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Free FRM Risk Management & Investment Management Practice Questions & Answers
400 exam-style Risk Management & Investment Management questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 61
What is 'gamma' in options risk management?
Select an option first.
Correct answer: B — The rate of change of delta with respect to the underlying asset price — high gamma means delta changes rapidly, requiring frequent rebalancing of a delta hedge. Gamma is highest for at-the-money options near expiry
Explanation: B is correct. Gamma (Γ): ∂²V/∂S² = ∂Δ/∂S. A large gamma means the delta hedge must be rebalanced more frequently (delta changes quickly with price). Long option positions have positive gamma (convex payoff — benefit from large moves in either direction). Short option positions have negative gamma. A is theta. C is vega. D is rho.
Question 62
What is 'theta' in options risk management?
Select an option first.
Correct answer: B — The rate at which an option's value decays with the passage of time, all else equal — long option holders lose value daily (negative theta); short option writers gain from theta decay
Explanation: B is correct. Theta (Θ): ∂V/∂t < 0 for long positions. At-the-money options experience the most time decay, especially as expiry approaches. Option sellers (short gamma/short options) earn theta daily but are exposed to adverse price moves. Long options pay theta but benefit from large price moves (positive gamma). A is delta. C is rho. D is gamma.
Question 63
What are 'Greeks' in options risk management and why are they important?
Select an option first.
Correct answer: B — The sensitivities of an option's price to changes in underlying variables — delta (price), gamma (delta's rate of change), vega (volatility), theta (time), rho (interest rate) — used to measure, decompose, and manage option risk
Explanation: B is correct. Greeks: together they describe the risk profile of an option position. A delta-neutral portfolio is still exposed to gamma, vega, and theta. Risk managers use Greeks to: understand risk exposures, hedge specific risks, and assess P&L attribution. A is performance measurement. C is mathematical derivation. D is regulatory treatment.
Question 64
What is the difference between 'expected loss' (EL) and 'unexpected loss' (UL) in credit risk?
Select an option first.
Correct answer: B — Expected loss is the average credit loss anticipated over a period (EL = PD × LGD × EAD) and is priced into loan spreads as a cost; unexpected loss is the deviation from EL (volatility of losses) that requires economic capital as a buffer
Explanation: B is correct. EL: the 'budget' for credit losses, covered by loan pricing and provisions. UL: the variability around EL — tail losses that cannot be predicted on average. Economic capital is held to cover UL (typically at a high confidence level). Regulatory capital addresses UL. A describes a temporal distinction. C is incorrect. D: provisions cover EL only; capital covers UL.
Question 65
What is a 'credit rating migration matrix'?
Select an option first.
Correct answer: B — A matrix showing the probability of a credit rating changing from one rating to another (e.g., from A to BBB) over a specified period (typically one year) — used in credit risk models and portfolio stress testing
Explanation: B is correct. Rating migration matrix (Moody's/S&P): rows = beginning rating, columns = ending rating. Diagonal = probability of maintaining rating. Off-diagonal: probability of upgrade or downgrade. Default column shows PD by rating grade. Used in credit VaR models and CLO/CDO analysis. A is an FX concept. C is a sector-level default analysis. D is a regulatory disclosure.
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Question 66
What is 'credit portfolio risk' and how does correlation matter?
Select an option first.
Correct answer: B — The risk of losses in a portfolio of credit exposures, where the key driver beyond individual default probabilities is the correlation between defaults — high correlation means multiple defaults happen simultaneously, increasing portfolio tail risk
Explanation: B is correct. Credit portfolio risk: individual loan PDs and LGDs matter, but correlation is the key factor for portfolio risk. Default correlation: during recessions, many borrowers default together (high correlation). Low correlation = diversification reduces portfolio risk substantially. High correlation (e.g., all borrowers in the same industry) = portfolio behaves like a single large loan. A ignores correlation. C is single-loan risk. D is a spread measure.
Question 67
What is 'risk-adjusted return on capital' (RAROC) and how is it used to evaluate business lines?
Select an option first.
Correct answer: B — Revenues minus costs minus expected losses divided by economic capital — used to compare the risk-adjusted profitability of different business lines and ensure resources are allocated to the highest-value activities relative to their risk consumption
Explanation: B is correct. RAROC: enables an apples-to-apples comparison between a high-return/high-risk activity and a low-return/low-risk activity. A business with RAROC > hurdle rate (e.g., 12%) creates value; one below destroys value. Used by banks to: price loans, allocate capital, evaluate manager compensation. A has incorrect components. C describes Jensen's alpha. D is ROE.
