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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 301
The 'four-eyes principle' in operational risk governance requires:
Select an option first.
Correct answer: B — Important transactions or decisions to require approval or review by at least two individuals to prevent errors or fraud.
Explanation: The four-eyes principle is a key operational risk control: requiring a second person to review or approve decisions reduces the risk of undetected errors and single-point-of-failure fraud. It is a fundamental segregation of duties control, particularly important in payments, credit approval, and model validation.
Question 302
Which of the following is a 'key risk indicator' (KRI) commonly used for operational risk in a bank's payments function?
Select an option first.
Correct answer: B — The number of failed payment settlements or payment processing errors per week.
Explanation: KRIs are leading indicators of operational risk build-up. For payments: failed settlements, processing errors, system downtime are early warnings of control deterioration. They allow management to act before a loss event occurs. A is market risk; C is liquidity/balance sheet; D is capital adequacy.
Question 303
Historical stress testing uses:
Select an option first.
Correct answer: B — Actual historical episodes of market stress (e.g., 2008 financial crisis, 1987 crash, 9/11) applied to the current portfolio to estimate potential losses.
Explanation: Historical stress testing: apply the actual return patterns (factor moves, correlations) from a past crisis to today's portfolio. Advantages: real and credible. Limitations: current portfolio may differ from historical, and novel risks not in history are missed. A is hypothetical; C is a stress-calibrated model; D is reverse stress testing.
Question 304
Which of the following best explains why stress testing and VaR are complementary rather than substitutes?
Select an option first.
Correct answer: B — VaR provides a probabilistic summary of loss under assumed distributions; stress testing explores specific extreme scenarios that may be outside the VaR's confidence level or distributional assumptions.
Explanation: VaR: statistical, probabilistic, relies on distributional assumptions; misses risks outside its confidence range. Stress testing: scenario-based, explores specific extreme events (including those not in history or outside the VaR confidence interval). Together they provide a fuller picture. A and D are wrong; C is not always true.
Question 305
A bank's loan portfolio has: PD = 2%, LGD = 45%, EAD = $500 million. The expected credit loss is:
Select an option first.
Correct answer: A — $4.5 million
Explanation: ECL = PD × LGD × EAD = 0.02 × 0.45 × $500m = 0.009 × $500m = $4.5 million. B uses LGD×EAD without PD; C uses 0.02×0.45×$1000m; D halves the correct answer.
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Question 306
A credit rating transition matrix shows that a BBB-rated firm has a 0.5% probability of defaulting within one year. If the recovery rate is 40%, what is the expected annual credit loss per $1,000 of exposure?
Select an option first.
Correct answer: B — $3.00
Explanation: ECL = PD × LGD × EAD = 0.5% × 60% × $1,000 = 0.005 × 0.6 × 1000 = $3.00. LGD = 1 − recovery = 1 − 0.40 = 60%. A uses LGD=100%; C halves LGD; D uses only PD×EAD.
Question 307
Which of the following correctly describes the relationship between credit spread and probability of default?
Select an option first.
Correct answer: A — Credit spread = LGD × PD (approximately).
Explanation: Rough approximation: Credit spread ≈ PD × LGD (hazard rate × LGD). If PD = 1% and LGD = 60%, spread ≈ 60 bps. More precisely, the spread compensates for expected loss (PD × LGD) plus a risk premium. B, C, D are mathematically incorrect approximations.
Question 308
The 'correlation' parameter in credit portfolio models (e.g., Gaussian copula) captures:
Select an option first.
Correct answer: B — The degree to which defaults of different borrowers tend to cluster together — high correlation means many firms default simultaneously during economic downturns.
Explanation: Default correlation: if defaults are highly correlated, a recession hits many borrowers simultaneously, producing severe portfolio losses (high credit VaR). With zero correlation, defaults are independent and diversification is maximum. The Gaussian copula models this correlation to generate joint default distributions in CDO pricing and credit VaR models.
Question 309
Which of the following best describes the 'wrong-way risk' problem specific to credit risk in derivatives?
Select an option first.
