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Free FRM Valuation and Risk Models Practice Questions & Answers
400 exam-style Valuation and Risk Models questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 361
Bank's 99.9% operational VaR = $150m, expected annual operational loss = $15m. Operational risk capital (unexpected loss):
Select an option first.
Correct answer: C — $135m
Explanation: Capital = Unexpected Loss = Total VaR − Expected Loss = $150m − $15m = $135m. Expected losses are priced into fees/margins and covered by provisions; capital covers adverse deviations from expected. A is total VaR; B adds EL to VaR (incorrect double-counting); D is just EL.
Question 362
Applying stress default correlations (replacing normal-period correlations) in a credit portfolio model most likely:
Select an option first.
Correct answer: B — Increases credit VaR significantly — higher correlations eliminate diversification benefits and concentrate tail losses.
Explanation: Stress correlations: in recessions, default correlations rise sharply. Replacing normal-period (low) correlations with crisis-period (high) correlations in the credit portfolio model removes the assumed diversification benefit, concentrating tail losses and increasing credit VaR. This is a standard credit stress testing exercise.
Question 363
EAD for a revolving credit facility includes:
Select an option first.
Correct answer: B — Drawn balance plus CCF × undrawn commitment — reflecting additional drawdowns before default.
Explanation: EAD = Drawn + CCF × Undrawn. Borrowers under stress draw more before defaulting. The CCF (credit conversion factor) ranges from 20-100% depending on facility type and regulatory approach. Under A-IRB, banks estimate their own CCFs. A understates; C overstates; D applies to bond portfolios, not revolving credit.
Question 364
Advanced IRB additionally uses which supervisory input alongside bank-estimated PD, LGD, EAD, M?
Select an option first.
Correct answer: B — A supervisory asset correlation parameter ρ in the capital formula, which depends on borrower PD.
Explanation: IRB capital formula: K = LGD × N[...PD, ρ...] − PD × LGD. The asset correlation ρ is prescribed by supervisors (not bank-estimated) and captures the systematic risk component. Lower-PD borrowers have higher ρ (more correlated with systemic conditions); higher-PD borrowers have more idiosyncratic risk (lower ρ). A is Foundation IRB; C and D are incorrect inputs.
Question 365
Model risk in IRB credit capital arises primarily from:
Select an option first.
Correct answer: B — PD, LGD, EAD estimates relying on historical data that may not predict future losses accurately, particularly across economic cycles.
Explanation: IRB model risk: (1) PD estimated on benign periods understates downturn PDs; (2) LGD on upcycle understates recession recovery rates; (3) TTC calibration may understate downturn severity; (4) prescribed asset correlations may not match actual portfolio. Basel output floors (72.5%) partially limit model-driven capital reduction.
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Question 366
Scorecard capital reduction requires what critical validation step?
Select an option first.
Correct answer: B — Backtest whether higher scorecard scores historically correspond to lower subsequent operational losses.
Explanation: Scorecard validation: demonstrate empirically that improving control scores predict lower future loss frequencies and severities. Without this demonstrated link, the scorecard reflects management self-assessment rather than a risk-predictive tool. Regulators require evidence of this relationship before accepting scorecard-based capital adjustments.
Question 367
'Double default' framework reduces IRB capital for guaranteed exposures because:
Select an option first.
Correct answer: B — Both the primary borrower AND the guarantor must default for a loss to occur — joint probability is much lower than either individual PD.
Explanation: Double default: P(Loss) = P(borrower defaults) × P(guarantor defaults | borrower defaults). For uncorrelated defaults: joint PD ≈ PD_borrower × PD_guarantor. If PD_borrower = 5% and PD_guarantor = 2%, joint PD ≈ 0.1% — dramatically lower. Basel A-IRB provides capital relief for eligible guarantees using this double-default framework.
Question 368
Scenario analysis in operational risk capital modelling primarily estimates:
Select an option first.
Correct answer: A — Frequency and severity for rare high-impact events absent from internal loss history.
Explanation: Scenario analysis bridges the data gap for high-severity/low-frequency events: major cyberattack, catastrophic fraud, pandemic, fire or flood. Expert panels estimate plausible frequency (e.g., once per 50 years) and severity (e.g., $500m). These inputs supplement internal data in LDA tail estimation to ensure adequate capital for black swan operational risks.