Question 68
What is 'fund manager selection risk' and what factors are assessed?
Select an option first.
Correct answer: B — The risk that a selected investment manager underperforms expectations — evaluated through: investment process analysis, risk management quality, organisational stability, performance attribution, operational infrastructure, and track record analysis over multiple market cycles
Explanation: B is correct. Manager selection risk: key due diligence factors — investment philosophy (is it consistent and well-reasoned?), risk management (position sizing, drawdown controls), people (stable team, depth), process (repeatable, documented), performance (attribution analysis, risk-adjusted metrics across cycles), and operational controls. A is key-person risk. C is peer group benchmarking error. D is fee risk.
Question 69
What is 'pension fund liability risk' and how is it measured?
Select an option first.
Correct answer: B — The risk that the present value of pension obligations increases — driven by: declining discount rates (increases PV of liabilities), increasing longevity assumptions (members live longer), and wage inflation — measured using actuarial present value techniques and liability duration
Explanation: B is correct. Pension liability risk: liabilities = PV of future benefit payments, discounted at corporate bond yields (IAS 19). A 1% fall in discount rates can increase liabilities by 20-30% for a mature pension fund. Longevity risk: if members live 1 year longer than assumed, liabilities increase ~5%. These risks dwarf pure investment risk in many pension funds. A is contribution risk. C is withdrawal risk (not typical in DB pensions). D is investment risk.
Question 70
What is 'risk capacity' vs 'risk appetite' vs 'risk tolerance'?
Select an option first.
Correct answer: B — Risk capacity: the maximum risk the organisation could absorb without threatening its survival; Risk appetite: the level of risk management is willing to accept in pursuit of objectives; Risk tolerance: the acceptable variation around the risk appetite
Explanation: B is correct. Three-tier hierarchy: Capacity (absolute maximum — above this = existential threat) > Appetite (desired level — strategic choice) > Tolerance (acceptable range around appetite — day-to-day variation). Example: Capacity = 20% CET1 depletion; Appetite = 5% VaR; Tolerance = 4-6% VaR band. A conflates them. C is wrong — ordering varies. D is too narrow.
Question 71
What is a 'risk committee' at the board level and what are its responsibilities?
Select an option first.
Correct answer: B — A committee of the board responsible for overseeing the firm's overall risk framework — including reviewing risk appetite, monitoring risk exposures, overseeing risk management effectiveness, receiving escalated risk reports, and providing risk oversight to the full board
Explanation: B is correct. Board risk committee: distinct from management-level risk committees. Board-level: strategic oversight, risk appetite approval, framework review. Management-level: operational risk management. The board risk committee should include independent non-executive directors with relevant risk expertise. A is an investment committee function. C is management risk function. D is a trading limit committee.
Question 72
What is 'reverse stress testing' and how does it differ from standard stress testing?
Select an option first.
Correct answer: B — Identifying scenarios that would cause an organisation to fail (or breach a specific threshold) and working backwards to understand what conditions would produce that outcome — opposite of standard stress testing (which starts from scenarios and calculates impact)
Explanation: B is correct. Reverse stress testing: start from the outcome (failure or breach) and identify the scenarios or combinations of events that would cause it. This forces risk managers to think about tail scenarios they might not normally consider. Required by FCA/PRA for banks and insurers. A is post-hoc analysis. C is not a type of stress test. D is regulatory stress testing of a different kind.
Question 73
What is 'conduct risk' in financial services?
Select an option first.
Correct answer: B — The risk that a firm's behaviours and decisions cause poor outcomes for customers, market integrity, or market participants — including inappropriate advice, mis-selling, market manipulation, or unfair treatment of customers. A growing regulatory focus following PPI mis-selling and LIBOR scandals
Explanation: B is correct. Conduct risk (FCA focus): goes beyond compliance to outcomes — are customers being treated fairly? Are markets functioning properly? PPI mis-selling (UK banks paid £40bn+ in redress), payment protection insurance, and LIBOR manipulation are examples of major conduct risk materialising. A is a subset. C is a consequence. D is reputation risk (related but different).