Correct answer: B — The credit exposure on a derivative increases precisely when the counterparty's probability of defaulting also increases (e.g., buying protection from a bank that is exposed to the same risk).
Explanation: Wrong-way risk: positive correlation between counterparty credit quality and derivatives MTM. Example: a bank buys credit protection from a monoline insurer on a basket of mortgages. When mortgages deteriorate, the CDS MTM rises (the bank has a large positive exposure) exactly when the monoline's credit quality falls most. The exposure peaks at the worst possible time.
Question 310
Under the Basel II Internal Ratings Based (IRB) approach, banks estimate which of the following credit risk parameters internally?
Select an option first.
Correct answer: B — PD, LGD, EAD, and maturity (M) under the Advanced IRB; PD only under the Foundation IRB.
Explanation: IRB Framework: Foundation IRB (F-IRB): banks estimate PD; supervisors set LGD and EAD. Advanced IRB (A-IRB): banks estimate PD, LGD, EAD, and maturity. Both approaches use supervisory correlation assumptions. Basel IV has constrained A-IRB for certain portfolios due to variability in bank estimates.
Question 311
The 'operational risk event type' category 'Clients, Products and Business Practices' (CPBP) in Basel II includes:
Select an option first.
Correct answer: B — Losses from unintentional or negligent failure to meet professional obligations to clients, or from the nature or design of a product (e.g., mis-selling, suitability failures).
Explanation: CPBP covers: mis-selling, suitability failures, fiduciary breaches, market manipulation, antitrust violations, and product defects. This is one of the largest categories of operational risk losses at retail banks. A is BDFL (Business Disruption and System Failures/Damage to Physical Assets); C is EDPM (Execution, Delivery and Process Management); D is Internal Fraud.
Question 312
Scenario analysis in operational risk modelling is used primarily to:
Select an option first.
Correct answer: B — Estimate the frequency and severity of rare but plausible high-impact operational risk events that have not occurred historically at the firm.
Explanation: Scenario analysis bridges the data gap for high-severity, low-frequency operational risks. Expert panels estimate frequency and severity of scenarios like: major cyberattack, rogue trading, pandemic. These estimates supplement internal data in the LDA to ensure the tail of the loss distribution is adequately captured.
Question 313
Which of the following is the best definition of 'country risk premium' in equity valuation?
Select an option first.
Correct answer: B — The additional expected return demanded by investors for bearing the unique risks of operating or investing in a specific country versus a risk-free benchmark.
Explanation: Country risk premium = additional return demanded for country-specific risks (political instability, currency risk, expropriation, legal uncertainty). When estimating a WACC for a project in an emerging market, a country risk premium is added to the equity risk premium. A is capital; C is the sovereign spread (a proxy for CRP but not the definition); D is a risk measure.
Question 314
Which of the following metrics is most commonly used to measure a country's ability to service its external debt?
Select an option first.
Correct answer: B — External debt-to-GDP ratio and debt service coverage (interest and principal payments as a percentage of export revenues).
Explanation: Debt service capacity: external debt/GDP measures total burden; debt service/exports measures near-term payment capacity. Countries with high external debt relative to their export earnings are most vulnerable to external shocks. A is equity valuation; C is market valuation; D is credit expansion, not capacity.
Question 315
A 'haircut' on collateral posted for a derivative means:
Select an option first.
Correct answer: B — A reduction applied to the market value of collateral to account for potential decline in value before it can be liquidated (reflects market and liquidity risk of the collateral itself).
Explanation: Haircuts: if a bond with market value $100 is posted as collateral with a 10% haircut, only $90 of credit is given. The haircut protects the secured party against the risk that the bond's value falls between the posting date and the point when it is liquidated after default. Higher haircuts for riskier, more volatile collateral.
Question 316
The Basel II/III credit risk formula for minimum capital under IRB calculates unexpected credit loss using which input factors?
Select an option first.
Correct answer: A — PD, LGD, EAD, maturity, and an asset correlation assumption.
Explanation: IRB formula: K = LGD × N[...PD, ρ...] − PD × LGD (where N[...] is the normal CDF, ρ is asset correlation, and the formula captures unexpected loss). Inputs: PD, LGD, EAD, M (maturity adjustment). The formula is derived from the Vasicek single-factor model. B simplifies too much; C and D are wrong.