Question 369
Tier 1 capital under Basel III consists of:
Select an option first.
Correct answer: B — Common Equity Tier 1 (CET1) plus Additional Tier 1 — highest quality, going-concern loss-absorbing capital.
Explanation: Tier 1 = CET1 (common equity, retained earnings, OCI) + AT1 (perpetual non-cumulative instruments like CoCos that convert or write down at pre-specified triggers). Tier 1 absorbs losses while the bank operates as a going concern. Tier 2 (subordinated debt, general provisions) is gone-concern capital. A includes Tier 2; C is Tier 2 characteristic; D is reserve requirements.
Question 370
Basel IV output floor requires internal model capital to be at least:
Select an option first.
Correct answer: B — 72.5% of the capital calculated under standardised approaches.
Explanation: Output floor (Basel IV): RWA from internal models ≥ 72.5% × RWA from standardised approaches. Prevents excessive model-driven capital reduction. Phased in from 2025 to 2030. This limits the benefit banks can derive from sophisticated internal models relative to simpler standardised rules, ensuring a floor on minimum capital.
Question 371
High default correlation is a systemic risk amplifier because:
Select an option first.
Correct answer: B — When correlations are high, many firms default simultaneously — hitting multiple lenders together, creating potential systemic contagion.
Explanation: High default correlation = simultaneous credit losses across many banks. If several major institutions face large losses together, the financial system faces a systemic credit crunch — exactly the 2008 dynamic. This is why macroprudential policy focuses on system-wide stress rather than individual institution risk, and why stress tests use severe correlated default scenarios.
Question 372
Procyclical LGD occurs because:
Select an option first.
Correct answer: B — Collateral values (real estate, assets) decline in recessions, reducing recovery amounts precisely when defaults are highest.
Explanation: Double recession effect: (1) PD rises as borrowers are stressed; (2) LGD rises simultaneously as collateral values fall (property, equipment, receivables are all worth less in a recession). Actual credit losses = PD × LGD × EAD — both PD and LGD are elevated simultaneously, making recession losses far exceed the product of baseline parameters.
Question 373
The Vasicek single-factor model assumes all borrower defaults are driven by:
Select an option first.
Correct answer: B — A systematic risk factor (state of the economy) plus idiosyncratic firm-specific factors.
Explanation: Vasicek: asset return = √ρ × Z + √(1−ρ) × ε. Z = systematic factor (economy); ε = idiosyncratic. Default when asset return < threshold (implied by PD). Conditional on Z, all defaults are independent. The distribution of Z determines how many firms default simultaneously. The IRB capital formula is derived from this model assuming an infinitely granular portfolio.
Question 374
External operational loss databases (e.g., ORX) supplement internal data primarily because:
Select an option first.
Correct answer: B — Rare, catastrophic operational events (rogue trading, major cyberattack) may not appear in a single firm's 5-year internal history — external data provides tail severity estimates.
Explanation: External loss databases: industry-wide anonymised loss events provide information on rare, high-severity occurrences that any single firm is unlikely to have experienced in its recent history. Incorporating external data into LDA severity distributions ensures the modelled tail captures catastrophic but plausible scenarios. A, C, D are incorrect.
Question 375
Bank with Tier 1 = $8bn considering a $500m single-borrower loan. The large exposure regulatory limit concern:
Select an option first.
Correct answer: B — The loan ($500m) is well within the large exposure limit (25% × $8bn = $2bn) — but concentration risk should still be monitored.
Explanation: Basel III large exposure limit: single-counterparty exposure ≤ 25% × Tier 1 capital. 25% × $8bn = $2bn. $500m
Question 376
CDO correlation trading: equity tranches are 'long correlation' meaning they benefit when:
Select an option first.
Correct answer: B — Default correlation is high — in high-correlation worlds, either all survive (equity gets residual) or all default (equity is wiped out but was cheap to buy), making equity a bet on extreme outcomes.