Question 74
What is 'fair value accounting' (mark-to-market) and its implications for risk management?
Select an option first.
Correct answer: B — Reporting assets and liabilities at their current market value — provides timely information about economic exposure but can increase reported volatility and may trigger procyclical behaviour (forced selling when mark-to-market losses trigger margin calls or regulatory capital breaches)
Explanation: B is correct. MTM (IFRS 13, ASC 820): Level 1 (quoted prices), Level 2 (observable inputs), Level 3 (unobservable inputs). Risks: MTM losses during illiquid markets may not reflect long-term value; creates procyclical effects (2008 — forced selling due to MTM losses). 'Mark-to-myth' criticism for Level 3. A is historical cost. C is realised accounting. D is historical cost averaging.
Question 75
What is 'funding risk' in a bank and how is it managed?
Select an option first.
Correct answer: B — The risk that a bank cannot access sufficient funding at reasonable cost to meet its obligations — managed through: diversification of funding sources (retail deposits, wholesale debt, covered bonds), maintaining a buffer of liquid assets, limiting reliance on short-term wholesale funding, and stress testing funding plans
Explanation: B is correct. Funding risk: over-reliance on short-term wholesale funding (as Northern Rock did) creates vulnerability — if the market freezes, the bank cannot roll maturing short-term debt. Solutions: retail deposits (stickier), longer maturity wholesale debt, committed credit facilities, liquid asset buffer. A is equity market access risk. C is credit risk. D is interest rate risk.
Question 76
What is 'contagion risk' in financial markets?
Select an option first.
Correct answer: B — The risk that financial distress in one institution or market spreads to others through interconnectedness — channels include: direct credit exposures, common asset holdings (fire-sale contagion), counterparty relationships, and loss of confidence driving bank runs
Explanation: B is correct. Financial contagion: 1997 Asian crisis, 2008 GFC demonstrated contagion mechanisms. Direct: Bank A defaults → Bank B has a loan to Bank A → Bank B suffers losses. Indirect (fire-sale): all banks hold the same assets → one forced sale drives down prices → others face mark-to-market losses → more selling. Confidence: loss of trust in banks generally. A is cybersecurity. C is competition risk. D is sentiment contagion (related but narrower).
Question 77
What is the 'pro-cyclical' nature of Value at Risk (VaR) models?
Select an option first.
Correct answer: B — VaR models tend to generate low risk estimates during calm periods (low recent volatility in the lookback window) encouraging increased risk-taking, and high estimates during stress (recent volatility spiked) requiring capital increases and de-risking exactly when liquidity is scarce — amplifying market cycles
Explanation: B is correct. VaR procyclicality: the model looks backward (30/252-day lookback). In calm markets: low volatility → low VaR → capital freed → increased risk-taking. In crises: high volatility → high VaR → capital breached → forced deleveraging (buy low/sell low). This is destabilising. Countercyclical buffers and stressed VaR address this. A describes the reverse. C and D are incorrect.
Question 78
What is 'wrong-way risk' in a pension fund's liability-driven investing (LDI) context?
Select an option first.
Correct answer: B — The correlation between asset performance and liability growth that creates adverse outcomes — for example, if a pension fund holds equity (its largest asset class) and a market crash both reduces asset values AND the resulting rate cuts increase pension liabilities (lower discount rates), both sides of the balance sheet move adversely simultaneously
Explanation: B is correct. LDI wrong-way risk: in 2020 COVID crash, equity assets fell AND central banks cut rates (lowering discount rates and inflating liabilities). Funded status deteriorated from both sides simultaneously. This motivates LDI: hedge the interest rate risk of liabilities with bonds/swaps so at least the liability side is immunised. A describes the risk but not 'wrong-way' specifically. C and D are different errors.
Question 79
What is 'risk reporting' and what should a good risk report contain?
Select an option first.
Correct answer: B — A regular, structured communication of risk information to management and the board — containing: current risk exposures vs limits, key risk indicators (KRIs), limit breaches and actions taken, stress test results, emerging risks, and commentary on material risk changes
Explanation: B is correct. Risk reporting: tailored to audience — board-level: high-level summary, key exposures, material changes; management: detailed exposure analysis, KRIs, drill-down capability; desk-level: real-time position limits and P&L. Good report: accurate, timely, actionable, relevant to decision-making. A is a P&L report. C is a regulatory report. D is marketing.
