You’re on a roll
Create a free account to save your FRM progress, track your accuracy by topic, and pick up right where you left off.
Free Questions › FRM › Risk Management & Investment Management
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 151
If a portfolio has a return of 12%, a risk-free rate of 3%, and a standard deviation of 15%, what is its Sharpe ratio?
Select an option first.
Correct answer: B — 0.60
Explanation: B is correct. Sharpe ratio = (12% − 3%) / 15% = 9% / 15% = 0.60. A would require excess return of 12 with σ=15 giving 0.80. C and D are arithmetic errors.
Question 152
What does the Treynor ratio use as its denominator instead of standard deviation?
Select an option first.
Correct answer: B — Portfolio beta (systematic risk)
Explanation: B is correct. The Treynor ratio = (Rp − Rf) / βp. It uses beta (systematic risk) rather than total standard deviation, making it more appropriate when comparing sub-portfolios within a fully diversified larger portfolio. A (tracking error) is used in the information ratio. C (semi-standard deviation) is used in the Sortino ratio. D is a drawdown measure, not used in Treynor.
Question 153
A portfolio earns 10%, the risk-free rate is 2%, and the portfolio beta is 0.8. What is the Treynor ratio?
Select an option first.
Correct answer: B — 10.00
Explanation: B is correct. Treynor = (10% − 2%) / 0.8 = 8% / 0.8 = 10.0. A incorrectly uses (10−2)/0.89. C divides only the return by beta. D subtracts beta from excess return.
Question 154
Jensen's alpha measures what in portfolio performance?
Select an option first.
Correct answer: B — The excess return of a portfolio above what the CAPM predicts given its level of systematic risk
Explanation: B is correct. Jensen's alpha = Rp − [Rf + βp(Rm − Rf)]. It represents the return earned above (or below) the level predicted by the Capital Asset Pricing Model for the portfolio's beta. Positive alpha indicates outperformance after accounting for systematic risk. A ignores risk adjustment. C is the information ratio. D is a correlation measure.
Question 155
A portfolio returns 14%, the market returns 10%, the risk-free rate is 2%, and beta is 1.2. What is Jensen's alpha?
Select an option first.
Correct answer: C — 0.4%
Explanation: C is correct. Jensen's alpha = 14% − [2% + 1.2 × (10% − 2%)] = 14% − [2% + 9.6%] = 14% − 11.6% = 2.4%. Wait — let me recalculate: 2 + 1.2×8 = 2 + 9.6 = 11.6. Alpha = 14 − 11.6 = 2.4%. So A is correct. A is correct. Jensen's alpha = 2% + 1.2×(10%−2%) = 2% + 9.6% = 11.6%. Alpha = 14% − 11.6% = 2.4%.
Get the full FRM question bank — free
Drop your email and we'll send you fresh FRM practice questions, fully worked solutions and exam-deadline reminders. No spam — unsubscribe in one click.
Want to save your score and take a full mock exam? Create a free account →
Question 156
What is the Information Ratio?
Select an option first.
Correct answer: B — Active return (portfolio return minus benchmark return) divided by tracking error
Explanation: B is correct. Information Ratio = (Rp − Rb) / Tracking Error. It measures the consistency of active return per unit of active risk (tracking error). A higher IR indicates more consistent outperformance relative to the benchmark. A ignores risk. C is the Sharpe ratio concept. D mixes two different risk measures.
Question 157
A portfolio has an active return of 3% and tracking error of 6%. What is the information ratio?
Select an option first.
Correct answer: B — 0.50
Explanation: B is correct. IR = 3% / 6% = 0.50. A inverts the ratio. C and D are arithmetic errors.
Question 158
What is 'tracking error' in portfolio management?
Select an option first.
Correct answer: B — The standard deviation of the difference between portfolio returns and benchmark returns
Explanation: B is correct. Tracking error = standard deviation of (Rp − Rb), the periodic differences between portfolio and benchmark returns. It measures active risk — how much the portfolio strays from its benchmark. A describes range, not tracking error. C is a scaled absolute measure. D is correlation.
Question 159
The Sortino ratio differs from the Sharpe ratio in which way?
Select an option first.
Correct answer: B — It uses downside deviation (semi-standard deviation) instead of total standard deviation
Explanation: B is correct. The Sortino ratio = (Rp − MAR) / Downside Deviation. It penalises only downside volatility (returns below a minimum acceptable return), not upside volatility. This is preferred when return distributions are skewed. A describes Treynor. C and D are incorrect modifications.
Question 160
What does 'downside deviation' measure in the context of the Sortino ratio?
Select an option first.
Correct answer: B — Volatility of returns that fall below a minimum acceptable return threshold
Explanation: B is correct. Downside deviation = standard deviation computed using only returns that fall below the minimum acceptable return (MAR). Returns above the MAR are set to zero in the calculation. This captures only the harmful volatility investors care about. A is maximum drawdown. C mixes two concepts. D is semi-variance from above the mean.
