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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 331
The 'standardised duration-based' approach (pre-FRTB) for interest rate risk capital used:
Select an option first.
Correct answer: A — A bucket approach with prescribed risk weights for each maturity bucket and specified correlations between buckets
Explanation: A is correct: the pre-FRTB standardised duration-based approach (Basel II) divided the yield curve into 13-15 maturity buckets, each with a prescribed RW and assumed correlation between adjacent and non-adjacent buckets. The FRTB SA replaced this with the more sophisticated SBM using actual sensitivities. B is wrong — the standardised approach doesn't use internal models. C is wrong — only parallel shifts misses curve risk. D is wrong — market value alone doesn't measure rate risk.
Question 332
The 'FX risk' component of VaR for a bank with foreign assets requires:
Select an option first.
Correct answer: B — The joint distribution of foreign asset returns in local currency AND the exchange rate — since both affect the domestic-currency value of the position
Explanation: B is correct: the domestic-currency P&L from a foreign asset position = r_FX + r_asset_local + r_FX × r_asset_local (approximately r_FX + r_asset_local for small returns). The VaR must account for both the exchange rate movement and the local-currency asset return, plus their correlation. A is wrong — FX volatility is also critical. C is wrong — multiple exchange rates affect different foreign assets. D is wrong — the interest rate differential gives the forward rate, not the VaR of FX exposure.
Question 333
The 'vega risk' in FRTB SA applies to:
Select an option first.
Correct answer: B — Instruments containing optionality — the vega sensitivity measures the change in value for a 1% change in implied volatility of the relevant underlying
Explanation: B is correct: FRTB SA vega risk applies to all instruments with optionality: equity options, FX options, rate caps/floors/swaptions, commodity options, credit derivatives with optionality. Vega sensitivities are computed with respect to prescribed volatility risk factors. A is wrong — instruments without optionality have zero vega. C is wrong — vega applies across all option types. D is wrong — FX options are just one category.
Question 334
The 'curvature risk charge' in FRTB SA is designed to capture:
Select an option first.
Correct answer: B — The difference between the actual non-linear P&L and the linear P&L for large prescribed risk factor moves — essentially capturing the gamma of the position
Explanation: B is correct: FRTB SA curvature risk: CVR_k = −min(up scenario, down scenario) where each scenario applies a large prescribed shock to risk factor k and computes the P&L residual after removing the delta contribution. This captures convexity/non-linearity for positions with embedded optionality. A is wrong — linear risk is in delta. C is wrong — correlation risk has its own treatment. D is wrong — jump risk is in JtD.
Question 335
Under FRTB, the 'sensitivities-based method' aggregation within a risk class uses three correlation parameters (ρᵣₛ, ρₖₗ, γₒₑ) for:
Select an option first.
Correct answer: A — Intra-bucket, inter-bucket, and cross-class aggregation — combining sensitivities within a bucket, between buckets, and across risk classes using prescribed values
Explanation: A is correct: FRTB SA SBM uses: ρᵣₛ (correlation between risk factors r and s within a bucket), ρₖₗ (correlation between buckets k and l within a risk class), γₒₑ (correlation between risk classes o and e for cross-class aggregation). B is wrong — time scales are for liquidity horizons. C is wrong — confidence levels are for VaR/ES levels. D is wrong — asset types use bucket assignments.
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Question 336
The 'desk classification' in FRTB determines which desks:
Select an option first.
Correct answer: B — May apply for IMA approval — only desks meeting eligibility criteria can use internal models; others must use SA
Explanation: B is correct: FRTB requires desk-level IMA approval. Desks must pass both: (1) initial requirements (qualitative and quantitative); (2) ongoing requirements (backtesting, PLA tests). Desks failing these tests revert to SA capital calculation. A is wrong — reporting is a governance requirement. C is wrong — salaries are unrelated. D is wrong — derivative trading is a business decision.
Question 337
The 'economic scenarios' for insurance company stress testing differ from bank stress tests primarily in:
Select an option first.
