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Free FRM Foundations of Risk Management Practice Questions & Answers
400 exam-style Foundations of Risk Management questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 271
A bond has a face value of $1,000, an annual coupon of 5%, and 4 years to maturity. If it currently trades at $950, its current yield is approximately:
Select an option first.
Correct answer: B — 5.3%
Explanation: Current yield = Annual coupon / Current price = $50 / $950 ≈ 5.26% ≈ 5.3%. Note: current yield differs from YTM (which accounts for capital gain to par). A uses face value; C and D are incorrect.
Question 272
Which of the following best explains why 'historical simulation' VaR may underestimate risk during unprecedented market events?
Select an option first.
Correct answer: B — The historical window may not include a scenario similar to the unprecedented event, so the VaR is estimated from benign historical periods
Explanation: Historical simulation has no explicit distributional assumption — it relies on the historical sample. If the sample doesn't include a pandemic, a sovereign default cascade, or a systemic liquidity freeze, these risks will not appear in the VaR estimate. A is the parametric VaR criticism; C describes EWMA; D is incorrect.
Question 273
The 'equity risk premium' (ERP) is:
Select an option first.
Correct answer: B — The expected return on equities above the risk-free rate, compensating investors for bearing equity market risk
Explanation: ERP = E(Rm) − Rf. It is the core compensation for bearing systematic market risk. Historical estimates range from 3-7% depending on period and method. A is dividend yield (a component); C is the SMB factor; D is beta (= 1 by definition for the market portfolio).
Question 274
If the risk-free rate is 3%, the equity risk premium is 5%, and a stock has a beta of 1.2, the CAPM expected return for this stock is:
Select an option first.
Correct answer: B — 9%
Explanation: E(Ri) = Rf + β × ERP = 3% + 1.2 × 5% = 3% + 6% = 9%. B is correct. A (8%) ignores the beta multiplier on ERP. C (9.6%) would require ERP = 5.5%. D (6%) ignores beta entirely.
Question 275
Which of the following correctly describes the relationship between the Macaulay duration and Modified duration?
Select an option first.
Correct answer: B — Modified duration = Macaulay duration / (1 + y)
Explanation: Modified Duration = Macaulay Duration / (1 + y/m), where y is the yield and m is compounding frequency. For annual compounding: Mod D = Mac D / (1 + y). A inverts the relationship; C is incorrect; D has no basis.
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Question 276
Which of the following is the primary purpose of 'scenario stress testing' in a bank's Internal Capital Adequacy Assessment Process (ICAAP)?
Select an option first.
Correct answer: B — To assess how the bank's capital position would be affected under severe but plausible macro-economic scenarios, identifying whether it would remain above regulatory minima
Explanation: ICAAP scenario stress testing evaluates capital adequacy under adverse scenarios (severe recession, financial market crash). The purpose is to identify capital vulnerabilities and guide capital planning — not to predict exact losses (A), set pricing (C), or replace standard models (D).
Question 277
The 'leverage effect' in options markets refers to:
Select an option first.
Correct answer: B — The tendency for equity volatility to increase when stock prices fall (and decrease when prices rise), because falling equity prices increase financial leverage
Explanation: The leverage effect: when stock prices fall, the ratio of debt to equity (financial leverage) rises, making equity riskier and increasing volatility. This explains the observed negative correlation between equity returns and volatility changes — the basis for the volatility skew in equity options markets.
Question 278
A portfolio manager reports a Sharpe ratio of 1.5. Which of the following correctly interprets this figure?
Select an option first.
Correct answer: B — The portfolio earned 1.5 units of excess return per unit of total risk (standard deviation)
Explanation: Sharpe = (Rp − Rf) / σp = 1.5 means for every 1 unit of total volatility, the manager earned 1.5 units of excess return above the risk-free rate. A, C, and D all misidentify what Sharpe measures.
Question 279
The 'terminal value' in a DCF valuation captures:
Select an option first.
Correct answer: B — The present value of all cash flows expected to occur beyond the explicit forecast period, usually modelled as a growing perpetuity
Explanation: Terminal value (Gordon Growth Model approach) = FCFn × (1+g) / (WACC − g). It captures the going-concern value beyond the detailed forecast period, often representing 60-80% of total DCF value. A is liquidation value; C is debt face value; D is dividend sum.
Question 280
Which of the following is a key advantage of Monte Carlo VaR over historical simulation VaR?
Select an option first.