Question 317
A bank's operational risk loss data shows a high frequency of small losses and rare but very large losses. This pattern suggests the loss severity distribution is:
Select an option first.
Correct answer: B — Positively skewed with a heavy right tail — typical of operational risk losses.
Explanation: Operational risk losses: many small events (data entry errors, minor processing failures) and rare catastrophic events (rogue trading, major fraud, natural disaster). This produces a heavy-tailed, positively skewed distribution — modelled by log-normal, Pareto, or GPD distributions in the LDA. Normal (A), negative skew (C), and uniform (D) are inappropriate.
Question 318
Regulatory stress tests (e.g., Fed CCAR, EBA stress tests) typically involve:
Select an option first.
Correct answer: A — The regulator selecting adverse economic scenarios and requiring banks to estimate their capital position under those scenarios.
Explanation: Regulatory stress tests: regulators specify the scenarios (e.g., GDP −5%, unemployment +4pp, equity −40%), banks apply them to their own portfolios using their internal models, and the regulator assesses whether capital ratios remain above minimums. Results inform capital distribution restrictions (CCAR) or capital planning (EBA). B, C, D are wrong.
Question 319
A 'systemic stress test' differs from a 'firm-specific stress test' in that:
Select an option first.
Correct answer: B — Systemic tests assess the resilience of the financial system as a whole, including second-round effects and feedback loops between institutions, rather than each institution in isolation.
Explanation: Firm-specific stress tests: assess one institution under a scenario. Systemic stress tests: assess the system's resilience including interbank exposures, fire sale dynamics, and behavioural feedback. Network effects can amplify system-wide losses far beyond the sum of individual losses. A, C, D are all incorrect.
Question 320
The difference between 'expected loss' and 'unexpected loss' in credit risk is significant because:
Select an option first.
Correct answer: B — Expected loss is priced into loan rates and covered by provisions; unexpected loss represents the tail risk that must be absorbed by capital.
Explanation: EL is predictable — priced into credit spreads and covered by provisions. UL is the adverse deviation from EL — the loss that capital must absorb. Credit VaR = UL at a given confidence. Basel capital requirements are calibrated to cover UL (not EL). A is wrong; C and D are both incorrect.
Question 321
Which of the following most accurately describes 'migration risk' in a credit bond portfolio?
Select an option first.
Correct answer: B — The risk that a credit is downgraded, reducing its market value even if the borrower does not default.
Explanation: Migration risk: even without default, a downgrade (e.g., BBB to BB) widens credit spreads, reducing bond prices. This mark-to-market loss is migration risk. Credit VaR models (like CreditMetrics) capture both default risk and migration risk across the full rating transition matrix. A, C, D are unrelated.
Question 322
Which of the following is a primary source of model risk in credit VaR models?
Select an option first.
Correct answer: B — The choice of default correlation parameters, which are difficult to estimate empirically and highly sensitive to the distribution chosen (e.g., Gaussian vs Clayton copula).
Explanation: Default correlations are the most critical and most uncertain parameter in credit portfolio models. Empirical estimation requires decades of default history during multiple economic cycles. The 2008 crisis showed that Gaussian copula underestimated tail dependence (simultaneous defaults across structured products). Copula choice and correlation assumptions are the primary sources of model risk.
Question 323
Under Basel's Operational Risk Standardised Approach (which replaced AMA in Basel IV), capital is based on:
Select an option first.
Correct answer: B — A 'Business Indicator' (a measure of bank size/activity) multiplied by 'Internal Loss Multiplier' factors based on the firm's own historical loss experience.
Explanation: Basel IV SMA (Standardised Measurement Approach / New Standardised Approach): capital = BI Component × ILM (Internal Loss Multiplier). BI (Business Indicator) = sum of revenue components; ILM = max(1, multiplier based on historical losses). This links capital to both firm size and actual loss experience. A is the old BIA; C is the AMA; D is a generic capital ratio.
Question 324
A negative pledge clause in a loan agreement is designed to:
Select an option first.
