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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 811
Utility function U = E(R) − ½Aσ², A=4. Portfolio A: E(R)=14%, σ=22%. What is the utility (expressed in %)?
Select an option first.
Correct answer: A — 4.32%
Explanation: U = 0.14 − ½×4×(0.22)² = 0.14 − 2×0.0484 = 0.14 − 0.0968 = 0.0432 = 4.32%. B would require σ=15%. C is wrong. D is wrong.
Question 812
Assets A and B have σA=16%, σB=12%, and correlation=0.4. What is their covariance (in %² units)?
Select an option first.
Correct answer: A — 76.8
Explanation: Cov(A,B) = ρ × σA × σB = 0.4 × 16 × 12 = 76.8 (%²). B would be 0.4×16×3 or wrong. C and D are wrong.
Question 813
Portfolio: 60% equities (σ=18%), 40% bonds (σ=8%), correlation=−0.2. Portfolio standard deviation is closest to:
Select an option first.
Correct answer: C — 10.6%
Explanation: σp² = (0.6)²(0.18)² + (0.4)²(0.08)² + 2(0.6)(0.4)(0.18)(0.08)(−0.2) = 0.011664+0.001024−0.001382 = 0.011306. σp = √0.011306 = 10.63% ≈ 10.6%. A would result from positive correlation. B is too high. D is too low.
Question 814
Asset A earns 5% in Year 1, 10% in Year 2, and -8% in Year 3. The geometric mean return is closest to:
Select an option first.
Correct answer: A — 2.1%
Explanation: GR = [(1.05)(1.10)(0.92)]^(1/3) − 1 = [1.0626]^(1/3) − 1 = 1.02066 − 1 = 2.07% ≈ 2.1%. Arithmetic mean = (5+10−8)/3 = 2.33%. B is arithmetic. C is close but slightly off. D ignores compounding.
Question 815
Which of the following best explains why the geometric mean return is always less than or equal to the arithmetic mean return?
Select an option first.
Correct answer: B — Geometric mean penalizes volatility — greater variance causes the geometric mean to fall further below the arithmetic mean
Explanation: The relationship is: Geometric mean ≈ Arithmetic mean − ½σ². Greater volatility (σ²) causes larger divergence between the two. This is why volatile assets' actual wealth accumulation underperforms their arithmetic average return. A is the opposite. C and D are wrong.
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Question 816
Which of the following is NOT a way to diversify a portfolio internationally?
Select an option first.
Correct answer: C — Investing in domestic companies with exclusively domestic operations
Explanation: Domestic companies with only domestic operations provide no international diversification — their returns are driven by domestic factors. A, B, D all involve exposure to foreign markets and currencies. D (multinational) provides indirect international exposure.
Question 817
The power of diversification is best illustrated by the fact that as you add more assets to a portfolio:
Select an option first.
Correct answer: C — Idiosyncratic risk is reduced while systematic risk remains
Explanation: Diversification reduces and ultimately eliminates unsystematic (idiosyncratic) risk. Systematic risk remains regardless of how many assets are held. A is not guaranteed. B is false for non-zero covariances. D is not a requirement.
Question 818
Which statement is most accurate about the relationship between portfolio size and risk?
Select an option first.
Correct answer: B — Risk reduction is fastest with the first few assets added; additional assets provide diminishing marginal benefit
Explanation: The marginal benefit of adding one more asset is highest when the portfolio is small. By 20-30 stocks, most diversifiable risk is eliminated and additional assets provide little further reduction. A and C suggest linearity. D is false — 5 stocks retain significant idiosyncratic risk.
Question 819
An asset has a positive expected return and a correlation of −1.0 with an existing portfolio. Adding this asset would:
Select an option first.
Correct answer: C — Reduce portfolio risk significantly, potentially to near zero if weights are chosen optimally
Explanation: Perfect negative correlation (ρ=−1) allows a portfolio to be constructed with very low or zero variance by choosing the right weights. This is the maximum possible diversification benefit. A is the ideal case with optimal weights. B is not guaranteed. D is wrong.
Question 820
The Sharpe ratio of a portfolio depends on:
Select an option first.