Correct answer: B — Including longer-horizon scenarios (decades) and risks like longevity risk, pandemic risk, and catastrophe risk — reflecting insurance companies' much longer liability durations
Explanation: B is correct: insurance companies have long-dated liabilities (life policies, pension obligations) requiring stress scenarios over decades. They also face specific risks like longevity (people living longer than expected), catastrophe (mass casualty events), and pandemic risk that are not primary concerns for bank stress testing. A is wrong — scenarios differ. C is wrong — market risk is included in insurance stress tests. D is wrong — scenarios can be equally or more severe.
Question 338
When mapping an FX forward position for VaR, the forward creates sensitivity to:
Select an option first.
Correct answer: B — The spot exchange rate and domestic and foreign interest rates — via covered interest parity, the forward price depends on spot × interest rate differential
Explanation: B is correct: FX forward = S × (1+r_d)/(1+r_f). Changes in S, r_d, and r_f all affect the forward value. VaR mapping of an FX forward involves sensitivity to all three underlying risk factors. A is wrong — rate risk is also significant. C is wrong — domestic rates matter too. D is wrong — maturity affects the sensitivity but not a separate risk factor.
Question 339
The 'key rate duration' (KRD) for a bond with respect to the 5-year node:
Select an option first.
Correct answer: B — Measures the bond's price sensitivity to a 1 basis point change in the 5-year yield while holding all other maturity yields constant — the partial duration at the 5-year point
Explanation: B is correct: KRD(5y) = −(1/P) × dP/dr(5y), where r(5y) is the 5-year yield holding all others fixed. The sum of all KRDs equals the modified duration. KRDs decompose total interest rate risk into contributions from each curve point. A is wrong — that is the standard modified duration. C is wrong — full duration is the sum of all KRDs. D is wrong — all bonds have 5y KRD if cash flows overlap with the 5y maturity.
Question 340
A bank conducts a 'fire sale' stress scenario where it must liquidate a large bond portfolio. The stress P&L impact compared to normal conditions would include:
Select an option first.
Correct answer: B — The standard market VaR loss plus the additional bid-ask spread widening and market impact cost from selling a large portfolio into a stressed, illiquid market
Explanation: B is correct: fire sale scenarios combine: (1) market risk loss (prices fall in the stress scenario); (2) liquidity adjustment (bid-ask spreads widen dramatically in stressed markets, and selling large positions moves prices adversely). The combined effect is much larger than VaR alone. A is wrong — fire sale adds liquidity costs. C is wrong — market risk is also included. D is wrong — credit and other risks are also relevant.
Question 341
Under IRRBB, the 'non-maturity deposits' (e.g. current accounts, savings accounts) present a modelling challenge because:
Select an option first.
Correct answer: B — They have no contractual maturity but exhibit behavioral stability — depositors don't withdraw immediately when rates change, requiring behavioral assumptions about effective maturity
Explanation: B is correct: non-maturity deposits (NMDs) like current accounts technically have zero notice but historically show stable balances. Banks model their effective maturity (e.g. 3-5 years) based on behavioral assumptions about how long deposits stay. This modeling choice significantly affects measured EVE and NII sensitivity. A is wrong — NMDs have no fixed maturity. C is wrong — NMDs are a major source of IRRBB. D is wrong — NMDs are often repriced slowly relative to market rates.
Question 342
The 'global systemically important bank' (G-SIB) surcharge for market risk capital is based on:
Select an option first.
Correct answer: B — The G-SIB's systemic importance score, which includes size, interconnectedness, cross-jurisdictional activity, complexity (including trading book size), and substitutability
Explanation: B is correct: the G-SIB surcharge (0.25% to 3.5% CET1 of RWA) is determined by an assessment methodology using five equal-weighted categories, with complexity (including trading and OTC derivatives volume) as one component. The surcharge is applied on top of all other capital requirements. A is wrong — complexity is just one of five factors. C is wrong — VaR alone is not the determining factor. D is wrong — the surcharge varies by bucket (0.25% to 3.5%).
Question 343
The 'sensitivity-based stress test' methodology used by the EBA for EU bank stress tests:
Select an option first.
