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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 241
What is 'loss aversion' and how does it affect investment behaviour?
Select an option first.
Correct answer: B — The tendency for investors to feel the pain of losses more acutely than the pleasure of equivalent gains — loss aversion of approximately 2:1 (losing $100 hurts twice as much as gaining $100 feels good). Leads to suboptimal behaviour: holding losers, refusing to rebalance, excessive risk aversion in new investments after a loss
Explanation: B is correct. Loss aversion (Kahneman and Tversky, 1979): the value function in prospect theory is steeper for losses than gains. Consequences: disposition effect, status quo bias, reluctance to cut losers, myopic loss aversion (excessive short-term focus on volatility). A is a general risk aversion. C is extreme risk aversion. D is the certainty effect.
Question 242
What is 'survivorship bias' in the context of mutual fund performance evaluation?
Select an option first.
Correct answer: B — The overstatement of average mutual fund performance because databases only include currently existing funds — funds that were closed due to poor performance are excluded, making the average of surviving funds appear higher than the true average of all funds
Explanation: B is correct. Survivorship bias in mutual funds: poor-performing funds are merged into better ones or liquidated. The historical database then shows only the survivors' performance, creating an upward bias in average returns. Studies estimate survivorship bias of 0.5-1.5% per annum in mutual fund databases. A is not survivorship bias. C and D are different biases.
Question 243
What is 'persistence of performance' in active fund management?
Select an option first.
Correct answer: B — The tendency for past outperformance (or underperformance) to predict future performance — generally weak for positive alpha persistence but stronger for negative persistence (bad managers consistently underperform). Evidence of performance persistence is weak for most active equity strategies
Explanation: B is correct. Performance persistence: academic evidence shows little persistence in positive alpha — last year's winners are only marginally more likely to be this year's winners. However, loser persistence is stronger (consistently bad processes produce consistently bad results). Fees, turnover, and strategy capacity all erode persistence. A and C overstate persistence. D is incorrect.
Question 244
What is 'return smoothing' and why does it affect risk measurement?
Select an option first.
Correct answer: B — When reported returns are artificially smooth (common in illiquid asset valuations) — this understates true volatility, makes Sharpe ratios appear better than they are, and understates correlations with other asset classes, leading to overestimation of diversification benefits
Explanation: B is correct. Smoothing: illiquid assets (private equity, real estate, some hedge funds) are valued infrequently. When marks don't reflect daily market moves, measured volatility is too low and measured correlation with public markets is too low. De-smoothing techniques (Geltner/Getmansky) can recover the 'true' risk. A is literal smoothing. C is real return calculation. D is fee adjustment.
Question 245
What is the 'capital adequacy ratio' (CAR) in banking?
Select an option first.
Correct answer: B — Total regulatory capital divided by risk-weighted assets — measures the bank's capital buffer relative to its risk exposure. Minimum CAR under Basel III = 8% (total capital), with higher minimums for specific tiers (4.5% CET1)
Explanation: B is correct. CAR = Total Capital (Tier 1 + Tier 2) / Risk-Weighted Assets. Higher CAR = more capital buffer. Too low = regulatory action; too high = capital inefficiency. Regulators set minimum ratios and stress-test banks against capital floors. A is the leverage ratio concept. C is the efficiency ratio. D is the debt/equity ratio.
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Question 246
What is 'liquidity-adjusted VaR' (LVaR)?
Select an option first.
Correct answer: B — VaR adjusted for the additional risk from holding illiquid positions — includes the bid-ask spread and market impact of liquidating positions, adding a liquidity premium to standard VaR to reflect realistic exit costs
Explanation: B is correct. LVaR: standard VaR assumes positions can be liquidated at mid-prices instantaneously. LVaR adds the liquidation cost: LVaR = VaR + Liquidity Cost. Liquidation cost = 0.5 × bid-ask spread × position size for small positions; larger positions face market impact. FRTB introduced liquidity horizons (10-120 days) instead of the standard 10-day VaR for different asset classes. A is not LVaR. C and D are incorrect.
Question 247
What is 'stress VaR' (sVaR) and why was it introduced in Basel 2.5?
Select an option first.
