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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 781
The covariance of an asset's returns with itself equals:
Select an option first.
Correct answer: C — Its variance
Explanation: Cov(X, X) = E[(X−μ)(X−μ)] = E[(X−μ)²] = Variance(X). The covariance of a variable with itself is its own variance. A and D are wrong. B is wrong — correlation of X with itself = 1.
Question 782
A portfolio of three assets has weights 40%, 35%, and 25% with expected returns 10%, 8%, and 6% respectively. The portfolio expected return is:
Select an option first.
Correct answer: B — 8.3%
Explanation: E(Rp) = 0.40×10 + 0.35×8 + 0.25×6 = 4.0 + 2.8 + 1.5 = 8.3%. A uses simple average. C and D are wrong.
Question 783
An asset's annual returns for 3 years are: Year 1: +30%, Year 2: -20%, Year 3: +10%. The geometric mean return is closest to:
Select an option first.
Correct answer: D — 4.4%
Explanation: Geometric mean = [(1.30)(0.80)(1.10)]^(1/3) − 1 = [1.144]^(1/3) − 1 = 1.04543 − 1 = 4.54% ≈ 4.4%. Arithmetic mean = (30-20+10)/3 = 6.67%. A, B, C are wrong.
Question 784
Asset 1: σ=20%, Asset 2: σ=15%, ρ=0.2. The minimum-variance portfolio weight in Asset 1 using w1=(σ2²−ρσ1σ2)/(σ1²+σ2²−2ρσ1σ2) is closest to:
Select an option first.
Correct answer: A — 32.7%
Explanation: w1 = (225 − 0.2×20×15) / (400+225−2×0.2×20×15) = (225−60)/(625−120) = 165/505 = 32.67% ≈ 32.7%. B, C, D are wrong.
Question 785
Which of the following correlation values between two assets would provide the greatest risk reduction in a portfolio?
Select an option first.
Correct answer: D — ρ = -0.8
Explanation: The lower (more negative) the correlation, the greater the diversification benefit and risk reduction. ρ = −0.8 provides the greatest offset between the two assets' movements. A provides almost no benefit. B and C provide some benefit. D is the best.
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Question 786
A portfolio's variance is lower than the weighted-average variance of its components. This is because:
Select an option first.
Correct answer: B — The covariance terms in the variance formula reduce total portfolio variance when assets are not perfectly correlated
Explanation: Portfolio variance = Σwᵢ²σᵢ² + Σᵢ≠ⱼ2wᵢwⱼCov(i,j). When covariances are less than the product of standard deviations (i.e., correlation < 1), the portfolio variance is less than the weighted-average variance. A, C, D are not accurate explanations.
Question 787
An investor constructs a portfolio of 30 stocks. The unsystematic risk of the portfolio is:
Select an option first.
Correct answer: C — Significantly reduced but approximately equal to the average covariance between stocks
Explanation: With 30 well-chosen stocks, most idiosyncratic risk is eliminated. The remaining portfolio risk is mostly systematic — approximately the average covariance among the stocks. A and D are wrong. B is too absolute — complete elimination requires infinite stocks or zero covariances.
Question 788
The utility function in mean-variance analysis is often written as U = E(R) − ½Aσ², where A is the risk aversion coefficient. If A increases, the investor:
Select an option first.
Correct answer: C — Places a greater penalty on portfolio variance and prefers lower-risk portfolios
Explanation: A higher A means the utility loss from variance is larger. The investor penalizes risk more heavily and therefore prefers portfolios with lower variance, even at the cost of lower expected return. A and B describe lower A. D is risk neutrality (A=0).
Question 789
An investor with a utility function U = E(R) − ½Aσ² has A = 4. Portfolio X has E(R)=10%, σ=15%. Portfolio Y has E(R)=8%, σ=10%. Which portfolio has higher utility?
Select an option first.
Correct answer: B — Portfolio Y (U = 6.0%)
Explanation: U_X = 10 − ½×4×(0.15)² = 10 − 2×0.0225 = 10 − 4.5 = 5.5% (in %). U_Y = 8 − ½×4×(0.10)² = 8 − 2×0.01 = 8 − 2.0 = 6.0%. Portfolio Y has higher utility (6.0% > 5.5%). B is correct.
Question 790
The global minimum-variance portfolio (GMVP) is:
Select an option first.