Correct answer: B — Applies common macroeconomic scenarios (adverse and baseline) to banks' balance sheets, using prescribed sensitivities or banks' own approved models, to project capital ratios
Explanation: B is correct: EBA stress tests: (1) start with supervisory baseline and adverse macro scenarios; (2) apply these to each bank using the bank's own (approved) projection methodology under EBA guidelines; (3) project capital ratios over 3 years; (4) publish results to promote market discipline. A is wrong — scenarios are provided by EBA/ECB. C is wrong — credit risk (loan losses) is the largest component. D is wrong — results are publicly disclosed.
Question 344
The 'credit equivalent amount' for OTC derivatives in Basel capital frameworks is computed as:
Select an option first.
Correct answer: B — Current replacement cost + potential future exposure (PFE) — reflecting the current value and the potential change in value over the remaining life
Explanation: B is correct: credit equivalent = max(MtM, 0) + add-on, where the add-on (PFE) is a regulatory percentage of the notional based on asset class and residual maturity. This credit equivalent then receives a risk weight (based on counterparty quality) to give the RWA contribution. A is wrong — notional alone overstates exposure. C is wrong — current MtM misses potential future exposure. D is wrong — delta is a sensitivity measure.
Question 345
The 'standardised approach for measuring counterparty credit risk exposures' (SA-CCR) under Basel III calculates EAD as:
Select an option first.
Correct answer: B — Replacement cost (RC) + potential future exposure (PFE), where PFE = aggregated add-on × multiplier — using prescribed add-ons by asset class and maturity, allowing netting
Explanation: B is correct: SA-CCR (replacing CEM from 2017): EAD = 1.4 × (RC + PFE_aggregate), where RC = max(V − C, 0) (V = portfolio value, C = collateral), and PFE_aggregate = multiplier × sum of add-ons. SA-CCR allows netting within asset classes and reflects hedging and diversification. A is wrong — full notional ignores netting and collateral. C is wrong — positive MtM is RC but misses PFE. D is wrong — that describes delta contribution.
Question 346
The 'Basel standardised approach for credit risk' (SA-CR) under the revised framework assigns risk weights based on:
Select an option first.
Correct answer: B — External credit ratings (where available and permitted) or prescribed risk weights by exposure class and creditworthiness indicators — higher quality exposures receive lower risk weights
Explanation: B is correct: Revised SA-CR (Basel IV): risk weights depend on exposure class (sovereign, bank, corporate, retail) and credit quality. For corporates: rated exposures use external ratings (20-150%); unrated use a due diligence-based alternative approach. Collateral reduces effective exposure through credit risk mitigation. A is wrong — counterparty type and quality both matter. C is wrong — collateral adjusts the EAD but doesn't determine the primary RW. D is wrong — maturity is relevant for some exposures.
Question 347
The 'model validation' process for FRTB IMA models involves:
Select an option first.
Correct answer: B — Independent review of model appropriateness: backtesting at firm and desk level, PLA testing, stress testing, sensitivity analysis, and documentation review — ensuring the model accurately represents the risks
Explanation: B is correct: comprehensive FRTB IMA validation includes: (1) backtesting (exception tests); (2) PLA tests (HPL vs RTPL); (3) stress testing of model assumptions; (4) sensitivity to model parameters; (5) documentation of model design; (6) regular internal and external model review. A is wrong — positive VaR is a trivial requirement. C is wrong — model validation is about accuracy, not minimum compliance. D is wrong — internal validation is required before regulatory review.
Question 348
The 'joint VaR' of two portfolios (as reported to senior management) compared to the sum of individual VaRs:
Select an option first.
Correct answer: B — Is typically less than the sum due to imperfect correlations between the two books' risk factors — the diversification benefit equals sum(VaR_i) − portfolio VaR
Explanation: B is correct: for two portfolios with correlation ρ < 1, the joint VaR = √(VaR₁² + VaR₂² + 2ρVaR₁VaR₂) < VaR₁ + VaR₂. The difference is the diversification benefit. Risk managers report this decomposition to justify why the total is less than the sum. A is wrong — equality only holds at ρ = 1. C is wrong — joint VaR ≤ sum (not greater). D is wrong — parametric approach doesn't need Monte Carlo.