Correct answer: B — VaR calculated using a 12-month historical window that includes a period of significant financial stress (e.g., 2007-2008 crisis) — introduced by Basel 2.5 after the GFC to prevent banks from reducing capital during calm markets
Explanation: B is correct. Stressed VaR (sVaR): Basel 2.5 (2011) added sVaR to the market risk capital requirement. Banks must calibrate their VaR model to a one-year period of significant stress relevant to the bank's portfolio. This prevents pro-cyclical capital reduction during calm markets. The FRTB (Basel IV) further reformed this using ES under stress periods. A is the sVaR concept but imprecisely stated. C is ex-post. D is not sVaR.
Question 248
What is a 'long-short equity' hedge fund's typical risk profile?
Select an option first.
Correct answer: B — Lower market beta than long-only equity (typically 0.3-0.6), with returns driven more by stock selection (longs outperform shorts) — has equity-like upside capture in strong markets but significantly lower drawdowns in market declines
Explanation: B is correct. Long-short equity: net long by definition (long book > short book) → positive but reduced market beta. Performance attributed to stock selection skill (longs generate more return than shorts lose). During market crashes, losses are typically smaller than long-only. A is wrong — beta < 1 typically. C and D understate the remaining market exposure.
Question 249
What is 'dynamic asset allocation' (DAA) vs 'strategic asset allocation' (SAA)?
Select an option first.
Correct answer: B — SAA sets fixed long-term target weights based on fundamental return and risk expectations. DAA adjusts weights tactically around SAA targets based on shorter-term market views (valuation, momentum, macro) — it aims to add return by overweighting relatively attractive asset classes and underweighting expensive ones
Explanation: B is correct. SAA: anchor weights (e.g., 60% equity, 40% bonds). DAA: tilts around anchor (e.g., reduce equity to 50% when valuations are stretched). DAA adds value if market timing skill exists. Research: most institutions modestly employ DAA. A has the distinction reversed. C conflates them. D: both use a variety of instruments.
Question 250
What is 'volatility of volatility' (vol of vol) risk in a portfolio?
Select an option first.
Correct answer: B — The uncertainty about the level of future volatility — when vol of vol is high, volatility itself is unpredictable, making options positions and volatility strategies riskier. Strategies that sell options face the risk that volatility spikes unexpectedly, generating larger losses than modelled
Explanation: B is correct. Vol of vol: measured by VVIX (VIX of VIX). High vol of vol: uncertainty whether volatility will be 10% or 30% makes hedging difficult. For variance swap sellers: you're exposed to the realised variance which is more uncertain when vol of vol is high. A is simple volatility. C is a VaR breach. D is volatility risk premium.
Question 251
What is 'risk-adjusted performance measurement' under GIPS?
Select an option first.
Correct answer: B — A standardised framework (Global Investment Performance Standards) for calculating and presenting investment performance — ensuring comparability, consistency, and credibility of performance records. Key requirements: composites (group similar portfolios), time-weighted returns, full disclosure of fees and methodology
Explanation: B is correct. GIPS (CFA Institute): voluntary standards allowing fair comparison of investment managers. Key: all fee-paying discretionary portfolios must be included in at least one composite; no cherry-picking of portfolios. TWR required to eliminate cash flow timing effects. GIPS verification by an independent verifier adds credibility. A is too narrow. C: GIPS applies to all investment management. D: GIPS requires standardised metrics.
Question 252
What is 'the equity risk premium' (ERP) and how is it estimated?
Select an option first.
Correct answer: B — The expected excess return of equities over the risk-free rate — estimated using: (1) Historical approach: long-run average equity excess return (~5-6% US); (2) Forward-looking: dividend discount model implied (E/P − rf or D₁/P + g − rf); (3) Survey-based: market participants' expectations. ERP varies over time with market conditions
Explanation: B is correct. ERP: the compensation investors demand for bearing equity market risk. Damodaran (NYU) publishes monthly implied ERP estimates. Current ERP varies (e.g., 4-5% in 2024). Used in: CAPM (E(R) = Rf + β × ERP), DCF valuations (discount rate), SAA (expected returns). A is dividend yield. C is the HML value premium. D is the size/SMB premium.
Question 253
What is 'portable alpha' in institutional portfolio management?
Select an option first.
