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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 361
The 'stress test capital requirement' under Basel is designed to ensure that banks hold:
Select an option first.
Correct answer: B — Capital sufficient to survive a severe but plausible stress scenario while maintaining the ability to continue lending — preventing a procyclical reduction in credit supply during stress
Explanation: B is correct: stress test capital buffers (capital conservation buffer, G-SIB surcharge, stress test-driven Pillar 2 additions) ensure banks have enough capital to absorb stress losses and continue operating as a going concern, maintaining credit supply. A is wrong — stress testing adds capital above minimums. C is wrong — maximum capital is inefficient. D is wrong — both Tier 1 and Tier 2 capital count.
Question 362
Under FRTB, a desk that fails the P&L attribution test faces:
Select an option first.
Correct answer: B — Revocation of IMA approval for that desk — its market risk capital must be computed under the standardised approach until the PLA test is passed consistently
Explanation: B is correct: if a desk's RTPL/HPL Spearman correlation falls below 0.70 (or other metrics fail) consistently, the desk loses IMA approval and must use SA capital for its positions. This creates a strong incentive for accurate risk model development. A is wrong — trading isn't stopped. C is wrong — SA (not a multiplier increase) is applied. D is wrong — independent validation is already required.
Question 363
The 'interest rate shock' methodology in IRRBB specifies shocks that are:
Select an option first.
Correct answer: B — Absolute and relative interest rate changes calibrated to severe but plausible levels — using the 99th percentile of historical rate changes observed over the past 16 years, with a floor on absolute moves
Explanation: B is correct: BCBS IRRBB specifies rate shocks calibrated to the 99th percentile of 1-year rate changes across 16 years of historical data, with floors (e.g. minimum 100bps for parallel shocks). Both upward and downward shocks are prescribed. A is wrong — historical rate changes are the calibration source but shocks are prescribed, not last year's changes. C is wrong — 99th percentile over 16 years is more extreme. D is wrong — downward shocks are also prescribed.
Question 364
The 'multiplier' applied to the 60-day average VaR/ES in pre-FRTB capital calculation reflects:
Select an option first.
Correct answer: B — A penalty factor increasing with backtesting exceptions: starts at 3 (green zone) and increases to 4 (red zone) — providing incentives for accurate model development and additional capital buffer
Explanation: B is correct: the multiplier (m_c or m_q) is the incentive mechanism: green zone (0-4 exceptions) m=3; yellow (5-9) m=3.4-3.85; red (10+) m=4. Higher multipliers punish banks with inaccurate models. A is wrong — profitability doesn't affect the multiplier. C is wrong — book ratio is not the basis. D is wrong — leverage ratio is a separate requirement.
Question 365
The 'concentration risk' for interest rate positions exists when:
Select an option first.
Correct answer: B — A large position in a single maturity or single issuer means that a specific rate move or credit event has disproportionate impact on the portfolio — standard VaR may underestimate this
Explanation: B is correct: if a portfolio has heavy concentration in, say, 10-year Treasuries, a large supply of 10-year bonds could cause disproportionate losses. Standard VaR based on historical correlations may not capture issuer-specific or maturity-specific concentration risks. A is wrong — many small positions = diversification. C is wrong — diversification is the opposite. D is wrong — government bonds can still exhibit concentration risk.
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Question 366
The 'third-party assessment' of a bank's VaR model is conducted by:
Select an option first.
Correct answer: B — External auditors, model risk teams, and regulators — providing an independent check on model assumptions, implementation, and performance
Explanation: B is correct: robust model governance requires multiple layers: (1) internal model risk team (MRM) — validation independent of model developers; (2) internal audit; (3) external auditors; (4) regulatory review (on-site inspections for IMA approval). No single party provides sufficient independence alone. A is wrong — internal alone lacks independence. C is wrong — trading desk developed the model. D is wrong — quants build the model.
Question 367
When FRTB was implemented, the 'structural FX risk' arising from banking book FX positions was:
Select an option first.