Correct answer: B — The leftmost point on the minimum-variance frontier — the portfolio with the absolute lowest possible variance
Explanation: The GMVP is at the leftmost tip of the minimum-variance frontier — the absolute minimum variance achievable from the universe of risky assets. A describes the tangency portfolio. C is naive diversification. D cannot exist for a portfolio of only risky assets.
Question 791
In mean-variance optimization, the tangency portfolio is:
Select an option first.
Correct answer: B — The portfolio where the CML is tangent to the efficient frontier of risky assets — the optimal risky portfolio
Explanation: The tangency portfolio is where the CAL (drawn from the risk-free rate) touches the efficient frontier of risky assets. It has the highest Sharpe ratio among all risky portfolios. Under CAPM, this is the market portfolio. A and C are other points. D is not a portfolio.
Question 792
As more assets are added to a portfolio, which of the following correctly describes how the number of covariance terms compares to variance terms?
Select an option first.
Correct answer: C — Covariance terms grow much faster — for N assets, there are N variance terms but N(N-1)/2 unique covariances
Explanation: For N assets: N variance terms but N(N−1)/2 covariance terms. For 10 assets: 10 variance, 45 covariance. For 100 assets: 100 variance, 4,950 covariance. Covariances dominate portfolio risk in large portfolios. A, B, D are wrong.
Question 793
An investor is considering adding Asset Z to an existing portfolio. Asset Z has a very high standard deviation but near-zero correlation with the portfolio. The portfolio's risk will most likely:
Select an option first.
Correct answer: C — Decrease or increase only marginally
Explanation: When adding an asset with near-zero correlation to an existing portfolio, the diversification benefit can actually reduce or only marginally change portfolio risk, even if the added asset is very volatile. The key driver is the correlation with the existing portfolio. A and D are wrong. B is too precise.
Question 794
The risk-return tradeoff implies that:
Select an option first.
Correct answer: B — Investors must accept more risk to achieve higher expected returns
Explanation: The risk-return tradeoff is foundational: to achieve higher expected returns, investors must accept higher risk. There is no free lunch — higher expected return requires bearing more risk. A uses 'realized' (actual returns can disappoint). C reverses the relationship. D is wrong.
Question 795
Which statement about the efficient frontier is most accurate?
Select an option first.
Correct answer: B — Efficient portfolios dominate all other feasible portfolios in terms of return per unit of risk
Explanation: The efficient frontier contains portfolios that offer the maximum expected return for each level of risk (or minimum risk for each return level) — they dominate all other portfolios. A is wrong (returns vary along the frontier). C includes inefficient portfolios. D is wrong — it's a set of portfolios.
Question 796
An investor who prefers more return is said to have a preference for:
Select an option first.
Correct answer: C — Non-satiation — they always prefer more wealth to less
Explanation: Non-satiation (more is preferred to less) is a basic assumption of investor behavior — investors always prefer higher returns to lower returns, all else being equal. A is not a preference for return. B and D are different concepts.
Question 797
Historical data shows that small-cap stocks have outperformed large-cap stocks over long periods. This premium most likely exists because:
Select an option first.
Correct answer: C — Small-cap stocks carry higher risk (including liquidity risk and greater uncertainty) that the market compensates
Explanation: The size premium (small-cap outperformance) is typically attributed to higher risk — small companies have more uncertainty, lower liquidity, and higher probability of distress. These risks warrant a higher return. A reverses the logic. B is wrong (small caps are less liquid). D is not the primary explanation.
Question 798
The Sharpe ratio of the tangency portfolio equals the slope of the:
Select an option first.
Correct answer: C — Capital allocation line
Explanation: The Sharpe ratio is exactly the slope of the CAL. The tangency portfolio has the maximum Sharpe ratio, so its CAL has the steepest slope possible. A is the SML slope (market risk premium). B is the frontier's slope. D is the investor's MRS.
Question 799
Which measure of return is most appropriate for evaluating multi-period compounded growth?
Select an option first.
Correct answer: B — Geometric mean return
Explanation: Geometric mean = [(1+R1)(1+R2)...(1+Rn)]^(1/n) − 1. It correctly compounds returns over time and reflects actual wealth accumulation. Arithmetic mean (A) is useful for single-period expected returns. C and D are the same as A in this context.
Question 800
Which of the following is closest to a 'mean-variance efficient' portfolio for a risk-averse investor?
Select an option first.
Correct answer: C — The portfolio that maximizes utility given the investor's risk-return tradeoff
Explanation: Mean-variance efficiency means maximizing utility (a function of both expected return and risk) for the given investor. The optimal portfolio depends on risk aversion. A ignores risk. B ignores return. D includes inefficient portfolios.