Question 349
The 'look-through' approach for collective investment schemes (CIS) in market risk capital requires:
Select an option first.
Correct answer: B — Looking through the CIS to its underlying positions and including each constituent's risk in the bank's market risk calculation — if the bank cannot look through, a conservative default approach applies
Explanation: B is correct: FRTB requires the look-through approach for CIS where possible — treating each underlying position as a direct holding. If look-through is not possible, the mandate-based approach uses the maximum allowed portfolio composition. If neither is possible, a 1,250% RW (effectively fully charged in capital) applies. A is wrong — NAV alone ignores the risk composition. C is wrong — CIS exposures create market risk. D is wrong — market risk treatment is required.
Question 350
When stress testing a derivatives portfolio for credit spread risk, the risk manager should consider:
Select an option first.
Correct answer: B — Both spread widening (credit deterioration scenario) and spread tightening (credit recovery) for different portfolio segments — a long credit position suffers from spread widening; a short credit position from tightening
Explanation: B is correct: a credit portfolio's stress test must cover both directions: long credit (CDS sold, bonds long) loses from spread widening; short credit (CDS bought, bonds short) loses from spread tightening. A comprehensive credit stress test covers both scenarios for all material positions. A is wrong — tightening also creates losses for short positions. C is wrong — all material counterparties should be stressed. D is wrong — corporate and bank spreads are also important.
Question 351
The 'risk contribution' report for a trading book desk shows:
Select an option first.
Correct answer: B — The desk's component VaR contribution to firm-wide VaR, its standalone VaR, and the diversification benefit it provides — allowing management to understand each desk's risk-adjusted profitability
Explanation: B is correct: a comprehensive risk contribution report for a desk includes: (1) standalone VaR (desk in isolation); (2) incremental VaR (desk's marginal contribution to firm VaR); (3) component VaR (risk allocation to the desk); (4) diversification benefit (standalone minus component). This supports RAROC calculations. A is wrong — P&L is a separate report. C is wrong — regulatory capital is more limited. D is wrong — transaction counts are operational data.
Question 352
The 'stressed expected shortfall' (SES) under FRTB is computed using data from the identified stress period. If the stress period is 2007-2009, the SES reflects:
Select an option first.
Correct answer: B — The portfolio's P&L distribution if the extreme market movements of 2007-2009 occurred with current positions — capturing the capital needed to survive a similar crisis
Explanation: B is correct: SES = ES computed using the 2007-2009 (or other identified stress period) risk factor changes applied to the current portfolio composition. This captures 'what would happen to our current book if the GFC occurred today?' A is wrong — it uses historical stress, not current. C is wrong — SES is historical scenario-based. D is wrong — SES uses a specific stress period, not an average.
Question 353
The 'net interest income (NII) sensitivity' under IRRBB measures:
Select an option first.
Correct answer: B — The change in expected NII over the next 12 months for a given interest rate shock — complementing EVE with a short-term earnings perspective
Explanation: B is correct: NII sensitivity = change in projected 12-month NII under a rate shock scenario. This short-term measure complements EVE (long-term balance sheet). A bank may have low EVE sensitivity but high NII sensitivity if its assets and liabilities reprice at different speeds. A is wrong — total NII is before the shock. C is wrong — trading book P&L is market risk. D is wrong — MtM changes describe EVE.
Question 354
Under the FRTB, the 'curvature risk charge' for a non-linear instrument is computed as:
Select an option first.
Correct answer: B — The difference between the full revaluation P&L for a large prescribed shock and the linear delta approximation — isolating the convexity component
Explanation: B is correct: curvature risk captures the residual second-order risk after the linear delta approximation. For option k: CVR_k = −[V(RW_k shock up) − V(no shock) + s_k × RW_k] under up shock, and similarly for down shock. The charge is the worse of the two. A is wrong — sum of delta risks is the delta charge. C is wrong — vega × vol is vega risk. D is wrong — JtD is the default risk charge.