Correct answer: B — Allowed to be excluded from market risk capital if the bank can demonstrate it is of a structural nature (hedging the CET1 ratio against FX fluctuations), subject to regulatory approval
Explanation: B is correct: FRTB allows a 'structural FX' exclusion for positions that naturally hedge the bank's CET1 ratio against currency movements (e.g. a EUR bank holding USD-denominated assets that create USD exposure equal to their USD RWA). These positions can be excluded from market risk capital with supervisory approval. A is wrong — structural FX can be excluded. C is wrong — the structural exemption reduces the charge. D is wrong — only qualifying structural positions are excluded.
Question 368
Under FRTB, the 'liquidity horizon' for equity of small-cap companies is:
Select an option first.
Correct answer: B — 40 days — reflecting that small-cap equities are less liquid and would take longer to liquidate in stressed market conditions
Explanation: B is correct: FRTB liquidity horizons: LH₁=10 days (large-cap liquid equity, major FX); LH₂=20 days (liquid commodity, investment-grade credit); LH₃=40 days (equity small cap, EM equity); LH₄=60 days (other credit); LH₅=120 days (illiquid credit, leveraged loans). A is wrong — 10 days is large-cap. C is wrong — 120 days is for the most illiquid. D is wrong — 20 days is for investment-grade credit.
Question 369
The 'expected shortfall backtesting' methodology proposed by Acerbi and Szekely (2014) tests:
Select an option first.
Correct answer: B — Whether the magnitude of losses given exceptions is consistent with the model's ES prediction — using a statistic based on the ratio of actual tail losses to predicted ES
Explanation: B is correct: the Acerbi-Szekely test statistic W₁ = (1/(n×ES)) × Σ_{t: exception} L_t − 1. Under H₀ (correct ES), E[W₁] = 0. The test checks whether actual tail losses, when they occur, are on average consistent with the predicted ES. A is wrong — that is the Kupiec POF test. C is wrong — overall return testing is performance evaluation. D is wrong — Basel traffic light is for VaR backtesting.
Question 370
The 'FRTB internal model eligibility criteria' require that a trading desk:
Select an option first.
Correct answer: B — Passes both the P&L attribution test and backtesting test consistently, has appropriate governance (documented trading strategy, risk limits, independent risk oversight), and uses observable market data
Explanation: B is correct: FRTB IMA eligibility requires: (1) desk-level P&L attribution test passage; (2) desk-level backtesting passage; (3) documented trading strategy and limits; (4) independent risk oversight; (5) observable market data for risk factors; (6) appropriate internal and external validation. A is wrong — external audit is one element among many. C is wrong — mere reporting is insufficient. D is wrong — no size threshold applies.
Question 371
The 'sensitivity analysis' for ES as a risk measure examines how ES changes when:
Select an option first.
Correct answer: B — Model parameters, confidence level, historical window, distributional assumptions, and correlation assumptions are varied — quantifying model risk from parameter uncertainty
Explanation: B is correct: sensitivity analysis for ES (or VaR) as a risk model quantifies model risk: how much does ES change if: confidence level is 97.5% vs 99%? Window is 250 vs 500 days? Normal vs t vs empirical distribution? These sensitivities identify which model choices have the largest impact on the risk estimate. A is wrong — confidence level is just one dimension. C is wrong — that is scenario analysis for the portfolio. D is wrong — that is the portfolio's market risk.
Question 372
The 'risk appetite statement' of a financial institution expresses:
Select an option first.
Correct answer: B — The amount and types of risk the institution is willing to accept in pursuit of its objectives — typically including both quantitative (VaR limits, ES thresholds) and qualitative (risk culture) dimensions
Explanation: B is correct: a risk appetite statement (RAS) sets the overall risk framework: (1) quantitative: VaR limits, loss thresholds, concentration limits; (2) qualitative: acceptable risk types (e.g. no reputational risk), risk culture statements; (3) risk capacity: maximum possible risk given capital constraints. A is wrong — RAS is more comprehensive. C is wrong — return requirements are separate. D is wrong — regulatory capital is a constraint, not appetite.
Question 373
The 'systemic risk contribution' of a financial institution, measured by SRISK, equals:
Select an option first.
