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Free Questions › CFA › Portfolio Management
Free CFA Portfolio Management Practice Questions & Answers
1,100 exam-style Portfolio Management questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 901
If risk-free rate = 4% and an investor puts all money into risk-free asset, the portfolio's:
Select an option first.
Correct answer: C — Standard deviation is 0% and expected return is 4%
Explanation: The risk-free asset offers a certain, known return with zero variance/standard deviation. E(R)=Rf=4%, σ=0%, β=0. A, B, D are wrong.
Question 902
In mean-variance optimization, the trade-off between risk and return is captured by:
Select an option first.
Correct answer: B — The utility function — specifically the risk aversion parameter (A)
Explanation: The risk aversion coefficient (A) in U = E(R) − ½Aσ² determines how much return the investor demands per unit of variance. Higher A = more penalty for risk = more conservative optimal portfolio. A is external benchmark. C is breadth. D affects portfolio risk calculation.
Question 903
Adding a low-correlation asset to an existing portfolio produces which of the following effects on the efficient frontier?
Select an option first.
Correct answer: B — The efficient frontier shifts outward (more favorable — higher return for same risk or lower risk for same return)
Explanation: More assets with low correlations expand the investment opportunity set, pushing the efficient frontier outward — offering better risk-return tradeoffs previously unavailable. A is the opposite. C ignores the new diversification opportunity. D is only with risk-free asset.
Question 904
Which of the following correctly describes the standard deviation of a portfolio as the number of assets grows very large, assuming all assets have equal weight, equal variance σ², and all pairwise correlations equal ρ?
Select an option first.
Correct answer: B — σp² approaches ρσ²
Explanation: As N→∞: σp² = (1/N)σ² + [(N-1)/N]ρσ² → ρσ² (the average covariance). Individual variance term (1/N)σ²→0 but the covariance term remains. A ignores diversification. C requires ρ=0. D is correct only if ρ=0.
Question 905
Returns over 4 years: +20%, +20%, -20%, -20%. What is the geometric mean return?
Select an option first.
Correct answer: C — -2.0%
Explanation: (1.2)(1.2)(0.8)(0.8) = 1.44×0.64 = 0.9216. GR = (0.9216)^0.25 − 1 = 0.97879−1 = −2.12% ≈ −2.0%. The investor actually lost money despite equal +/− swings. B is arithmetic mean = 0%. A and D are wrong.
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Question 906
An investor puts $50,000 in Stock A (σ=25%) and $50,000 in Stock B (σ=25%) with ρ=−1.0. Portfolio standard deviation is:
Select an option first.
Correct answer: C — 0%
Explanation: With ρ=−1 and equal weights and equal standard deviations: σp = |w_A×σ_A − w_B×σ_B| = |0.5×25 − 0.5×25| = 0%. Perfect cancellation. A is each asset's σ. B is a partial cancellation. D would be ρ=0.
Question 907
Asset P: E(R)=9%, σ=12%; Asset Q: E(R)=14%, σ=20%. Equal weights, ρ=0.25. Portfolio σ is closest to:
Select an option first.
Correct answer: A — 12.9%
Explanation: σp² = (0.5)²(0.12)²+(0.5)²(0.20)²+2(0.5)(0.5)(0.25)(0.12)(0.20) = 0.0036+0.01+0.003 = 0.0166. σp=√0.0166=12.88%≈12.9%. B is too high (ignores diversification). C and D are wrong.
Question 908
A $100,000 portfolio has σ=20%. An investor adds $100,000 in a zero-correlation asset with σ=20%. New portfolio σ (equal weights, ρ=0) is:
Select an option first.
Correct answer: B — 14.1%
Explanation: σp = σ/√2 = 20%/√2 = 14.14% ≈ 14.1%. Equal weights, same σ, zero correlation reduces σ by factor of √2. A ignores diversification. C and D are wrong.
Question 909
Which of the following is TRUE about the geometric mean return relative to the arithmetic mean?
Select an option first.
Correct answer: C — Arithmetic mean > geometric mean when returns are volatile, and they are equal only when all returns are identical
Explanation: For any set of returns with variance > 0, arithmetic mean > geometric mean. They converge to the same value only if all returns are identical (zero variance). A is wrong. B reverses the relationship. D is wrong — geometric mean is specifically for multi-period compounding.
