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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 151
Standard deviation is a measure of:
Select an option first.
Correct answer: B — The dispersion or spread of a data set around its mean
Explanation: Standard deviation measures how far data points deviate from the mean on average. It is the square root of variance. Mean measures central tendency (A); maximum value (C) is a range statistic; probability (D) is unrelated.
Question 152
The formula for Return on Equity (ROE) is:
Select an option first.
Correct answer: B — Net income / Shareholders' equity
Explanation: ROE = Net income / Shareholders' equity. It measures how effectively the firm uses equity capital to generate profit. A is Return on Assets (ROA), C is operating margin, D is a leverage coverage metric.
Question 153
Return on Assets (ROA) is calculated as:
Select an option first.
Correct answer: A — Net income / Total assets
Explanation: ROA = Net income / Total assets. It measures how efficiently the firm uses all its assets to generate profit. B is ROE; C is asset turnover; D is not a standard metric.
Question 154
Return on Capital Employed (ROCE) is best defined as:
Select an option first.
Correct answer: B — EBIT / Capital employed (total assets minus current liabilities)
Explanation: ROCE = EBIT / Capital Employed. Capital employed = total assets − current liabilities (or equivalently, equity + long-term debt). It measures operating efficiency relative to all long-term capital invested. A is ROE; C is gross margin; D is not standard.
Question 155
The debt-to-equity (D/E) ratio measures:
Select an option first.
Correct answer: A — How much of the firm's assets are financed by debt relative to equity
Explanation: D/E = Total debt / Total shareholders' equity. It measures financial leverage. B is a profitability metric; C is a liquidity metric (current ratio, quick ratio); D is an operating cost ratio.
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Question 156
The interest coverage ratio is calculated as:
Select an option first.
Correct answer: B — EBIT / Annual interest expense
Explanation: Interest coverage = EBIT / Interest expense. It measures how easily a firm can service its debt obligations from operating earnings. A is debt/interest (not standard); C is ROA; D is not a standard metric.
Question 157
Beta (β) in finance measures:
Select an option first.
Correct answer: B — The sensitivity of an asset's return to the overall market return
Explanation: Beta measures systematic risk — the tendency of an asset's return to move with the market. β = 1 means moves with market; β > 1 means more volatile; β < 1 means less volatile. A, C, and D are different measures.
Question 158
A correlation coefficient of +1 between two assets means:
Select an option first.
Correct answer: B — The assets move in exactly the same direction with the same proportional magnitude
Explanation: A correlation of +1 means perfect positive linear relationship — when one goes up by X%, the other goes up by X%. Correlation of −1 means perfectly opposite (A); 0 means no linear relationship (C); correlation says nothing about standard deviations (D).
Question 159
The covariance between two assets is positive when:
Select an option first.
Correct answer: B — They tend to move in the same direction
Explanation: Positive covariance means the two assets tend to move together — when one rises, the other tends to rise too. Negative covariance means they move in opposite directions (A). Covariance of zero means no linear relationship (D). C doesn't define covariance direction.
Question 160
What does the 'confidence level' in a VaR calculation represent?
Select an option first.
Correct answer: B — The probability that actual losses will NOT exceed the VaR figure
Explanation: At a 99% confidence level, the VaR is the loss level that will not be exceeded 99% of the time (or exceeded only 1% of the time). A misidentifies the underlying event; C describes exceptions; D is data quality, not confidence.
Question 161
Which of the following correctly describes the relationship between variance and standard deviation?
Select an option first.
Correct answer: A — Variance equals the standard deviation squared
Explanation: Standard deviation = √Variance, therefore Variance = Standard Deviation². B inverts the relationship. C and D are incorrect — this is a mathematical relationship, not conditional on the mean.
Question 162
In the context of portfolio theory, diversification works best when asset returns are:
Select an option first.
Correct answer: B — Uncorrelated or negatively correlated
Explanation: Diversification reduces portfolio risk when assets do not move together — zero or negative correlation provides the greatest risk reduction benefit. Perfect positive correlation (A) eliminates all diversification benefit. C and D are irrelevant to diversification effectiveness.
Question 163
The portfolio variance of a two-asset portfolio is affected by:
Select an option first.
Correct answer: B — The individual asset variances and the covariance (or correlation) between the assets
Explanation: Portfolio variance = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁₂. The covariance term (2w₁w₂σ₁₂) is critical — it captures the diversification benefit (if negative) or amplification (if positive). A ignores correlations; C and D are incorrect.
Question 164
The efficient frontier in Modern Portfolio Theory represents:
Select an option first.
Correct answer: B — The set of portfolios offering the maximum expected return for each level of risk
Explanation: The efficient frontier is the upper-left boundary of the feasible set — for each risk level, it shows the maximum achievable expected return. A describes the full feasible set; C is just the global minimum variance portfolio (one point); D ignores risk.
Question 165
The risk-free rate is typically proxied by:
Select an option first.
Correct answer: B — Short-term government Treasury bill yields
Explanation: Short-term government T-bill yields are used as the risk-free rate proxy in theory because they are default-free and have negligible inflation uncertainty over the short term. A has credit spread; C is not widely traded; D has bank credit risk.
Question 166
The Sharpe ratio measures:
Select an option first.
Correct answer: B — Excess return over the risk-free rate per unit of total risk (standard deviation)
Explanation: Sharpe ratio = (Rp − Rf) / σp. It is the most widely used risk-adjusted performance metric, rewarding portfolios that generate higher excess returns per unit of volatility.