Correct answer: B — Monte Carlo can incorporate forward-looking distributional assumptions, generate scenarios not present in historical data, and handle complex non-linear instruments more accurately
Explanation: Monte Carlo's flexibility: (1) scenarios not in history can be simulated, (2) distributional assumptions can be tailored (fat tails, stochastic vol), (3) non-linear instruments (options, MBS) are fully repriced. A is wrong (Monte Carlo is computationally intensive); C is incorrect; D is wrong (Monte Carlo requires explicit distributional assumptions).
Question 281
In bond mathematics, when a bond's yield equals its coupon rate, the bond's price relative to its face value is:
Select an option first.
Correct answer: C — Equal to par
Explanation: When yield = coupon rate, the discount rate equals the cash flow rate, so the PV of all cash flows exactly equals the face value. This is a fundamental bond pricing identity. A applies when coupon > yield; B when yield > coupon.
Question 282
Which of the following correctly describes how a 'credit default swap' (CDS) works?
Select an option first.
Correct answer: A — The protection buyer pays a fixed premium (spread) periodically and receives a contingent payment if a defined credit event (such as default) occurs on the reference entity
Explanation: CDS: protection buyer pays a regular spread (e.g., 100bp/year on notional) to the protection seller. If the reference entity defaults, the seller pays (1 − recovery rate) × notional. B reverses the logic; C is an interest rate swap structure; D describes something different.
Question 283
A firm calculates that its portfolio's 1-day 95% VaR is $1 million and its 1-day 99% VaR is $1.5 million. What does the difference between the two figures represent?
Select an option first.
Correct answer: B — The additional loss the portfolio is at risk of between the 95th and 99th percentile of the loss distribution
Explanation: The gap between 95% VaR ($1m) and 99% VaR ($1.5m) shows what additional loss is at risk in that 4% of trading days that fall between the 5th and 1st worst percentiles. It reflects the shape of the loss distribution in the 95-99% range. A is expected loss; C is standard deviation; D is ES (different concept).
Question 284
The primary role of a board of directors in the context of risk management is:
Select an option first.
Correct answer: B — Setting the overall risk appetite and ensuring the firm has adequate risk governance structures
Explanation: The board is responsible for oversight and governance — setting risk appetite, ensuring appropriate structures are in place, and holding management accountable. Day-to-day execution (A), model building (C), and individual credit decisions (D) are management/operational functions.
Question 285
Which of the following best describes the role of the Chief Risk Officer (CRO)?
Select an option first.
Correct answer: B — Overseeing the firm's risk management framework, reporting risks to the board, and ensuring risk culture is embedded across the organisation
Explanation: The CRO is the senior executive responsible for enterprise risk management — overseeing frameworks, escalating risks to the board, and embedding risk culture. A is a front-office role; C is a client relationship role; D is the CFO/audit committee function.
Question 286
A risk committee at the board level is typically responsible for:
Select an option first.
Correct answer: B — Overseeing the firm's risk management policies, reviewing material risk exposures, and challenging management's risk assessments
Explanation: A board risk committee provides governance oversight — it reviews policies, monitors material exposures, and ensures management's risk-taking is consistent with board-approved risk appetite. A and C are operational; D is external auditor's role.
Question 287
In Modern Portfolio Theory (MPT), the key insight about diversification is:
Select an option first.
Correct answer: B — By combining assets with less-than-perfect positive correlation, the portfolio's risk can be reduced without necessarily reducing expected return
Explanation: MPT's core insight: combining imperfectly correlated assets reduces total portfolio volatility (diversification benefit). Expected return is the weighted average of individual returns; risk (variance) benefits from correlations < 1. All risk cannot be eliminated (systematic remains). A, C, D are all incorrect.
Question 288
The Capital Asset Pricing Model (CAPM) states that the expected return on an asset is:
Select an option first.
Correct answer: A — Equal to the risk-free rate plus the asset's beta times the expected market risk premium
Explanation: CAPM: E(Ri) = Rf + βi × (E(Rm) − Rf). The required return consists of the risk-free rate plus a systematic risk premium. B, C, and D are all incorrect formulations of asset pricing.
Question 289
The market risk premium in the CAPM is defined as:
Select an option first.
Correct answer: B — The expected return on the market portfolio minus the risk-free rate
Explanation: Market risk premium = E(Rm) − Rf. It represents the additional expected return investors require for holding the risky market portfolio instead of the risk-free asset. A is just Rf; C is volatility; D is alpha (zero for market by definition).