Correct answer: B — Capital shortfall expected in a market-wide stress event: SRISK = max(0, k × (Debt + Equity) − Equity × (1 − LRMES)) where LRMES is long-run marginal expected shortfall
Explanation: B is correct: SRISK (Brownlees and Engle) measures the expected capital shortfall of a firm conditional on a systemic crisis. It incorporates: the firm's leverage (debt/equity ratio), the target capital ratio k, and LRMES (expected equity loss in a system-wide stress). A is wrong — VaR alone misses systemic dimension. C is wrong — market share is not the same as risk contribution. D is wrong — correlation is an input, not SRISK itself.
Question 374
When implementing stress testing for an equity portfolio, the 'bottom-up' approach:
Select an option first.
Correct answer: B — Applies shocks to individual securities and sectors, then aggregates to portfolio level — capturing security-specific sensitivities and sector correlations
Explanation: B is correct: bottom-up stress testing models the portfolio's response to shocks by starting with individual security sensitivities (beta to market, sector factor loadings, specific risk). This captures how the specific composition of the portfolio responds, unlike top-down which only applies index-level shocks. A is wrong — bottom-up goes deeper than index shocks. C is wrong — macro scenarios are top-down. D is wrong — beta alone captures only systematic risk.
Question 375
The 'risk limit breach' escalation process in a trading firm requires:
Select an option first.
Correct answer: B — Immediate escalation to risk management and senior management, position assessment, remediation plan, and documentation — with severity of response proportional to breach magnitude
Explanation: B is correct: a well-designed limit breach process includes: (1) automatic alert to risk management; (2) communication to management (desk head, CRO depending on severity); (3) assessment of whether breach is within tolerance or requires immediate action; (4) remediation plan; (5) documentation for audit trail. A is wrong — all breaches require response. C is wrong — action is required. D is wrong — automatic halt is just one possible action.
Question 376
The 'stress test horizon' for liquidity stress testing is different from market risk VaR because:
Select an option first.
Correct answer: B — Liquidity stress scenarios often run 30 days, 90 days, or longer — reflecting the time needed to restructure a balance sheet, raise capital, or liquidate positions in a crisis
Explanation: B is correct: LCR uses a 30-day stress horizon (HQLA ≥ net cash outflows over 30 days). NSFR uses a 1-year horizon for structural liquidity. Idiosyncratic liquidity crises may unfold over several months. These longer horizons reflect the realistic time needed for a bank to adjust its liquidity position. A is wrong — they use different horizons. C is wrong — liquidity stress testing is a key regulatory requirement. D is wrong — market risk VaR uses 1-day or 10-day horizons, shorter than many liquidity horizons.
Question 377
The 'BCBS 239' principles for risk data aggregation require that banks:
Select an option first.
Correct answer: B — Have robust risk data aggregation infrastructure — enabling rapid, accurate, and complete aggregation of risk data and risk reporting, especially during stress periods
Explanation: B is correct: BCBS Principles 239 (2013) establish requirements for G-SIBs: strong data governance, data architecture, IT infrastructure, accuracy and integrity of risk data, completeness, timeliness, adaptability of reports, and distribution of reports to senior management and board. A is wrong — robust systems are required. C is wrong — all risk types are covered. D is wrong — daily (or more frequent) reporting is required.
Question 378
The 'scenario generation' process for reverse stress testing involves:
Select an option first.
Correct answer: B — Working backwards from a specified adverse outcome (e.g. 20% capital loss) to identify what combination of risk factor changes would cause that outcome — using optimisation or systematic search
Explanation: B is correct: reverse stress testing uses optimisation: given an outcome constraint (e.g. loss = X), find the minimum probability market move that achieves it. This reveals the portfolio's specific vulnerabilities — scenarios that are less obvious from forward stress testing but more insightful about what could break the firm. A is wrong — random generation is not reverse stress testing. C is wrong — Basel scenarios are forward. D is wrong — historical scenarios work forward.
Question 379
The 'Pillar 2' add-on for market risk capital under Basel is driven by:
Select an option first.