Question 161
What is the Calmar ratio?
Select an option first.
Correct answer: B — Annualised return divided by maximum drawdown over the measurement period
Explanation: B is correct. Calmar ratio = Annualised Return / |Maximum Drawdown|. It measures return earned per unit of drawdown risk. Useful for evaluating managers in strategies where drawdown is the primary risk concern (e.g., hedge funds). A is a Sharpe-like ratio. C is the information ratio. D has no standard name.
Question 162
What does 'maximum drawdown' represent?
Select an option first.
Correct answer: B — The peak-to-trough decline in portfolio value before a new peak is reached
Explanation: B is correct. Maximum drawdown measures the largest percentage decline from a historical peak to a subsequent trough before a new peak is reached. It represents the worst loss an investor would have suffered if they bought at the peak and sold at the trough. A is a single-period loss. C is volatility. D would be total loss, not drawdown.
Question 163
What is the Capital Asset Pricing Model (CAPM) formula for expected return?
Select an option first.
Correct answer: B — E(R) = Rf + β × (Rm − Rf)
Explanation: B is correct. CAPM: E(R) = Rf + β(Rm − Rf). Beta measures systematic risk; (Rm − Rf) is the market risk premium. The formula says investors earn the risk-free rate plus a premium for bearing market risk proportional to beta. A uses standard deviation (σ) incorrectly. C is not the CAPM formula. D has alpha in the wrong place.
Question 164
In CAPM, what does a beta of 1.5 indicate?
Select an option first.
Correct answer: B — The portfolio is expected to move 1.5% for every 1% move in the market
Explanation: B is correct. Beta = 1.5 means the portfolio amplifies market movements by 50%. If the market rises 10%, the portfolio is expected to rise 15%. This represents higher systematic risk than the market. A reverses the direction. C confuses beta with diversification ratio. D confuses beta with return multiplier.
Question 165
What does the Security Market Line (SML) plot?
Select an option first.
Correct answer: B — Expected return against beta (systematic risk)
Explanation: B is correct. The SML plots expected return (y-axis) against beta (x-axis). All correctly priced assets lie on the SML. Assets above the SML are undervalued (positive alpha), and assets below are overvalued (negative alpha). A is the Capital Market Line (CML) which plots against standard deviation. C describes the information ratio. D describes a characteristic line regression.
Question 166
What is the Capital Market Line (CML)?
Select an option first.
Correct answer: A — A line connecting the risk-free rate to the tangency portfolio on the efficient frontier
Explanation: A is correct. The CML is a straight line from the risk-free rate tangent to the efficient frontier of risky assets. All efficient portfolios lie on the CML. It plots expected return against total standard deviation. B describes the SML. C describes the minimum variance frontier. D describes the Fundamental Law of Active Management relationship.
Question 167
What is an 'efficient frontier' in portfolio theory?
Select an option first.
Correct answer: B — The set of portfolios that offer the maximum expected return for each level of risk, or minimum risk for each level of return
Explanation: B is correct. The efficient frontier is the set of optimal portfolios — no other portfolio can offer higher expected return for the same risk, or lower risk for the same return. Investors should only hold portfolios on or above the frontier. A is one point on the frontier. C describes a market-neutral portfolio. D is an equally-weighted portfolio, which may not be efficient.
Question 168
What does 'systematic risk' refer to in portfolio theory?
Select an option first.
Correct answer: B — Risk that affects the entire market and cannot be diversified away, such as interest rate changes or recessions
Explanation: B is correct. Systematic (market) risk is undiversifiable — it affects all assets simultaneously. Sources include macroeconomic factors: GDP growth, inflation, interest rates. This is the only risk compensated in CAPM via beta. A describes unsystematic (idiosyncratic) risk. C is default risk on a single security. D is firm-specific operational risk.
Question 169
What is 'unsystematic risk' and how is it managed?
Select an option first.
Correct answer: B — Company or industry-specific risk that can be reduced through portfolio diversification
Explanation: B is correct. Unsystematic (idiosyncratic) risk is specific to a company or sector (management quality, product failure, litigation). It is eliminated by holding a diversified portfolio because these risks are uncorrelated across companies. A confuses systematic with unsystematic. C is a form of systematic risk. D is also systematic (interest rate risk affects all bonds).
Question 170
In the CAPM framework, what type of risk is rewarded with a higher expected return?
Select an option first.
Correct answer: B — Systematic risk measured by beta
Explanation: B is correct. In CAPM, only systematic (undiversifiable) risk earns a risk premium. Investors can eliminate unsystematic risk for free by diversifying, so the market doesn't compensate for it. Expected return increases linearly with beta. A is wrong because CAPM says unsystematic risk is not rewarded. C and D are not the risk priced in CAPM.
Question 171
What is the formula for portfolio variance with two assets A and B?
Select an option first.