Correct answer: C — The portfolio's expected excess return relative to total risk (standard deviation)
Explanation: Sharpe ratio = (Rp − Rf) / σp. Both excess return and total risk (standard deviation) determine the Sharpe ratio. A and B are only partial inputs. D describes the Treynor ratio.
Question 821
Returns from different asset classes in different countries tend to have lower correlations than returns within a single country. The primary implication for investors is:
Select an option first.
Correct answer: C — International diversification can reduce portfolio risk compared to investing domestically only
Explanation: Lower cross-country correlations provide diversification benefits — adding international assets to a domestic portfolio can lower overall portfolio risk. A is wrong. B overstates currency risk impact. D ignores empirical evidence of lower international correlations.
Question 822
What does it mean for a portfolio to 'dominate' another portfolio?
Select an option first.
Correct answer: C — It offers at least as much return with less risk, or at least as much risk with more return (not worse in both dimensions)
Explanation: Dominance in mean-variance analysis means a portfolio is at least as good as another on one dimension (return or risk) and strictly better on the other. A dominated portfolio would never be chosen by a rational risk-averse investor. A and B describe the dominated portfolio. D ignores risk.
Question 823
Which of the following best describes the investment opportunity set for two risky assets?
Select an option first.
Correct answer: C — A curved (parabolic) set of portfolios representing all possible weight combinations
Explanation: Combining two risky assets in varying proportions traces a curved (parabolic) path in risk-return space. The shape depends on the correlation between the assets. A is the CAL (with risk-free asset). B is too narrow. D involves the risk-free asset.
Question 824
Which of the following most accurately describes why low-volatility portfolios often outperform high-volatility portfolios on a risk-adjusted basis?
Select an option first.
Correct answer: C — Low-volatility portfolios avoid the return drag caused by compounding losses — lower variance improves long-run geometric returns
Explanation: High volatility creates a drag on compounded returns: geometric mean ≈ arithmetic mean − ½σ². Lower volatility means less drag, so the portfolio compounds more efficiently over time. A and D are wrong. B makes no sense.
Question 825
Portfolio: 50% Asset A (return=12%, σ=20%) and 50% Asset B (return=8%, σ=12%). With correlation=0, portfolio expected return and standard deviation are:
Select an option first.
Correct answer: A — E(Rp)=10%, σp=11.7%
Explanation: E(Rp) = 0.5×12+0.5×8 = 10%. σp² = (0.5)²(0.20)² + (0.5)²(0.12)² + 0 = 0.25×0.04+0.25×0.0144 = 0.01+0.0036 = 0.0136. σp = √0.0136 = 0.1166 = 11.66% ≈ 11.7%. A is correct. B uses ρ=1. C has wrong return. D is wrong.
Question 826
Portfolio: 40% in Asset X (σ=15%), 60% in Asset Y (σ=25%), covariance = 150 (in %² units). Portfolio variance is:
Select an option first.
Correct answer: A — 333
Explanation: σp² = (0.4)²(15²) + (0.6)²(25²) + 2(0.4)(0.6)(150) = 36 + 225 + 72 = 333 (%²). B is only the Y component. C and D are wrong.
Question 827
From the above, portfolio standard deviation (in %) is closest to:
Select an option first.
Correct answer: A — 18.2%
Explanation: σp = √333 = 18.25% ≈ 18.2%. B is σ of Asset X. C is σ of Asset Y. D is wrong.
Question 828
An investor holds 80% in equities (σ=22%) and 20% in risk-free asset. Portfolio standard deviation is:
Select an option first.
Correct answer: A — 17.6%
Explanation: σp = w_equity × σ_equity = 0.80 × 22% = 17.6%. Risk-free asset has zero variance. B is 100% equity. C is 20%×22%. D is wrong.
Question 829
3-asset portfolio: w1=30% (σ1=10%), w2=40% (σ2=15%), w3=30% (σ3=20%). All correlations=0. Portfolio standard deviation is:
Select an option first.
Correct answer: A — 9.0%
Explanation: σp² = (0.3)²(10)²+(0.4)²(15)²+(0.3)²(20)² = 9+36+36 = 81 (%²). σp = 9%. This is much lower than any single asset's σ. B, C, D are wrong.
Question 830
Two assets: equal weights, σ1=20%, σ2=10%, ρ=−0.5. Portfolio variance is:
Select an option first.
