets — leading to excessive trading, under-diversification, and insufficient risk premiums demanded for uncertainty
Explanation: B is correct. Overconfidence: manifests as excessive trading (costs erode returns), concentrated positions (under-diversification), and miscalibration of confidence intervals. Research shows overconfident investors trade more and underperform. A is a consequence. C is naive diversification. D is over-hedging.
Question 240
What is 'herding behaviour' in financial markets?
Select an option first.
Correct answer: B — The tendency of investors to follow the crowd — buying what others are buying and selling what others are selling — which can amplify asset price bubbles and crashes
Explanation: B is correct. Herding: in financial markets, herding can be rational (career risk — it's safer to be wrong with everyone) or irrational (information cascades). Herding amplifies price movements: creates bubbles (all buying) and crashes (all selling simultaneously). Related to systemic risk. A is coincidental correlated action. C is indexing. D is momentum investing.
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