Explanation: Correlation sensitivity: equity tranche = long correlation. High correlation creates binary outcomes — either most survive (equity collects residual cash flows) or most default simultaneously (equity is wiped, but that was priced in). Senior tranche = short correlation (prefers low correlation where losses spread out among junior tranches). Mezzanine is most sensitive to the correlation level at which it starts being hit.
Question 377
Pro-cyclicality in credit risk capital models means:
Select an option first.
Correct answer: B — Measured credit risk falls in booms (low PDs → low capital → more lending) and spikes in recessions (high PDs → high capital → forced deleveraging), amplifying the credit cycle.
Explanation: Pro-cyclicality is a fundamental flaw of PIT-calibrated IRB models. Low capital in booms incentivises excess lending; high capital in recessions forces deleveraging exactly when credit is most needed. Countercyclical capital buffers and TTC calibration partially address this — building buffers in booms and releasing them in busts to smooth the credit cycle.
Question 378
Sensitivity analysis showing PD stressed up 50% across all borrowers: base ECL=$100m, capital=$400m. Stressed ECL:
Select an option first.
Correct answer: B — $150m
Explanation: Stressed ECL = 1.5 × $100m = $150m. Capital ($400m) is held for unexpected losses and is not directly reduced by the $50m increase in expected loss — that increase affects provisions/pricing. The $50m additional ECL is a provisioning concern. B reflects the simple 50% PD stress applied to base ECL.
Question 379
Rating drift (systematic downward trend in portfolio credit quality) is concerning because:
Select an option first.
Correct answer: B — Downgrades reduce bond prices (spread widening), trigger forced selling by index-constrained investors, and increase regulatory capital requirements.
Explanation: Rating drift channels: (1) MTM loss from spread widening on downgrade; (2) forced selling by mandate-constrained investors (fallen angels below BBB−); (3) higher risk weights under Basel standardised approach (or higher PDs under IRB). A, C, D understate the consequences of systematic credit quality deterioration.
Question 380
IFRS 9 ECL three-stage model provisions based on:
Select an option first.
Correct answer: B — Stage 1 (no significant deterioration) uses 12-month ECL; Stage 2 (significant credit risk increase) uses lifetime ECL; Stage 3 (credit-impaired) uses lifetime ECL.
Explanation: IFRS 9 (2018): (1) Stage 1 — performing loans → 12-month ECL (expected loss from defaults within 12 months); (2) Stage 2 — significant credit risk increase → lifetime ECL; (3) Stage 3 — credit-impaired → lifetime ECL + interest on net carrying amount. Forward-looking macro scenarios are incorporated. Replaces IAS 39 incurred loss model, requiring earlier provisioning.
Question 381
Gaussian copula underestimated CDO senior tranche risk because:
Select an option first.
Correct answer: B — It has zero tail dependence — assets are asymptotically independent in the extreme tail, underestimating simultaneous large-scale defaults.
Explanation: Gaussian copula tail dependence = 0. In the extreme tail, assets become asymptotically independent. In 2008, subprime mortgages defaulted together massively — the Gaussian copula assigned near-zero probability to this level of co-default. Copulas with positive tail dependence (Student-t, Clayton, Gumbel) would have been more appropriate for modelling correlated credit crises.
Question 382
Credit portfolio model risk is particularly high relative to market risk models because:
Select an option first.
Correct answer: B — Defaults are rare, correlation estimation requires many joint default observations, and LGD/EAD estimates involve significant expert judgment — creating large parameter uncertainty.
Explanation: Credit model risk drivers: (1) defaults are rare — decades of data may contain only 1-2 economic cycles; (2) joint defaults needed to estimate correlation require even more data; (3) LGD varies dramatically by economic cycle and collateral type; (4) copula choice drives results significantly. Market risk has daily price data — richer than annual default observations.
Question 383
A stress test shows capital ratio falls from 13% to 8%, breaching the 10.5% conservation buffer. Most likely regulatory response:
Select an option first.
Correct answer: B — Automatic restrictions on distributions (dividends, buybacks, AT1 coupons) until capital is rebuilt.