Question 801
If an investor borrows at the risk-free rate to invest more than 100% of wealth in the risky portfolio, the position on the CAL is:
Select an option first.
Correct answer: C — Beyond the risky portfolio — a leveraged position
Explanation: Borrowing at Rf to invest more than 100% in the risky portfolio creates a leveraged position beyond the tangency point. This earns higher expected return but more risk. The position plots on the CAL but above the risky portfolio. A is a partial allocation. B is 100% risky.
Question 802
For a normal distribution of returns, approximately what percentage of observations fall within one standard deviation of the mean?
Select an option first.
Correct answer: B — 68%
Explanation: For a normal distribution: ±1σ ≈ 68.3%, ±2σ ≈ 95.4%, ±3σ ≈ 99.7%. A is wrong. C is ±2σ. D is ±3σ.
Question 803
The historical equity risk premium (ERP) represents:
Select an option first.
Correct answer: B — The excess return earned by equities over risk-free government bonds historically
Explanation: The ERP is the historical average excess return of stocks over T-bills or government bonds. It compensates investors for bearing equity risk. A is just Rf. C is total risk. D is a forward-looking concept.
Question 804
A leptokurtic return distribution (excess kurtosis > 0) implies:
Select an option first.
Correct answer: C — Extreme returns (both positive and negative) occur more frequently than a normal distribution predicts
Explanation: Leptokurtic (fat-tailed) distributions have more probability in the tails — more frequent extreme outcomes than a normal distribution. This is dangerous for risk models that assume normality. A is normal. B is platykurtic (thin tails). D is a skewness concept.
Question 805
In the context of portfolio construction, 'correlation' is preferable to 'covariance' for comparisons because:
Select an option first.
Correct answer: B — Correlation is standardized between -1 and +1, making comparisons across asset pairs easy
Explanation: Correlation = Cov(i,j)/(σiσj), scaling covariance to a [-1,+1] range. This normalization makes it easy to compare how strongly two asset pairs move together. Raw covariance values depend on the scale of returns. A and C are wrong. D is wrong.
Question 806
If an investor's indifference curve is steeper than the efficient frontier at the tangency point, the investor should:
Select an option first.
Correct answer: A — Move to a point with lower risk and return
Explanation: A steeper indifference curve than the frontier at the tangency means the investor is giving up too much return for risk at that point — their optimal is at a lower-risk, lower-return point. B would apply if the frontier is steeper (more risk-tolerant). C and D are wrong.
Question 807
Portfolio standard deviation calculation for a two-asset portfolio uses the formula σp² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov(1,2). If Cov(1,2) = 0, this simplifies to:
Select an option first.
Correct answer: B — σp² = w₁²σ₁² + w₂²σ₂²
Explanation: When Cov = 0 (uncorrelated), the cross term disappears: σp² = w₁²σ₁² + w₂²σ₂². Portfolio variance is just the weighted sum of individual variances. A is for ρ=+1. C and D are wrong.
Question 808
A portfolio of 100 equally weighted assets each with variance σ² and mutual covariance Cov approximates a variance of:
Select an option first.
Correct answer: B — Cov (the average covariance)
Explanation: For N equally weighted assets, portfolio variance ≈ (1/N)σ² + [(N-1)/N]Cov → Cov as N→∞. With 100 assets, most of the individual variance is diversified away; what remains is approximately the average covariance. A is approximately correct only if Cov=0.
Question 809
Asset X: E(R)=8%, σ=10%. Asset Y: E(R)=12%, σ=20%. Portfolio: 40% in X, 60% in Y, ρ=0.5. Portfolio standard deviation is closest to:
Select an option first.
Correct answer: A — 14.4%
Explanation: σp² = (0.4)²(0.10)² + (0.6)²(0.20)² + 2(0.4)(0.6)(0.10)(0.20)(0.5) = 0.16×0.01 + 0.36×0.04 + 0.48×0.01 = 0.0016+0.0144+0.0048 = 0.0208. σp = √0.0208 = 14.42% ≈ 14.4%. B, C, D are wrong.
Question 810
Using the same data, the portfolio expected return is:
Select an option first.
Correct answer: A — 10.4%
Explanation: E(Rp) = 0.40×8% + 0.60×12% = 3.2% + 7.2% = 10.4%. B, C, D are wrong.
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