Correct answer: B — Restrict the borrower from pledging its assets as security to other creditors, protecting the existing lender's relative position.
Explanation: Negative pledge: a covenant preventing the borrower from granting security interests to third parties that would subordinate the lender's position. This is a structural protection — the lender didn't take security but doesn't want to be disadvantaged by the borrower collateralising assets for other creditors. A is a cross-default clause; C is a financial covenant; D is a rating trigger/MAC clause.
Question 325
Which of the following approaches to operational risk capital is most sensitive to a firm's actual loss history?
Select an option first.
Correct answer: B — The new Standardised Approach (SA) under Basel IV, through the Internal Loss Multiplier.
Explanation: The Basel IV SA: ILM = exp(0.8 × ln(max(avg_losses/BI, 1))). Firms with higher historical loss ratios than peers get an ILM > 1, increasing capital. BIA and TSA ignore firm-specific loss history entirely. This makes the new SA more risk-sensitive than its predecessors while simpler than AMA.
Question 326
Which of the following is the most significant limitation of credit rating transition matrices for estimating future default probabilities?
Select an option first.
Correct answer: B — They are historically estimated and assume ratings are Markov (future only depends on current rating), ignoring that downturn PDs differ from benign-period ones and that credit quality has momentum.
Explanation: Transition matrix limitations: (1) historical frequencies may not reflect current conditions (TTC vs PIT), (2) Markov assumption ignores rating momentum (recently downgraded firms have higher PD than stable same-rating firms), (3) matrices differ dramatically across economic cycles — a benign-period matrix understates downturn PDs. A, C, D are wrong.
Question 327
The Gaussian copula, widely used in CDO pricing, failed during the 2008 crisis primarily because:
Select an option first.
Correct answer: B — It assumed a Gaussian (normal) dependence structure with no tail dependence — meaning it dramatically underestimated the probability of simultaneous default of many correlated assets in a systemic crisis.
Explanation: Gaussian copula failure: the normal copula has zero tail dependence — in the tail of the distribution, assets are asymptotically independent. During 2008, many correlated subprime assets defaulted simultaneously — a level of co-default the Gaussian copula's zero-tail-dependence structure could not model. Copulas with tail dependence (Clayton, Student-t) were more appropriate but less widely used.
Question 328
A bank's operational risk model uses 5 years of internal data. A major fraud event occurred 7 years ago but is excluded from the model window. Why is this a concern?
Select an option first.
Correct answer: B — The excluded fraud event represents a high-severity tail scenario that informs the operational risk capital estimate; excluding it underestimates the firm's actual tail loss exposure.
Explanation: Operational risk tail estimation requires capturing rare, large events. A major fraud excluded from the window means the modelled severity distribution has a thinner tail than the firm's actual exposure suggests. This is why regulators require consideration of historical losses beyond the model window and use of external data/scenarios to supplement limited internal data.
Question 329
The 'granularity adjustment' in credit portfolio models accounts for:
Select an option first.
Correct answer: B — The difference in portfolio credit VaR between a perfectly granular (infinitely diversified) portfolio and an actual concentrated portfolio with idiosyncratic risk.
Explanation: The Vasicek model assumes an infinitely granular portfolio (idiosyncratic risk fully diversified). Real portfolios are concentrated — single large exposures contribute idiosyncratic risk that the formula doesn't capture. The granularity adjustment adds an additional capital charge for this concentration beyond what the IRB formula provides.
Question 330
In constructing a 'credit stress test', a risk manager finds that under a severe recession scenario (GDP −5%, unemployment +5%), the portfolio PD doubles and LGD increases by 20%. If initial ECL = $50 million, the stressed ECL is:
Select an option first.
Correct answer: B — $120 million
Explanation: Stressed ECL = Stressed PD × Stressed LGD × EAD. Original: PD × LGD × EAD = $50m. If PD doubles: new PD factor = 2 × original PD. If LGD increases 20%: new LGD = 1.2 × original LGD. Stressed ECL = 2 × 1.2 × $50m = $120m. The product of both increases: 2 × 1.2 = 2.4× original ECL. $50m × 2.4 = $120m.
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