Question 290
Arbitrage Pricing Theory (APT) differs from CAPM by:
Select an option first.
Correct answer: B — Allowing for multiple macroeconomic factors to explain returns, rather than relying solely on the market portfolio
Explanation: APT (Ross, 1976) is a multifactor model — returns are explained by multiple common factors (e.g., interest rates, inflation, industrial production) not just the market. CAPM is a single-factor model. A incorrectly describes CAPM. C and D are wrong.
Question 291
In the context of corporate governance, an 'independent director' is one who:
Select an option first.
Correct answer: B — Has no material relationship with the company that could compromise their judgement in oversight of management
Explanation: Independent directors provide objective oversight of management. Their independence is compromised if they are former executives, major suppliers, or have personal/financial relationships with management. A, C, and D all describe conflicts of interest.
Question 292
Agency risk refers to:
Select an option first.
Correct answer: B — The risk arising from conflicts of interest between principals (e.g., shareholders) and agents (e.g., managers) who may act in their own interest rather than the principal's
Explanation: Agency problems occur when managers (agents) pursue their own interests (job security, perks, empire-building) at the expense of shareholders (principals). A is regulatory risk; C is operational risk; D is FX risk.
Question 293
Which of the following is the purpose of a firm's 'risk management policy'?
Select an option first.
Correct answer: B — To set out the principles, frameworks, and governance structures that guide how the firm identifies, measures, and manages risk
Explanation: A risk management policy is a governance document establishing the firm's approach to risk — principles, risk appetite, responsibilities, and processes. A is impossible; C is too operational; D is incorrect (policy does not replace capital).
Question 294
The concept of 'separation of duties' in risk management means:
Select an option first.
Correct answer: B — The people who take risk (front office) should be separate from those who measure and control it (middle office/risk management)
Explanation: Separation of duties prevents conflicts of interest — traders should not be setting their own risk limits or valuing their own books. Independent risk management and valuation controls are fundamental governance requirements. A conflates functions; C and D are wrong.
Question 295
The minimum variance portfolio (MVP) on the efficient frontier is:
Select an option first.
Correct answer: B — The portfolio that offers the lowest possible risk (variance) for any combination of the available assets
Explanation: The MVP is the leftmost point on the efficient frontier — the combination of risky assets that minimises total portfolio variance. A is the highest-return portfolio (right end of frontier); C is the tangency portfolio; D is the risk-free asset (a single asset, not a portfolio).
Question 296
In CAPM, a stock with a beta of 1.5 and a market risk premium of 6% has an expected return (assuming risk-free rate = 3%) of:
Select an option first.
Correct answer: C — 12%
Explanation: E(Ri) = Rf + β × (Rm − Rf) = 3% + 1.5 × 6% = 3% + 9% = 12%. A applies only the market premium; B applies beta = 1; D applies a fractional error.
Question 297
What is meant by 'risk limits' in a trading environment?
Select an option first.
Correct answer: B — Pre-defined thresholds (e.g., maximum VaR, maximum loss, maximum position size) that constrain risk-taking and trigger escalation if breached
Explanation: Risk limits are governance controls — they define acceptable boundaries for risk-taking and require action (reduction of positions, management escalation) when breached. A, C, and D are not risk limits in the standard sense.
Question 298
Which of the following best describes a 'stop-loss' limit?
Select an option first.
Correct answer: B — A pre-set maximum cumulative loss level at which trading activity must cease or be escalated to senior management
Explanation: Stop-loss limits define the point at which management must intervene — preventing runaway losses on a trading desk. A describes automatic hedging (not standard); C is a capital requirement; D is a product feature.
Question 299
Which of the following is a key benefit of a strong risk culture within a financial institution?
Select an option first.
Correct answer: B — It encourages employees to identify and escalate risks early, reducing the likelihood of risk events escalating into large losses
Explanation: A strong risk culture creates an environment where risks are proactively identified, honestly reported, and effectively managed. A is impossible to guarantee; C is incorrect — risk culture is about appropriate not more risk; D is incorrect — culture supports but does not replace formal governance.
Question 300
A firm's 'tone at the top' in risk management refers to:
Select an option first.
Correct answer: B — The attitudes, behaviours, and priorities demonstrated by senior leadership that set the standard for risk culture throughout the organisation
Explanation: 'Tone at the top' is a governance concept — if the CEO and board take risk management seriously and behave consistently with stated values, this cascades down. Poor tone (prioritising short-term profit over risk) is a root cause of many financial scandals.
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