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Free Questions › FRM › Market Risk Measurement and Management
Free FRM Market Risk Measurement and Management Practice Questions & Answers
400 exam-style Market Risk Measurement and Management questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 391
The 'convexity of ES' as a risk measure means that for two portfolios X and Y:
Select an option first.
Correct answer: B — ES(λX + (1-λ)Y) ≤ λES(X) + (1-λ)ES(Y) for λ ∈ [0,1] — the ES of a mixture is at most the weighted average of individual ESs (diversification principle)
Explanation: B is correct: coherent risk measures satisfy subadditivity and positive homogeneity, which together imply convexity. The convexity of ES means diversification between X and Y (taking a weighted combination) reduces ES below the weighted average of individual ESs. This is the mathematical justification for diversification in risk management. A is wrong — that would be concavity (anti-diversification). C is wrong — ES is convex, not linear. D is wrong — convexity holds for all distributions.
Question 392
Under FRTB, the 'credit spread risk' for non-securitisation positions uses prescribed risk weights based on:
Select an option first.
Correct answer: B — Credit quality (investment grade/high yield/not rated) and maturity bucket — with higher risk weights for lower credit quality and longer maturity positions
Explanation: B is correct: FRTB SA credit spread risk uses a matrix of risk weights by: (1) issuer credit quality bucket (investment grade ~0.5-2% for short maturities, high yield ~2-8%); (2) maturity tenor (10+ prescribed buckets). Positions are aggregated within buckets using prescribed correlations. A is wrong — historical CDS vol is used in IMA, not SA. C is wrong — both rating and maturity matter. D is wrong — flat weights don't distinguish credit quality.
Question 393
When a bank executes a 'macro hedge' (e.g. buying S&P 500 puts to hedge equity book losses), the FRTB treatment is:
Select an option first.
Correct answer: B — The macro hedge can only be applied at the aggregate level — it may not be assigned to specific desks, creating possible inefficiency in capital allocation but preventing manipulation of desk-level capital
Explanation: B is correct: FRTB addresses macro hedges by allowing their risk-reduction benefit at the aggregate (firm) level but restricting their allocation to specific desks. This prevents a firm from gaming desk-level capital requirements by attributing the entire benefit of a portfolio hedge to a specific desk. A is wrong — partial allocation restrictions apply. C is wrong — benefits depend on correlation with the portfolio. D is wrong — macro hedges do receive some capital benefit.
Question 394
The 'model risk reserve' in derivatives pricing and risk management is:
Select an option first.
Correct answer: B — A valuation adjustment (reserve) held against model uncertainty — representing the range of plausible values that a more sophisticated model might assign, typically computed as the difference between the base model price and an alternative model price
Explanation: B is correct: model risk reserves (or model uncertainty reserves) are set by pricing models for complex/illiquid instruments where the base model has significant uncertainty. The reserve = |base price − alternative price| or some fraction thereof, held as a P&L deduction. A is wrong — model risk can be partially quantified. C is wrong — no specific Basel mandate for model risk reserves in pricing. D is wrong — model risk includes both pricing and risk measurement uncertainty.
Question 395
The 'Christoffersen and Pelletier' duration-based test for backtesting VaR:
Select an option first.
Correct answer: B — Tests the duration (number of days between exceptions) — under a correctly specified model, durations between exceptions should follow a geometric distribution (memoryless property)
Explanation: B is correct: Christoffersen and Pelletier (2004) test the distribution of durations between VaR exceptions. Under H₀ (correct, independent VaR model), durations should be geometrically distributed (memoryless). Clustered exceptions produce short durations more often than expected. A is wrong — frequency is Kupiec's test. C is wrong — normality is a distributional test. D is wrong — magnitude testing is ES backtesting.
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Question 396
The 'FRTB simplified sensitivity approach' (SSA) is available to:
Select an option first.
Correct answer: B — Smaller, less complex banks with limited trading activities — it is a simplified version of the SA with fewer risk factors and simplified aggregation, reducing compliance burden
Explanation: B is correct: the FRTB SSA provides a simplified SA option for banks that meet specific criteria for small trading book size and limited complexity. It uses a subset of risk factors and simplified bucketing. A is wrong — the SSA is restricted to qualifying banks. C is wrong — G-SIBs use the full SA or IMA. D is wrong — the SSA is an alternative to, not part of, IMA.
Question 397
The 'risk attribution' for a fixed income portfolio decomposes total P&L into:
Select an option first.
Correct answer: B — Carry (coupon accrual), roll-down (yield curve riding), credit spread change, interest rate (duration) effect, and residual — providing a complete picture of return sources
Explanation: B is correct: fixed income P&L attribution: (1) carry = coupon accrual; (2) roll-down = P&L from the bond's yield falling as it 'rolls' to shorter maturity on the curve; (3) rate effect = duration × rate change; (4) spread effect = spread duration × spread change; (5) convexity/residual. A is wrong — carry and price are too coarse. C is wrong — more granular decomposition is needed. D is wrong — coupon is only one component.
Question 398
The 'forward guidance effect' on market risk VaR occurs when:
Select an option first.
Correct answer: B — Central bank forward guidance reduces interest rate volatility by anchoring rate expectations — lower yield volatility directly reduces interest rate VaR for fixed income portfolios
Explanation: B is correct: when a central bank credibly commits to keeping rates low for an extended period ('forward guidance'), market participants' uncertainty about future rates decreases, reducing implied and realised interest rate volatility. Lower volatility directly translates to lower interest rate VaR for portfolios with rate exposure. A is wrong — forward rates in VaR is just a pricing convention. C is wrong — forward contracts are part of the portfolio. D is wrong — forward prices don't define the risk measure.
Question 399
The 'procyclicality' of market risk models refers to:
Select an option first.
Correct answer: B — Risk models generating lower capital requirements during boom times (when volatility is low and correlations appear benign) and higher capital requirements during busts — amplifying economic cycles
Explanation: B is correct: procyclicality is a key regulatory concern: VaR-based capital falls in calm markets (encouraging more risk-taking and lending) and spikes in crises (forcing deleveraging and reducing lending). The countercyclical capital buffer (CCyB), stressed VaR, and ES were all partly designed to reduce this procyclicality. A is wrong — model performance varies by regime. C is wrong — VaR models don't predict economic cycles. D is wrong — procyclicality is about amplification, not data choice.
Question 400
The 'interest rate sensitivity' of a bank's mortgage portfolio differs from a standard bond portfolio because:
Select an option first.
Correct answer: B — Mortgages have embedded prepayment options — when rates fall, homeowners refinance (prepay), shortening the effective duration; when rates rise, prepayment slows (extension risk), lengthening the duration
Explanation: B is correct: residential mortgages contain embedded call options (prepayment options) that create 'negative convexity'. When rates fall: prepayment accelerates → duration shortens → the bank must reinvest at lower rates (prepayment risk). When rates rise: prepayment slows → duration extends → the bank is locked into below-market rates longer (extension risk). This makes mortgage portfolio IRRBB more complex than standard bond IRRBB. A is wrong — mortgages have substantial interest rate risk. C is wrong — effective duration varies with rates. D is wrong — mortgages are a core IRRBB exposure.
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