Question 910
A hedge fund reports monthly returns with high positive skewness. An investor using only mean and variance to evaluate this fund may:
Select an option first.
Correct answer: B — Underestimate the fund's risk because positive skew often involves tail risk
Explanation: Mean-variance analysis ignores skewness. Positive skewness often conceals embedded short positions in tail risk (like selling insurance) that look good in normal times but suffer in crises. A ignores skewness. C and D are wrong.
Question 911
The 'two-fund separation theorem' implies that a risk-averse investor who can access the risk-free rate:
Select an option first.
Correct answer: B — Should hold a portfolio that mixes risk-free and the tangency portfolio, with proportions reflecting their risk preference
Explanation: The theorem says all investors hold the same risky portfolio (tangency/market) — they adjust risk exposure by varying the mix with the risk-free asset. Less risk-averse investors: more in the risky portfolio. More risk-averse: more in risk-free. A is risk-free only. C is naive diversification. D ignores risk.
Question 912
Which of the following can shift the efficient frontier of risky assets outward (improve it)?
Select an option first.
Correct answer: B — Adding new risky assets with low correlation to the existing set
Explanation: Adding low-correlation assets expands the investment opportunity set, shifting the efficient frontier outward. C changes investor preferences, not the frontier. D reduces options. A is about the risk-free rate, not the risky asset frontier.
Question 913
The correlation between the returns of two assets in a portfolio is +1.0. The portfolio's standard deviation is:
Select an option first.
Correct answer: C — Equal to the weighted average of the two standard deviations
Explanation: When ρ=+1, there is no diversification benefit. σp = w1σ1 + w2σ2 (exactly the weighted average). A is for ρ < +1. B would require negative correlation. D requires ρ=−1 with specific weights.
Question 914
What does a negative covariance between two assets imply about how they tend to move together?
Select an option first.
Correct answer: B — They tend to move in opposite directions — when one is above its mean, the other tends to be below its mean
Explanation: Negative covariance indicates that the two assets tend to move in opposite directions relative to their respective means. This provides diversification benefit. A overstates ('always'). C is a specific case (Cov=0). D is unrelated.
Question 915
Which of the following is an example of 'downside risk' that variance alone does not fully capture?
Select an option first.
Correct answer: B — The probability and magnitude of large losses in adverse market conditions
Explanation: Variance treats upside and downside deviations symmetrically. Downside risk measures like CVaR, semi-variance, or max drawdown focus specifically on large negative outcomes. A is return. C is correlation. D is CAPM-related.
Question 916
The Markowitz efficient frontier assumes investors care about:
Select an option first.
Correct answer: C — Expected return and variance of portfolio returns
Explanation: Markowitz mean-variance analysis assumes investors evaluate portfolios based solely on expected return (maximize) and variance (minimize). D includes skewness which is beyond basic Markowitz. A and B are each only half the picture.
Question 917
Which of the following best describes 'semi-variance' as a risk measure?
Select an option first.
Correct answer: B — Variance computed using only returns below the mean (or a target), focusing on downside risk
Explanation: Semi-variance measures the dispersion of returns that fall below the mean or a specified target return. It is a downside risk measure that penalizes only negative deviations. A is standard deviation. C and D are wrong.
Question 918
Historical data for US markets shows that over long periods, equities have provided higher average nominal returns than bonds primarily because:
Select an option first.
Correct answer: C — Equities carry more risk (higher volatility and potential for losses), warranting a risk premium
Explanation: The equity risk premium compensates investors for bearing greater uncertainty and risk compared to bond investors. This is the foundational risk-return principle. A reverses the priority (bonds rank above equity). B and D are wrong.
Question 919
A portfolio with expected return 10% and standard deviation 18% has a coefficient of variation of:
Select an option first.
Correct answer: A — 1.8
Explanation: Coefficient of Variation = σ/E(R) = 18%/10% = 1.8. This measures risk per unit of return. B is the reciprocal. C and D are wrong (not ratios).
Question 920
The Capital Allocation Line becomes steeper as the Sharpe ratio of the chosen risky portfolio:
Select an option first.