Correct answer: B — Supervisor-identified risks not fully captured by Pillar 1 — including model risk, concentration risk, basis risk, and other market risks specific to the bank's business model
Explanation: B is correct: Pillar 2 (SREP) allows supervisors to impose additional capital requirements where Pillar 1 doesn't capture all material risks. For market risk, Pillar 2 add-ons might address: stress test results exceeding Pillar 1 capital, IRRBB limits breaches, model risk charges, and business-specific risks. A is wrong — model accuracy is one factor. C is wrong — volume doesn't determine Pillar 2. D is wrong — Pillar 2 is judgment-based.
Question 380
The 'commodity price risk' in a manufacturing company's financial statements arises from:
Select an option first.
Correct answer: B — Exposure to input costs (raw materials) and sometimes output prices — changes in commodity prices affect margins and can be hedged using commodity futures, forwards, or options
Explanation: B is correct: non-financial companies with material commodity price exposures (airlines hedging jet fuel, manufacturers hedging copper, food companies hedging wheat) face commodity price risk. Risk management uses commodity derivatives. A is wrong — any company with commodity exposures faces this risk. C is wrong — hedging, not speculation. D is wrong — all commodity types are relevant.
Question 381
The 'CVA (credit valuation adjustment) desk' in a bank manages:
Select an option first.
Correct answer: B — The credit risk embedded in OTC derivatives — computing and hedging the CVA, which represents the expected loss from counterparty default on derivative contracts
Explanation: B is correct: the CVA desk computes CVA = expected loss from counterparty default on derivatives = Σ PD × LGD × EE × DF for each counterparty. The desk uses CDS to hedge the CVA. Changes in counterparty credit quality create CVA P&L. Post-2008, CVA became a regulatory capital requirement (CVA risk charge). A is wrong — credit approvals are in credit risk management. C is wrong — that is consumer credit. D is wrong — that is credit trading.
Question 382
The 'FVA (funding valuation adjustment)' for uncollateralised derivatives:
Select an option first.
Correct answer: B — Reflects the funding cost (or benefit) of maintaining the uncollateralised position — when the bank must fund a positive MtM position, FVA = funding spread × EE × DF summed over time
Explanation: B is correct: FVA accounts for the fact that uncollateralised positive MtM derivatives require the bank to fund the difference between market value and any collateral received, at its own funding rate (above OIS). Negative FVA arises when the bank receives collateral it can invest. A is wrong — CVA is about default probability; FVA is about funding cost. C is wrong — FVA is non-zero for uncollateralised positions. D is wrong — FVA applies to any uncollateralised derivative.
Question 383
The 'market risk' in a pension fund differs from a bank's trading book because:
Select an option first.
Correct answer: B — Pension funds have long-duration liabilities — their risk is primarily measured relative to liabilities (asset-liability mismatch), with the focus on funding ratio risk rather than absolute P&L VaR
Explanation: B is correct: pension funds manage asset-liability risk: the funded ratio = assets/liabilities. If assets fall or liability values rise (falling discount rates), the funding ratio deteriorates. Risk management focuses on duration mismatch (assets shorter than liabilities), equity allocation, and inflation sensitivity. A is wrong — the frameworks differ materially. C is wrong — interest rate risk is typically the largest risk for DB pension funds. D is wrong — multiple asset classes contribute.
Question 384
The 'XVA' umbrella term encompasses:
Select an option first.
Correct answer: B — CVA (counterparty credit risk), DVA (own credit risk), FVA (funding), MVA (margin), KVA (capital) — the collection of valuation adjustments to OTC derivative prices reflecting real-world frictions
Explanation: B is correct: XVA = collective term for all valuation adjustments: CVA + DVA + FVA + ColVA (collateral) + MVA (initial margin) + KVA (regulatory capital cost) + LVA (liquidity). These adjustments bring theoretical derivative prices closer to real-world dealer prices. A is wrong — CVA is just one component. C is wrong — XVA includes credit and funding, not just market risk. D is wrong — DVA and FVA are not all regulatory.
Question 385
The 'wrong-way risk' (WWR) in derivatives refers to:
Select an option first.
