Free FRM Quantitative Analysis Practice Questions & Answers
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Question 331
The coherence property of a risk measure requires it to satisfy:
Select an option first.
Correct answer: B — Four properties: monotonicity, subadditivity, homogeneity, and translation invariance
Explanation: B
Question 332
Conditional Value at Risk (CVaR) equals:
Select an option first.
Correct answer: B — The expected loss in the tail beyond VaR, i.e., E[Loss | Loss > VaR]
Explanation: B
Question 333
When backtesting a 99% one-day VaR model over 250 trading days, the Basel traffic light system classifies a model as 'red zone' when:
Select an option first.
Correct answer: C — 10 or more exceptions occur
Explanation: C
Question 334
Volatility clustering refers to:
Select an option first.
Correct answer: B — The empirical pattern where periods of high volatility tend to follow high volatility, and calm periods follow calm periods
Explanation: B
Question 335
The Treynor ratio differs from the Sharpe ratio in that:
Select an option first.
Correct answer: B — Treynor normalises excess return by systematic risk (beta) rather than total risk (standard deviation)
Explanation: B
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Under the parametric approach, the 1-day 99% VaR for a single asset with daily return volatility σ and zero mean is:
Select an option first.
Correct answer: B — 2.326 × σ
Explanation: B
Question 337
Principal Component Analysis (PCA) applied to yield curve movements identifies:
Select an option first.
Correct answer: B — Orthogonal (uncorrelated) factors that explain the greatest variance in yield changes, with the first factor typically being a parallel shift
Explanation: B
Question 338
The increase in correlation between risky assets during market stress events is known as:
Select an option first.
Correct answer: B — Correlation breakdown or correlation contagion, where diversification benefits decline precisely when they are most needed
Explanation: B
Question 339
Which of the following is a coherent risk measure?
Select an option first.
Correct answer: B — Expected Shortfall (ES/CVaR)
Explanation: B
Question 340
Specific risk in the standardised approach to market risk capital refers to:
Select an option first.
Correct answer: B — Idiosyncratic (issuer-specific) risk in bond and equity positions that is not driven by general market movements
Explanation: B
Question 341
In risk management, the difference between VaR and Stressed VaR is:
Select an option first.
Correct answer: B — Stressed VaR uses a historical period of financial stress (typically 2007-2009) to compute a higher capital charge that does not shrink during calm markets, preventing pro-cyclicality
Explanation: B
Question 342
Tracking error of a portfolio relative to a benchmark is:
Select an option first.
Correct answer: B — The standard deviation of the portfolio's active returns (portfolio return minus benchmark return) over time
Explanation: B
Question 343
The Omega ratio, unlike the Sharpe ratio, is:
Select an option first.
Correct answer: B — A risk-adjusted measure that captures the full return distribution by computing the probability-weighted ratio of gains above a threshold to losses below it, thus sensitive to higher moments (skewness, kurtosis)
Explanation: B
Question 344
The information ratio can be improved by:
Select an option first.
Correct answer: B — Either increasing active returns (alpha) or reducing tracking error (more consistent active returns), or both simultaneously — the IR measures skill in active management
Explanation: B
Question 345
The Cornish-Fisher approximation adjusts VaR for non-normality by:
Select an option first.
Correct answer: B — Applying a correction factor to the normal z-score that accounts for skewness (γ₁) and excess kurtosis (γ₂): z_CF ≈ z + (z²-1)γ₁/6 + (z³-3z)γ₂/24 - (2z³-5z)γ₁²/36, then using z_CF instead of z in the VaR formula
Explanation: B
Question 346
The Newey-West standard errors are used in time series regression to produce:
Select an option first.
Correct answer: B — Heteroskedasticity and autocorrelation consistent (HAC) standard errors that are valid when residuals exhibit both heteroskedasticity and serial correlation — common in financial return data
Explanation: B
Question 347
A portfolio consisting of a long bond and a long payer swaption has:
Select an option first.
Correct answer: B — Combined exposure to interest rates (from the bond), plus convex exposure from the swaption (long vega, long gamma) — the swaption provides protection if rates rise sharply while the bond loses value
Explanation: B
Question 348
The Sortino ratio improves on the Sharpe ratio by:
Select an option first.
Correct answer: B — Using downside deviation (volatility of only below-target returns) rather than total standard deviation — reflecting that only downside risk matters to investors, not upside volatility
Explanation: B
Question 349
Incremental VaR (IVaR) of a position measures:
Select an option first.
Correct answer: B — The change in total portfolio VaR from adding the position — reflecting its marginal contribution including diversification effects with the rest of the portfolio
Explanation: B
Question 350
The Calmar ratio measures:
Select an option first.
Correct answer: B — Annualised compound return divided by maximum drawdown — a risk-adjusted performance measure favoured by hedge fund investors concerned about catastrophic losses
Explanation: B
Question 351
A bank reports 99% daily VaR of $5M. Under Basel III's standardised approach for market risk (FRTB), the risk measure that replaces VaR is:
Select an option first.
Correct answer: B — 97.5% Expected Shortfall (ES) over a liquidity-adjusted time horizon
Explanation: B
Question 352
Incremental Risk Charge (IRC) in the FRTB framework captures:
Select an option first.
Correct answer: B — Default risk and credit migration risk for non-securitisation positions in the trading book over a one-year capital horizon at 99.9% confidence
Explanation: B
Question 353
The major limitation of historical simulation VaR compared to Monte Carlo simulation is:
Select an option first.
Correct answer: B — Historical simulation assumes the future will resemble the past; it cannot generate scenarios more extreme than those historically observed and is limited to the length of the historical window
Explanation: B
Question 354
Expected Shortfall (ES) at confidence level α is:
Select an option first.
Correct answer: B — ES = E[L | L > VaR_α] = (1/(1-α)) × ∫_α^1 VaR_u du
Explanation: B
Question 355
The stressed VaR (sVaR) requirement under Basel II.5 and Basel III:
Select an option first.
Correct answer: B — Requires computing VaR using a one-year historical stress period (typically including the 2007-2009 crisis), added to the regular VaR to increase the minimum capital requirement
Explanation: B
Question 356
Model risk in financial risk management arises from:
Select an option first.
Correct answer: B — Errors or incorrect assumptions in the mathematical models used for pricing and risk measurement, which can lead to mispriced securities and inaccurate risk estimates
Explanation: B
Question 357
The square-root-of-time rule for VaR scaling assumes:
Select an option first.
Correct answer: B — Daily returns are independent and identically distributed (i.i.d.) and normally distributed, so that T-day variance = T × daily variance
Explanation: B
Question 358
In risk-neutral pricing, expected returns on all assets equal the risk-free rate because:
Select an option first.
Correct answer: B — Investors are risk-neutral in the risk-neutral measure, and the risk-neutral probability measure Q is chosen to make all discounted asset prices martingales, enabling consistent derivative pricing regardless of the actual physical return
Explanation: B
Question 359
The use of Expected Shortfall (ES) at 97.5% rather than VaR at 99% in FRTB (Basel IV) produces:
Select an option first.
Correct answer: B — A higher and more informative measure of tail risk that is also a coherent risk measure, with the capital level calibrated to be broadly comparable to 99% VaR for normal distributions but more sensitive to tail losses
Explanation: B
Question 360
The dispersion of option payoffs that is not captured by delta-gamma approximation is called:
Select an option first.
Correct answer: B — Higher-order risk — speed (dGamma/dS), color (dGamma/dt), and other higher-order Greeks become significant for large moves or path-dependent options
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