Correct answer: B — A strategy where the alpha source (typically a market-neutral hedge fund or skill-based strategy with zero beta) is separated from beta exposure (obtained cheaply via derivatives). The alpha is 'ported' onto any desired benchmark, creating higher expected returns than a simple long-only approach
Explanation: B is correct. Portable alpha construction: (1) Invest $100M in a market-neutral strategy targeting alpha (beta ≈ 0); (2) Overlay $100M of equity index futures (gaining desired beta). Result: equity beta + alpha source. The alpha doesn't originate from equity selection — it's portable from any uncorrelated source. A is currency overlay. C is persistent alpha. D is momentum alpha.
Question 254
What is the 'characteristic line' in portfolio analysis?
Select an option first.
Correct answer: B — The regression line of security returns against market returns — the slope is beta, the intercept is Jensen's alpha, and the residual from the line represents unsystematic risk. Plotting actual returns against this line reveals over/underperformance relative to CAPM predictions
Explanation: B is correct. Characteristic line: R_i = α + β_i × R_m + ε_i. Alpha = consistent over/underperformance versus CAPM. Points above the line = outperformance for that period. The standard error of the regression reflects idiosyncratic risk. A is the CML. C is the maximum return point. D is the efficient frontier.
Question 255
What is 'asset class correlation' and why does it matter for diversification?
Select an option first.
Correct answer: B — The statistical relationship between returns of different asset classes — when correlations are low or negative, combining assets reduces portfolio volatility below the weighted average of individual volatilities. The benefit of diversification is greatest when correlations approach −1
Explanation: B is correct. Correlation in diversification: σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂. If ρ = 0, portfolio variance is less than the weighted average of individual variances. If ρ = −1, variance can be reduced to zero. In crises, correlations often converge toward +1, reducing diversification exactly when needed. A is benchmark correlation. C is price discovery speed. D is a different calculation.
Question 256
What is 'convexity bias' in portfolio strategies?
Select an option first.
Correct answer: B — The observation that positively convex instruments (long options, bonds with positive convexity) systematically outperform simple duration-matched linear instruments over time — because the price gains from large yield moves exceed the losses from equivalent moves in the opposite direction
Explanation: B is correct. Convexity value: for two bonds with the same duration, the more convex bond is worth more. Convexity creates asymmetric returns — gain more when rates fall, lose less when rates rise. Long convexity costs money (options premium) but the positive carry trades off against the convexity benefit. A is a yield curve shape preference. C applies the equity concept incorrectly. D is a calculation error.
Question 257
What is 'Appraisal Ratio' as a performance metric?
Select an option first.
Correct answer: B — Jensen's alpha divided by the standard deviation of the residual return (unsystematic risk) — measures the abnormal return per unit of unsystematic risk. A higher appraisal ratio indicates more alpha generated per unit of idiosyncratic risk taken
Explanation: B is correct. Appraisal ratio = α / σ(ε), where σ(ε) is the standard deviation of the regression residuals. It measures active management skill — how much alpha is generated relative to the idiosyncratic risk taken. Useful for comparing managers who take different amounts of unsystematic risk. A is a return ratio. C is the long/short ratio. D is a fee concept.
Question 258
What is 'rebalancing cost' and how does it affect portfolio performance?
Select an option first.
Correct answer: B — The transaction costs (commissions, bid-ask spreads, market impact) incurred when rebalancing a portfolio back to its target allocation — these costs must be weighed against the diversification and risk-management benefits of rebalancing. High-turnover strategies are most affected by rebalancing costs
Explanation: B is correct. Rebalancing cost: a 2% rebalancing cost for a 20% annual turnover portfolio equals 40bps drag. For illiquid assets (emerging market bonds), costs can be 50-200bps per transaction. Cost-efficient rebalancing: use cash flows for natural rebalancing, use derivatives overlay, or widen rebalancing bands. A is manager change cost. C is a partial component. D is tax drag.
Question 259
What is the 'equity premium puzzle'?
Select an option first.