Correct answer: B — The adverse correlation between counterparty default probability and derivative exposure — when exposure to a counterparty increases precisely when they are most likely to default
Explanation: B is correct: WWR means that when the underlying moves adversely (increasing the bank's credit exposure on the derivative), the counterparty is also more likely to default. Example: a bank that has a large positive swap exposure to an oil producer when oil prices fall — the producer's credit quality deteriorates as the exposure increases. WWR makes CVA higher than without the adverse correlation. A is wrong — moneyness is separate. C is wrong — model error is different. D is wrong — wrong-way is specifically about the correlation between credit and market risk.
Question 386
Under FRTB, the 'curvature risk' capital for a delta-hedged options position is computed as the:
Select an option first.
Correct answer: B — Difference between the full revaluation P&L under a prescribed up-shock and the delta-approximated P&L — capturing the net gamma exposure after delta hedging
Explanation: B is correct: curvature risk = full revaluation P&L(shock) − delta_k × shock_k. This directly captures the convexity (gamma) that a delta approximation misses. For a short gamma position, this is negative (a loss), giving a positive curvature risk charge. A is wrong — that is delta P&L. C is wrong — that combines different risk types. D is wrong — theta is time decay.
Question 387
The 'one-factor Gaussian copula' used in CDO pricing before 2008 failed because:
Select an option first.
Correct answer: B — It assumed all asset correlations came from a single market factor with constant loading — in a real crash, correlations spike and the single-factor structure dramatically underestimated joint default probabilities
Explanation: B is correct: the Gaussian copula model calibrated to a single market-wide correlation parameter assumed copula correlation ρ was stable. During the 2007-2009 crisis, correlations between mortgage defaults spiked massively (a nationwide housing decline caused simultaneous defaults across geographies). The model's low calibrated correlation dramatically underestimated the probability of mass simultaneous defaults that wiped out senior CDO tranches. A is wrong — it was too simple. C is wrong — it was too simple, not too complex. D is wrong — it modelled continuous default losses.
Question 388
The 'CCAR stress test capital action' allows banks to:
Select an option first.
Correct answer: B — Submit capital plans (dividends, buybacks) that must be approved by the Fed based on stress test projections — banks with insufficient capital under the adverse scenario must reduce capital distributions
Explanation: B is correct: CCAR is both a stress test (quantitative) and a capital plan review (qualitative). Banks submit planned capital actions (dividends, buybacks, issuance). The Fed approves or rejects plans based on whether the bank maintains capital above minimums under the severely adverse scenario. Banks with capital shortfalls must restrict distributions. A is wrong — capital buffers are binding constraints. C is wrong — stress test results directly affect capital actions. D is wrong — capital transfers between legal entities require regulatory approval.
Question 389
The 'internal loss data' requirement for operational risk under the SMA is:
Select an option first.
Correct answer: B — Required for the Internal Loss Multiplier (ILM) calculation — banks with higher historical loss experience relative to their BI pay higher capital through the ILM
Explanation: B is correct: the SMA's ILM = ln(e−1 + (LC/BIC)^0.8) where LC = loss component (sum of losses above €10k and €1m thresholds over 10 years) and BIC = BI coefficient (BI multiplied by marginal coefficient). Banks with higher relative historical losses have higher ILM and higher capital. A is wrong — internal losses are required for ILM. C is wrong — internal loss data feeds directly into capital. D is wrong — the BI is the primary scaling factor.
Question 390
The 'market manipulation risk' (a form of operational risk) in trading is addressed by:
Select an option first.
Correct answer: B — Surveillance systems, conduct risk controls, and separation of duties — risk management systems that detect unusual trading patterns and prevent insider trading or market manipulation
Explanation: B is correct: market manipulation (e.g. spoofing, front-running, benchmark manipulation) is an operational/conduct risk addressed by: automated trade surveillance systems, pre-trade controls, separation of duties, compliance monitoring, and regulatory reporting. A is wrong — VaR measures price movement risk, not conduct risk. C is wrong — credit risk models don't address market manipulation. D is wrong — liquidity limits don't address manipulation.
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