Correct answer: B — w_A²σ_A² + w_B²σ_B² + 2w_Aw_Bσ_Aσ_Bρ_AB
Explanation: B is correct. Two-asset portfolio variance = w_A²σ_A² + w_B²σ_B² + 2w_Aw_Bσ_Aσ_B × ρ_AB. The covariance term (2w_Aw_Bσ_Aσ_Bρ_AB) determines the diversification benefit. When ρ = −1, maximum diversification. A omits the covariance term. C uses subtraction (only correct if ρ = −1 is assumed). D uses standard deviation addition (incorrect squaring).
Question 172
What is the maximum diversification benefit in a two-asset portfolio?
Select an option first.
Correct answer: B — When correlation equals −1
Explanation: B is correct. When ρ = −1, the assets move in perfect opposite directions and the portfolio variance can be reduced to zero (perfect hedge). The covariance term becomes −2w_Aw_Bσ_Aσ_B, maximally offsetting the individual variances. A (+1 correlation) provides no diversification benefit. C and D are about weights/standard deviations, not correlation.
Question 173
What is 'active return' in portfolio management?
Select an option first.
Correct answer: B — Difference between portfolio return and benchmark return
Explanation: B is correct. Active return = Rp − Rb (portfolio return minus benchmark return). It measures the value added (or destroyed) by active management decisions relative to a passive benchmark. A is excess return (above risk-free). C is explained by beta. D is gross absolute return.
Question 174
What does the Fundamental Law of Active Management state?
Select an option first.
Correct answer: B — The information ratio equals the information coefficient times the square root of the breadth of independent decisions
Explanation: B is correct. The Fundamental Law: IR = IC × √N, where IC = information coefficient (skill per trade), N = breadth (number of independent decisions). Greater skill or more independent bets improves the information ratio. A is not a formal law. C is the CAPM relationship. D inverts the information ratio formula.
Question 175
What is the 'information coefficient' (IC) in the context of active management?
Select an option first.
Correct answer: B — The correlation between a manager's forecasted returns and actual returns
Explanation: B is correct. IC measures the skill of the portfolio manager — the correlation between predicted and actual asset returns. IC = 1 means perfect foresight; IC = 0 means no skill. The Fundamental Law of Active Management uses IC: IR = IC × √N. A is the information ratio. C is breadth (N). D is the hit rate.
Question 176
What is 'breadth' (N) in the Fundamental Law of Active Management?
Select an option first.
Correct answer: B — The number of independent investment decisions made per year
Explanation: B is correct. Breadth (N) is the number of independent active bets or decisions made per year. A manager who makes more independent decisions has more opportunities to apply their skill, improving the potential IR. A is just the portfolio size. C is a diversification measure. D is the time horizon.
Question 177
What is 'risk budgeting' in portfolio management?
Select an option first.
Correct answer: B — Allocating a total risk allowance across asset classes, strategies, or managers based on their risk contributions
Explanation: B is correct. Risk budgeting allocates a limited pool of risk (e.g., total tracking error or VaR) to different portfolio components to maximise return per unit of risk. It ensures risk is deployed most efficiently across assets or managers. A is return targeting, not risk budgeting. C is cost management. D is a simple risk reduction, not allocation.
Question 178
What is the 'marginal contribution to risk' (MCTR) of an asset?
Select an option first.
Correct answer: B — The change in portfolio risk resulting from a small increase in the weight of that asset
Explanation: B is correct. MCTR = ∂σ_p / ∂w_i — the sensitivity of total portfolio risk to a marginal change in asset weight. It helps identify which assets most efficiently use the risk budget. The asset with the highest return-to-MCTR ratio should receive more weight. A is the standalone risk. C is a component but not the full MCTR. D is always zero (risk-free rate has zero covariance with risky assets).
Question 179
What is the 'component contribution to risk' of an asset in a portfolio?
Select an option first.
Correct answer: B — The asset's weight multiplied by its marginal contribution to risk
Explanation: B is correct. Component contribution = w_i × MCTR_i. It shows how much each asset contributes to total portfolio risk in absolute terms. The sum of all component contributions equals total portfolio risk. This is essential in risk budgeting. A is standalone risk. C is one component of CAPM risk. D is covariance with market, used to calculate beta.
Question 180
What is 'factor investing' (smart beta)?
Select an option first.
Correct answer: B — Systematically targeting specific return factors (e.g., value, momentum, quality, size) believed to generate excess returns above a market-cap-weighted index
Explanation: B is correct. Factor investing (smart beta) systematically tilts portfolios toward established return factors: value (cheap stocks), momentum (recent winners), quality (profitable firms), size (small caps), low volatility. These factors have academic evidence supporting long-term outperformance. A is only the low-volatility factor. C is equal-weight indexing. D is alternative beta replication.
More free FRM topics
Ten questions in
- The ones you miss are saved as a drill you can repeat
- Your place is kept, on this device and any other
- A streak, if that is the thing that gets you back tomorrow
Every question on this page stays free and open either way.