Question 355
The 'aggregation of capital across business lines' in operational risk capital under the SMA:
Select an option first.
Correct answer: B — Is computed at the firm level — the BI and ILM are determined for the total firm, not separately per business line, unlike the old TSA which used business line allocation
Explanation: B is correct: unlike the old TSA which computed capital separately per business line (e.g. commercial banking, trading, asset management), the SMA aggregates the BI and ILM at the firm level, simplifying computation and avoiding gaming of business line allocation. A is wrong — the SMA uses a formula, not simple summation. C is wrong — the SMA is an analytic formula. D is wrong — the ILM incorporates historical losses.
Question 356
The FRTB 'equity risk' for large/liquid equities (Bucket 1) uses a risk weight of:
Select an option first.
Correct answer: B — 55% for small cap; 15% for large cap — FRTB prescribes different risk weights by bucket based on market liquidity and size
Explanation: B is correct: FRTB SA equity risk weights vary by bucket: Bucket 1 (large-cap, liquid equities in developed markets) receives 15% RW; Bucket 2 (small-cap, EM equities) receives 55%; Bucket 8 (other sectors) receives higher weights. B approximates the correct structure. A is wrong — 15% applies to large-cap only. C is wrong — 100% is not an equity FRTB risk weight. D is wrong — different buckets use different weights.
Question 357
When performing a 'scenario plausibility check' in stress testing, risk managers verify that:
Select an option first.
Correct answer: B — The assumed risk factor moves are internally consistent and physically possible — for example, credit spreads cannot be negative, and movements across correlated assets should be directionally consistent
Explanation: B is correct: plausibility checking ensures that stress scenarios are: (1) internally consistent (correlated factors move in consistent directions); (2) bounded by physical/economic constraints (e.g. non-negative interest rates in some cases, non-negative credit spreads); (3) plausibly linked to real-world events. A is wrong — maximum loss is not the goal. C is wrong — hypothetical scenarios need not match historical events exactly. D is wrong — exceeding VaR is expected for severe scenarios but not the plausibility check.
Question 358
The 'mapping' of a structured credit product (e.g. ABS) to risk factors for VaR requires:
Select an option first.
Correct answer: B — Identification of the underlying pool's risk drivers (credit spreads by sector, prepayment speeds, correlation assumptions) and the tranche's position in the capital structure — a complex multi-factor decomposition
Explanation: B is correct: ABS VaR mapping is complex: (1) the underlying pool has exposures to multiple credit segments; (2) the tranche's position determines loss exposure profile; (3) correlation between defaults is critical; (4) prepayment risk adds interest rate sensitivity. A simple mapping to a single factor misrepresents the risk. A is wrong — credit rating alone is insufficient. C is wrong — ABS has complex underlying risk. D is wrong — credit risk is the primary factor for ABS.
Question 359
The 'goodness-of-fit' for a stress testing model is assessed by checking whether:
Select an option first.
Correct answer: B — Historical stress events are well-replicated — the model should produce losses consistent with what actually occurred during observed crises like 2008 or 2020 COVID
Explanation: B is correct: stress model validation includes checking whether the model correctly replicated observed historical stress periods. If the model would have predicted smaller losses than actually occurred in 2008, it is underestimating stress severity. A is wrong — always exceeding VaR would be overly conservative. C is wrong — no exceptions would indicate an overly conservative model. D is wrong — option market fitting is for volatility model validation.
Question 360
The 'sensitivity of NII to interest rate changes' under IRRBB depends on:
Select an option first.
Correct answer: B — The repricing gap between rate-sensitive assets and liabilities at different maturity buckets — a bank with more rate-sensitive assets than liabilities benefits from rate increases
Explanation: B is correct: NII sensitivity = Σ(RSA_bucket − RSL_bucket) × Δr for each maturity bucket. RSA = rate-sensitive assets; RSL = rate-sensitive liabilities. A positive repricing gap in a bucket means rising rates increase NII from that bucket. A is wrong — equity level doesn't determine NII sensitivity. C is wrong — size is one factor among many. D is wrong — credit ratings affect funding costs but are not the primary NII sensitivity driver.
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