Correct answer: C — Increases
Explanation: The slope of the CAL equals the Sharpe ratio. A higher Sharpe ratio = steeper CAL = better risk-return tradeoff for investors combining the risky portfolio with the risk-free asset. A is flatter. B is no change. D is downward sloping (suboptimal).
Question 921
Which of the following correctly describes the relationship between the investment opportunity set and the efficient frontier?
Select an option first.
Correct answer: B — The efficient frontier is a subset of the investment opportunity set — it contains only non-dominated portfolios
Explanation: The investment opportunity set includes ALL feasible portfolios. The efficient frontier includes only the non-dominated ones (maximum return per risk level). A, C, D are wrong.
Question 922
All else equal, which factor has the LARGEST influence on reducing portfolio variance through diversification?
Select an option first.
Correct answer: B — The pairwise correlations between assets in the portfolio
Explanation: In a large portfolio, portfolio variance ≈ average pairwise covariance (= ρ × σ²_avg). The level of correlation between assets is the most powerful determinant of how much diversification benefit is achieved. A matters early but becomes less important beyond ~30 assets. C affects individual risk but not the diversification effect. D is return, not risk.
Question 923
A portfolio of assets where all pairwise correlations equal +1.0 is:
Select an option first.
Correct answer: C — Not diversified — equivalent to holding a single asset
Explanation: When all pairwise correlations = +1, there is zero diversification benefit. The portfolio variance equals the weighted-average variance. There is no risk reduction from combining assets. A, B are wrong. D is wrong — this portfolio is on the minimum-variance frontier but is inefficient due to concentration.
Question 924
Which of the following is MOST likely to be negatively correlated with equities, providing the best diversification benefit?
Select an option first.
Correct answer: C — Gold or government bonds during market stress
Explanation: Gold and high-quality government bonds often exhibit negative or low correlation with equities during market stress (flight to safety). A and B are positively correlated with equities. D (high-yield bonds) has substantial equity-like risk and is positively correlated.
Question 925
An investor who plots indifference curves that are very steep (near vertical) in mean-standard deviation space is:
Select an option first.
Correct answer: C — Highly risk averse — requires large return increments for accepting more risk
Explanation: Very steep (nearly vertical) indifference curves mean the investor requires huge return compensation for any increase in risk — indicating extreme risk aversion. A (near horizontal) is risk neutral. B is risk-seeking. D is irrelevant.
Question 926
Which of the following would shift the entire efficient frontier to the LEFT (lower risk for same returns) for all portfolios?
Select an option first.
Correct answer: B — Discovering a new asset class with very low correlation to existing assets
Explanation: Adding an asset class with very low correlation shifts the efficient frontier outward (lower risk for same return = leftward shift in risk-return space). A shifts it upward (higher return for same risk). C and D are harmful.
Question 927
The variance of a portfolio with two perfectly positively correlated assets (ρ=+1) equals:
Select an option first.
Correct answer: A — (w1σ1 + w2σ2)²
Explanation: When ρ=+1: σp² = w1²σ1² + w2²σ2² + 2w1w2σ1σ2 = (w1σ1+w2σ2)². So σp = w1σ1+w2σ2 (weighted average of standard deviations). B ignores the cross term. C requires ρ=−1 with equal weights. D has a minus sign (would be ρ=−1).
Question 928
An investor has a portfolio with expected return 12% and σ=20%. Sharpe ratio (Rf=4%) is:
Select an option first.
Correct answer: A — 0.40
Explanation: Sharpe=(12-4)/20=8/20=0.40. B would need excess return=10%. C and D are wrong.
Question 929
If the Sharpe ratio of a portfolio is 0.6 and σ=15%, the excess return above Rf is:
Select an option first.
Correct answer: A — 9.0%
Explanation: Excess return = Sharpe × σ = 0.6 × 15% = 9.0%. B, C, D are wrong.
Question 930
Which of the following combinations would produce a portfolio with the HIGHEST possible Sharpe ratio?
Select an option first.
Correct answer: C — High-return assets combined with zero-correlation diversifiers
Explanation: A portfolio that combines high expected returns with assets that reduce risk through zero correlation (diversification) maximizes the Sharpe ratio. A has high return but limited diversification. B has low return limiting numerator. D is random.
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