Question 80
What is 'operational risk capital' under Basel II and how is it calculated under the basic indicator approach?
Select an option first.
Correct answer: B — Operational risk capital = 15% × average annual gross income over the last three years (Basic Indicator Approach, BIA). The Standardised Approach uses different multipliers (12-18%) for different business lines. Advanced Measurement Approach (AMA) uses internal models
Explanation: B is correct. BIA (Basel II Pillar 1): simplest approach. Gross income proxy for operational risk. Standardised: divides bank into 8 business lines with different α multipliers (12-18%). AMA (now SA under Basel IV): uses loss data, scenario analysis, BEICF. Basel IV replaced AMA with a new Standardised Approach (SMA) based on a business indicator. A is VaR-based (market risk). C applies a credit scaling. D is unsupported.
Question 81
What is 'credit VaR' and how does it differ from market VaR?
Select an option first.
Correct answer: B — Credit VaR measures the potential unexpected credit loss (beyond expected loss) in a credit portfolio at a given confidence level over a holding period, typically 1 year. It is calculated using credit portfolio models (e.g., CreditMetrics, CreditRisk+) that account for default correlations. Differs from market VaR: horizon is 1 year (vs 1-10 days), distributions are highly skewed (vs near-normal), computation is more complex
Explanation: B is correct. Credit VaR differences from market VaR: (1) Longer horizon (1 year vs 1-10 days); (2) Highly skewed, non-normal loss distributions (most periods zero loss, occasional large defaults); (3) Requires modelling default correlation; (4) Less liquid portfolios (harder to exit). CreditMetrics (JP Morgan) and CreditRisk+ are the standard models. A is credit rating migration, not credit VaR. C and D are incorrect.
Question 82
What is the 'recovery rate' in credit risk and what factors influence it?
Select an option first.
Correct answer: B — The percentage of the outstanding loan or bond value that is recovered after a default — influenced by: seniority of the claim (senior secured vs unsecured), collateral quality, industry (tangible assets recover more), legal jurisdiction (bankruptcy law), and macroeconomic conditions
Explanation: B is correct. Recovery rate (1 − LGD): varies significantly. Senior secured: 60-80%; Senior unsecured: 40-60%; Subordinated: 20-40%; Equity: near zero. In 2008 recession, recovery rates on leveraged loans fell below historical averages. Moody's/S&P publish historical recovery data. A is a specific time horizon. C is a cure rate. D is price recovery, not credit recovery.
Question 83
What is 'portfolio construction risk' and how does it arise?
Select an option first.
Correct answer: B — The risk of building a portfolio that does not optimally reflect the intended risk and return objectives — arising from: estimation errors in inputs (expected returns, covariances), model limitations, implementation constraints (transaction costs, minimum sizes), and cognitive biases in manager judgement
Explanation: B is correct. Portfolio construction risk: even a skilled manager with genuine alpha can build a suboptimal portfolio if: (1) Errors in parameter estimation → wrong weights; (2) Constraints (no short, turnover limits) prevent full expression of views; (3) Transaction costs erode theoretical alphas; (4) Behavioural biases (overconfidence, loss aversion) distort decisions. A is benchmarking risk. C is operational/model risk. D is mandate conflict.
Question 84
What is 'value-at-risk back-testing' (Basel traffic light system)?
Select an option first.
Correct answer: B — A regulatory framework for evaluating VaR model accuracy: compare daily P&L against 1-day 99% VaR. Green zone: 0-4 exceptions in 250 trading days (model acceptable). Yellow zone: 5-9 exceptions (model questionable, capital multiplier increases from 3 to up to 3.65). Red zone: 10+ exceptions (model rejected, maximum multiplier of 4.0 applied)
Explanation: B is correct. Basel traffic light (Basel II.5): monitors 'exceptions' — days when actual loss > VaR. For 99% VaR, expect ≤2.5 exceptions per year (250 days × 1% = 2.5). Green (0-4): acceptable. Yellow (5-9): added scrutiny. Red (10+): model suspected inadequate, maximum capital penalty applied. This aligns model performance with capital requirements. A has wrong details. C and D are unrelated.
Question 85
What is 'limit management' in trading risk management?
Select an option first.