Correct answer: B — The observation that the historical equity risk premium (~6% in US) is far larger than standard consumption-based asset pricing models predict — rational investors would need implausibly high levels of risk aversion to justify such a large premium, suggesting either market imperfections or limitations of the model
Explanation: B is correct. Equity premium puzzle (Mehra & Prescott, 1985): under standard CRRA utility models, the observed ERP requires risk aversion coefficient of 30-50 (implausibly high). Proposed explanations: transaction costs, liquidity risk, rare disaster risk (Rietz, Barro), long-run consumption risk, survival bias in US data. The puzzle motivates alternative asset pricing theories. A is crash risk. C is the dividend-price decline. D is valuation dispersion.
Question 260
What is 'multi-period portfolio optimisation'?
Select an option first.
Correct answer: B — An extension of single-period optimisation that considers the investor's long-term objectives, recognising that the optimal portfolio today depends on future investment opportunities, labour income, and the evolution of risk preferences over the lifecycle — dynamic programming or simulation methods are used
Explanation: B is correct. Multi-period optimisation: single-period (Markowitz) ignores future states. Multi-period: considers path dependency (e.g., sequence of returns risk), changing risk capacity over time (younger investor can take more risk), and the link between current and future investment opportunities. Tools: dynamic programming, Monte Carlo simulation. A is repeated single-period optimisation. C is multi-benchmark optimisation. D is model selection.
Question 261
What is 'sequence of returns risk' for investors?
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Correct answer: B — The risk that the timing of negative returns significantly harms the investor, particularly when they are withdrawing from (or contributing to) a portfolio — early negative returns combined with withdrawals cause much greater wealth depletion than the same returns experienced in reverse order
Explanation: B is correct. Sequence of returns risk: most critical in the 'retirement red zone' (10 years before and after retirement). Same average return, different sequence → dramatically different outcomes when withdrawals occur. Example: -30% return in year 1 with annual withdrawals depletes capital before recovery. Solutions: bucket strategy, dynamic withdrawal, annuitisation. A is average return risk. C is market timing. D is correlation risk.
Question 262
What is 'risk decomposition by factor' and how is it used in portfolio management?
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Correct answer: B — Attributing total portfolio risk to contributions from each systematic factor (market, size, value, momentum, credit, rates) and the residual (idiosyncratic) risk — enables identification of unintended factor exposures, ensures risk is being taken where expected return is highest, and guides hedging of unwanted exposures
Explanation: B is correct. Factor risk decomposition: a 'balanced' portfolio may appear diversified but could have 80% of risk coming from the equity market factor. Risk decomposition reveals: Is the risk budget allocated to the intended factors? Are there unintended exposures (e.g., hidden credit beta)? Tools: risk factor models (Barra, Axioma). A is a simple two-way split. C is temporal decomposition. D is manager attribution.
Question 263
What is 'capital efficiency' in portfolio construction?
Select an option first.
Correct answer: B — Using the available risk budget as effectively as possible — maximising expected return per unit of risk taken. Techniques: leverage (to scale up low-risk assets), derivatives overlay (gain exposure without cash), and concentration in highest-conviction ideas rather than spreading risk thinly across many positions
Explanation: B is correct. Capital efficiency: a risk-parity approach uses leverage to bring low-risk assets (bonds) to the same risk contribution as equities. Derivatives overlay: gain equity exposure using futures, freeing cash for alpha strategies (portable alpha). Concentration: avoid diluting high-conviction bets with low-conviction ones. A is fee management. C is a cost target. D is full investment.
Question 264
What is the 'Modigliani-Modigliani' (M²) measure?
Select an option first.
Correct answer: B — A risk-adjusted performance measure that rescales the portfolio's return to have the same total risk as the market, then compares to the market return — expresses performance in percentage return terms (unlike Sharpe ratio which is dimensionless), making it more intuitive for communication
Explanation: B is correct. M² (Franco and Leah Modigliani, 1997): adjusts portfolio to have the same risk as the market by combining with the risk-free asset, then compares to market return. M² = Sharpe_portfolio × σ_market + Rf. A positive M² means the portfolio earned more than the market at the same risk level. Intuitively expressed as a return %. A is capital structure theory. C is not a performance metric. D is duration analysis.
Question 265
What is 'index construction methodology' and how does it affect performance?
Select an option first.