Question 167
Which of the following best describes 'duration' in the context of fixed income?
Select an option first.
Correct answer: B — A measure of a bond's price sensitivity to changes in interest rates, expressed in years
Explanation: Duration (specifically modified duration) measures how much a bond's price changes for a given change in yield. Higher duration = greater interest rate sensitivity. A is the legal maturity; C is a count of payments; D is credit risk.
Question 168
Modified duration of a bond is used to estimate:
Select an option first.
Correct answer: B — The approximate percentage change in bond price for a 1% change in yield
Explanation: Modified duration ≈ −(ΔP/P) / Δy. A 1% yield rise in a bond with modified duration of 5 years implies roughly a −5% price change. A is PD; C is yield-to-maturity; D is trading liquidity.
Question 169
Convexity in fixed income refers to:
Select an option first.
Correct answer: B — The curvature in the price-yield relationship — bonds typically gain more from yield decreases than they lose from equivalent yield increases
Explanation: Convexity captures the non-linear (curved) price-yield relationship. Positive convexity means that for large yield moves, the duration approximation understates the actual price increase and overstates the actual price decrease — a favourable property for holders.
Question 170
The yield-to-maturity (YTM) of a bond is:
Select an option first.
Correct answer: B — The discount rate that equates the present value of all cash flows to the bond's current market price
Explanation: YTM is the internal rate of return (IRR) of the bond — the single discount rate that makes the PV of all cash flows equal to the current price. A is the coupon rate; C is an assumption embedded in YTM (not its definition); D is credit spread.
Question 171
The current ratio is calculated as:
Select an option first.
Correct answer: B — Current assets / Current liabilities
Explanation: Current ratio = Current assets / Current liabilities. It is the most common short-term liquidity measure. A is an assets-to-liabilities ratio (solvency); C is a cash coverage ratio; D is equity ratio (leverage).
Question 172
The quick ratio (acid test ratio) differs from the current ratio in that it:
Select an option first.
Correct answer: B — Excludes inventory (and sometimes prepaid expenses) from current assets, as these may not be quickly convertible to cash
Explanation: Quick ratio = (Cash + Short-term investments + Receivables) / Current liabilities. Inventory is excluded because it may not be quickly converted to cash in a stress situation. This gives a more conservative liquidity view than the current ratio.
Question 173
The Treynor ratio differs from the Sharpe ratio in that it uses:
Select an option first.
Correct answer: B — Beta (systematic risk) rather than total risk (standard deviation) in the denominator
Explanation: Treynor ratio = (Rp − Rf) / βp. It measures excess return per unit of systematic risk (beta), making it appropriate for evaluating a portfolio that is part of a larger diversified whole. Sharpe uses total risk (σ).
Question 174
Jensen's alpha (α) measures:
Select an option first.
Correct answer: B — The excess return of a portfolio over what the Capital Asset Pricing Model would predict given its beta
Explanation: Jensen's α = Rp − [Rf + β(Rm − Rf)]. Positive alpha indicates the manager added value beyond what systematic risk exposure explains. A is the risk-free component; C is the Sharpe ratio; D is a correlation statistic.
Question 175
The Capital Market Line (CML) in portfolio theory connects:
Select an option first.
Correct answer: B — The risk-free asset to the market portfolio, representing optimal portfolios for investors
Explanation: The CML combines the risk-free asset with the market portfolio (tangency portfolio), showing the optimal capital allocation between risk-free and risky assets. All points on the CML are combinations of these two.
Question 176
Which of the following describes the 'time value of money' concept?
Select an option first.
Correct answer: B — A dollar received today is worth more than a dollar received in the future because of its potential to earn a return
Explanation: The time value of money (TVM) underpins all discounted cash flow analysis: present dollars can be invested to generate returns, making them more valuable than future dollars. A is too narrow (only inflation); C inverts the concept; D ignores opportunity cost.
Question 177
The present value (PV) of $1,000 to be received in 2 years, using a discount rate of 5% per year, is approximately:
Select an option first.
Correct answer: C — $907
Explanation: PV = 1000 / (1.05)² = 1000 / 1.1025 ≈ $907. A ($900) is slightly off; B ($1,050) mistakenly grows rather than discounts; D ($952) is the 1-year PV not 2-year.
Question 178
The future value (FV) of $1,000 invested today at 6% per year for 3 years (compounded annually) is:
Select an option first.
Correct answer: C — $1,191
Explanation: FV = 1000 × (1.06)³ = 1000 × 1.191016 ≈ $1,191. A is only 1-year growth; B is simple interest for 3 years (1000 × 1.18); D uses 6.67% per year erroneously.
Question 179
Which of the following is the correct formula for the Sharpe ratio?
Select an option first.
Correct answer: B — (Portfolio return − Risk-free rate) / Portfolio standard deviation
Explanation: Sharpe ratio = (Rp − Rf) / σp. A is information ratio; C is Treynor ratio; D is not a standard risk-adjusted measure.
Question 180
If a bond has a modified duration of 7 and yield rises by 50 basis points (0.50%), the approximate percentage change in the bond's price is:
Select an option first.
Correct answer: B — −3.5%
Explanation: ΔP/P ≈ −Modified Duration × Δy = −7 × 0.005 = −0.035 = −3.5%. The negative sign indicates price falls when yield rises. A has wrong sign; C and D apply a 1% yield change.
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