Correct answer: B — The system of risk limits (VaR limits, notional limits, stop-loss limits, concentration limits, counterparty limits) used to control risk-taking — monitoring utilisation, investigating and approving limit excesses, escalating breaches, and adjusting limits as market conditions change
Explanation: B is correct. Limit management: the operational backbone of market risk management. Types: VaR limit (market risk), notional limit (gross exposure), stress loss limit (maximum loss under stress), stop-loss limit (P&L trigger for review), concentration limit, counterparty/country limit. A breach triggers escalation to senior management and potential position reduction. A is target-setting. C is credit regulation. D is client management.
Question 86
What is 'margin' in derivatives markets and what types exist?
Select an option first.
Correct answer: B — A form of collateral posted by derivatives participants to cover potential losses — initial margin (posted at trade inception to cover potential future exposure) and variation margin (daily cash settlement of mark-to-market gains/losses to prevent accumulation of large unpaid obligations)
Explanation: B is correct. Margin types: Initial Margin (IM): upfront collateral against future exposure. Variation Margin (VM): daily cash flow settling accumulated MTM changes. Central clearing CCPs require both; bilateral (non-cleared) OTC derivatives face EMIR/Dodd-Frank margin requirements. Margin calls: a source of liquidity risk if large amounts of cash must be posted quickly (LDI crisis 2022). A is a transaction fee. C is partial. D is trading P&L margin.
Question 87
What is 'central counterparty clearing' (CCP) and how does it reduce systemic risk?
Select an option first.
Correct answer: B — An entity that interposes itself between buyers and sellers in a derivatives transaction — becoming the buyer to every seller and seller to every buyer. CCPs reduce systemic risk by: multilateral netting (reducing total exposures), standardised margin requirements, daily settlement, and loss-mutualisation through default funds
Explanation: B is correct. CCP: post-2008 G20 mandate required standardised OTC derivatives to be centrally cleared. Benefits: multilateral netting reduces total system-wide exposure, daily margin prevents accumulation, transparent pricing, default fund mutualisés losses. Risks: CCPs are systemically important themselves — a CCP failure would be catastrophic. A is a regulatory body. C is a payment clearing bank. D is a stock exchange CCP (different context).
Question 88
What is 'risk-neutral pricing' in derivatives?
Select an option first.
Correct answer: B — A mathematical framework where derivatives are priced under a 'risk-neutral measure' (Q measure) in which all assets earn the risk-free rate — the actual (real-world) probabilities of outcomes are adjusted to risk-neutral probabilities, making discounting at the risk-free rate self-consistent
Explanation: B is correct. Risk-neutral pricing: in the Black-Scholes model, the stock's drift is replaced by the risk-free rate in the Q measure. Options are priced as the expected payoff under Q, discounted at the risk-free rate. This doesn't mean investors are actually risk-neutral — it's a mathematical convenience that gives arbitrage-free prices. A is the definition of the risk-neutral measure but imprecisely stated. C is wrong — it's a mathematical transformation. D is a misunderstanding.
Question 89
What is 'tail correlation' and why is it important for portfolio risk management?
Select an option first.
Correct answer: B — The correlation between asset returns specifically in the tails of the distribution (extreme events), which is typically higher than average correlations — assets that appear uncorrelated during normal conditions may become highly correlated during market crises (flight to quality or flight from everything)
Explanation: B is correct. Tail correlation (tail dependence): measured by copula models. In 2008: equities, credit, and even commodities fell simultaneously — assets that were supposedly uncorrelated converged to correlation near +1. This is captured by fat-tailed copulas (Clayton, Gumbel) rather than Gaussian copula (which assumes tail independence). A is about position size. C and D are different concepts.
Question 90
What is 'regulatory capital arbitrage' and how has Basel IV tried to address it?
Select an option first.
Correct answer: B — Using model complexity and parameter choices to reduce calculated risk-weighted assets below their true economic risk — e.g., banks using internal models (IRB approach) could assign very low risk weights to certain exposures. Basel IV addresses this through: the SA floor (internal model outputs cannot be below 72.5% of standardised approach output)
Explanation: B is correct. Basel IV / final Basel III (effective 2025/2028): introduces the Output Floor — constrains the benefit of using internal models. The output floor: total RWA from internal models ≥ 72.5% of what the Standardised Approach would require. Prevents excessive RWA optimisation. Also restricts IRB modelling for specific exposure classes. A is tax planning. C is intragroup structuring. D is jurisdictional arbitrage.
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