Correct answer: B — The rules governing which securities are included in an index, how they are weighted, how frequently they are reconstituted, and how corporate actions are treated — affects: performance (reconstitution effect, inclusion/exclusion rebalancing), tradability (liquidity of index constituents), and factor exposures (cap-weight vs equal-weight vs fundamental-weight)
Explanation: B is correct. Index construction: market-cap weight (S&P 500): self-rebalancing, momentum tilt, overweights expensive stocks. Equal weight: contrarian, overweights small caps, higher turnover. Fundamental weight (RAFI): value tilt, rebalances to fundamentals. Reconstitution effect: index addition → price spike (inclusion premium), removal → decline. A is price return vs total return. C is administration. D is eligibility screening.
Question 266
What is 'gross exposure' vs 'net exposure' in a hedge fund?
Select an option first.
Correct answer: B — Gross exposure = total long positions + total short positions (absolute value). Net exposure = long positions − short positions. Gross measures overall market activity; net measures directional bias. A fund with $80M long and $60M short has $140M gross and $20M net exposure
Explanation: B is correct. Gross exposure: total market footprint. Net: directional bet. A $100M NAV fund with $140M gross and $20M net has moderate net market exposure but significant gross (trading activity). Leverage ratio = gross/NAV = 1.4x. A conflates the two. C and D are incorrect. Both are pre-fee measures.
Question 267
What is 'portfolio concentration' risk and how is the Herfindahl-Hirschman Index (HHI) used to measure it?
Select an option first.
Correct answer: B — Concentration risk: excessive exposure to a single issuer, sector, or factor. HHI = Σ(w_i²), where w_i = portfolio weight of position i. HHI ranges from 0 (perfectly diversified) to 1 (single holding). A higher HHI indicates more concentration risk
Explanation: B is correct. HHI in portfolios: a 10-stock equal-weight portfolio has HHI = 10 × (0.1²) = 0.10. A 2-stock 50/50 portfolio has HHI = 2 × (0.5²) = 0.50. Higher HHI → more concentrated. HHI is also used by regulators to measure market concentration in antitrust law. A is too narrow. C: HHI applies to portfolios too. D: number of positions alone doesn't capture weight concentration.
Question 268
What is 'maximum Sharpe ratio portfolio' (tangency portfolio)?
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Correct answer: B — The portfolio on the efficient frontier with the highest ratio of excess return to standard deviation — found by drawing a line from the risk-free rate tangent to the efficient frontier. All investors combining the risk-free asset with risky assets should hold this portfolio of risky assets
Explanation: B is correct. Tangency portfolio: in CAPM, all investors hold the same risky portfolio (the tangency/market portfolio) combined with varying amounts of the risk-free asset based on their risk tolerance. The tangency portfolio maximises the Sharpe ratio. A is the maximum return portfolio. C is the minimum variance portfolio. D is the equal-weight portfolio.
Question 269
What is 'currency risk' (FX risk) in international portfolio management and how does it contribute to total return volatility?
Select an option first.
Correct answer: B — FX risk arises when holding foreign assets — the total return in domestic currency = local asset return + currency return + cross term. Currency volatility can add significantly to total portfolio volatility. For developed market equities, currency risk typically adds 5-10% to annual volatility
Explanation: B is correct. FX risk contribution: a US investor in Japanese equities faces: equity return (yen-denominated) + USD/JPY return. Even if the yen-equity is low-volatility, large yen swings create significant USD-return volatility. Total portfolio σ² ≈ σ²_local + σ²_FX + 2×ρ×σ_local×σ_FX. Whether to hedge depends on: cost, correlation, and investment horizon. A is wrong — hedging decisions vary. C is wrong. D: country risk encompasses political, economic, AND currency.
Question 270
What is 'Bayesian updating' in the context of investment views?
Select an option first.
Correct answer: B — A statistical method for updating probability estimates as new evidence arrives — in portfolio management (Black-Litterman model), investor views are expressed with a confidence level and blended with prior market equilibrium returns using Bayes' theorem. Higher confidence weights views more heavily
Explanation: B is correct. Bayesian updating: prior (market equilibrium returns) + views (investor forecasts) + likelihood (confidence in views) → posterior (blended expected returns). The Black-Litterman model formalises this. The strength of the view determines how much the posterior moves away from the prior. A is return averaging. C is forecast replacement. D is consensus forecasting.
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