Correct answer: A — 75 (%²)
Explanation: σp² = (0.5)²(20)²+(0.5)²(10)²+2(0.5)(0.5)(20)(10)(−0.5) = 100+25+2×0.25×(−100) = 125−50 = 75 (%²). B ignores the negative covariance. C and D are wrong.
Question 831
The arithmetic mean of returns {4%, 9%, -2%, 15%, 8%} is:
Select an option first.
Correct answer: A — 6.8%
Explanation: Mean = (4+9+(−2)+15+8)/5 = 34/5 = 6.8%. B, C, D are wrong.
Question 832
Returns: {4%, 9%, -2%, 15%, 8%}. Population variance is closest to:
Select an option first.
Correct answer: A — 31.8 (%²)
Explanation: Mean=6.8%. Deviations²: (4-6.8)²=7.84, (9-6.8)²=4.84, (-2-6.8)²=77.44, (15-6.8)²=67.24, (8-6.8)²=1.44. Sum=158.8. Variance=158.8/5=31.76≈31.8. B, C, D are wrong.
Question 833
Returns: {10%, 14%, -4%, 20%}. Mean=10%. Population standard deviation is closest to:
Select an option first.
Correct answer: A — 8.83%
Explanation: Pop variance = [(0²+4²+(−14)²+10²)]/4 = [0+16+196+100]/4 = 312/4 = 78. σ = √78 = 8.83%. B uses sample variance. C and D are wrong.
Question 834
An asset has returns of 15%, -10%, 20%, -5%. The arithmetic mean is:
Select an option first.
Correct answer: A — 5.0%
Explanation: Mean = (15-10+20-5)/4 = 20/4 = 5.0%. B, C, D are wrong.
Question 835
Returns: {15%, -10%, 20%, -5%}. Geometric mean return is closest to:
Select an option first.
Correct answer: A — 4.22%
Explanation: GR = [(1.15)(0.90)(1.20)(0.95)]^(0.25) − 1 = [1.1799]^0.25 − 1 = 1.0422 − 1 = 4.22%. B is arithmetic mean. C and D are wrong.
Question 836
An investor splits $200,000 equally between two assets. Asset A rises 40% and Asset B falls 20%. Portfolio return is:
Select an option first.
Correct answer: A — 10%
Explanation: Each asset starts at $100,000. A → $140,000; B → $80,000. Total = $220,000. Return = ($220,000−$200,000)/$200,000 = 10%. Alternatively: 0.5×40% + 0.5×(−20%) = 20% − 10% = 10%. B is Asset A only. C and D are wrong.
Question 837
Which asset class has historically had the LOWEST average nominal return?
Select an option first.
Correct answer: C — Treasury bills (cash equivalents)
Explanation: Treasury bills (short-term government securities) have historically earned the lowest nominal returns among asset classes — essentially just compensating for inflation with minimal risk premium. A has highest. D is between B and A. C is lowest.
Question 838
An investor wants the minimum possible portfolio variance from two assets with σ1=20%, σ2=30%, and ρ=0. Which weight in Asset 1 achieves this?
Select an option first.
Correct answer: B — 69.2%
Explanation: w1_MVP = σ2² / (σ1²+σ2²) when ρ=0: = 900/(400+900) = 900/1300 = 69.2%. A and C are wrong. D is wrong.
Question 839
Which of the following best describes the concept of 'return per unit of risk' for a portfolio on the efficient frontier?
Select an option first.
Correct answer: B — It is maximized at the tangency portfolio (highest Sharpe ratio)
Explanation: The tangency portfolio maximizes the Sharpe ratio (excess return per unit of total risk). Other portfolios on the efficient frontier are efficient but not optimal in terms of risk-adjusted return relative to the risk-free asset. A, C, D are wrong.
Question 840
An investor who wants maximum return regardless of risk should choose:
Select an option first.
Correct answer: C — The portfolio at the highest end of the efficient frontier (maximum return portfolio)
Explanation: The maximum return portfolio (top of efficient frontier) offers the highest expected return but also the highest risk. Only a risk-neutral or risk-seeking investor would choose this. A minimizes risk. B maximizes risk-adjusted return. D is an arbitrage concept.
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