Explanation: Capital conservation buffer mechanism: when CET1 falls into the buffer zone (4.5%–7%), automatic distribution restrictions activate. The restriction becomes more severe as CET1 falls deeper into the buffer. This is not immediate revocation (A) — that only occurs if minimum requirements are breached. D may eventually be required but is not automatic.
Question 384
Moving from Standardised Approach to Foundation IRB for corporate exposures: the key benefit is:
Select an option first.
Correct answer: B — Foundation IRB allows bank-estimated PDs (more risk-sensitive) while supervisors set LGD and EAD — better aligning capital with actual portfolio risk.
Explanation: Foundation IRB: bank estimates PD from internal rating models; supervisors set LGD (45% unsecured, lower for secured) and CCF. Bank-estimated PDs are more granular and risk-sensitive than standardised rating buckets. A is not guaranteed; C undermines the purpose of IRB; D is wrong — output floors apply to all IMA approaches.
Question 385
Credit cycle timing risk refers to:
Select an option first.
Correct answer: B — Loans originated at credit cycle peaks (lax underwriting, optimistic PDs) defaulting disproportionately in subsequent downturns.
Explanation: Vintage risk: loans originated at peak credit conditions have the most optimistic underwriting assumptions, loosest covenants, and highest origination volumes. When the cycle turns, these vintages experience elevated default rates and LGDs. The 2006-07 US mortgage vintages exemplified this — originated at peak prices with lax standards, defaulted massively in 2008-09.
Question 386
Dynamic provisioning builds excess provisions in booms and releases them in busts because:
Select an option first.
Correct answer: B — Pre-built buffers allow banks to absorb recessionary losses without simultaneously recognising all provision expenses, preventing pro-cyclical credit crunches.
Explanation: Countercyclical provisioning: building provisions during benign credit conditions creates a buffer that can absorb downturn losses without the cliff-effect of sudden massive provisions all at once. Spain's dynamic provisioning (pre-2008) partially buffered its banking system. IFRS 9 (C) is forward-looking but not explicitly countercyclical — it provisions based on estimated conditions without a smoothing mandate.
Question 387
GDP falls 5%, unemployment rises 5pp: PD increases 2%→6%, LGD rises 40%→60%. Stressed ECL / base ECL ratio:
Select an option first.
Correct answer: B — 4.5×
Explanation: Base ECL ∝ PD×LGD = 2%×40% = 0.8%. Stressed ECL ∝ 6%×60% = 3.6%. Ratio = 3.6/0.8 = 4.5×. A uses only PD ratio (3×); C uses only LGD ratio (1.5×); D multiplies 3×2=6× (wrong — both PD and LGD change, but ratio is their product not sum).
Question 388
Climate transition risk vs physical risk:
Select an option first.
Correct answer: B — Physical risk = damage from climate events (floods, wildfires, droughts); transition risk = financial impairment from policy, technology, and market shifts toward a low-carbon economy.
Explanation: Climate risk channels: (1) physical — acute events (hurricanes, wildfires) and chronic changes (sea level rise, temperature increases) damaging assets and disrupting supply chains; (2) transition — carbon taxes, emission regulations, technology disruption (EV), market repricing of carbon-intensive assets (stranded assets). Both channels affect borrower PD and LGD and asset values. A, C, D are wrong.
Question 389
Credit concentration risk is more dangerous than diversified exposure because:
Select an option first.
Correct answer: B — A single adverse event (sector downturn, regulatory shock) causes simultaneous defaults across all concentrated exposures, dramatically increasing credit VaR.
Explanation: Concentration risk amplifies tail losses: all exposures share a common risk factor, so when that factor turns adverse, losses cluster. Expected loss may be similar to a diversified portfolio, but the unexpected tail loss (credit VaR) is dramatically higher. Regulatory large exposure limits (25% Tier 1) and internal sector limits address this.
Question 390
Bank's credit VaR (99.9%) = $800m, expected credit loss = $50m. Operational risk capital (unexpected loss) for credit purposes:
Select an option first.
Correct answer: C — $750m
Explanation: Credit risk capital = Unexpected Loss = Total credit VaR − Expected Loss = $800m − $50m = $750m. Capital covers adverse deviation from expected; provisions cover expected losses. A is total VaR; B adds EL to VaR (double-counting); D is just EL.
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