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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 871
If you add a new asset to a portfolio and its beta with the existing portfolio equals zero, the new asset's contribution to portfolio risk is:
Select an option first.
Correct answer: B — Zero
Explanation: If the asset has zero beta (zero correlation) with the portfolio, it contributes zero systematic risk. In a large portfolio, its individual variance is also diversified away. B is the correct inference for a well-diversified portfolio adding a zero-beta, zero-correlation asset. A applies to small portfolios.
Question 872
The equity risk premium (ERP) exists primarily because:
Select an option first.
Correct answer: C — Equities are riskier than bonds and investors require compensation for bearing that additional risk
Explanation: The ERP compensates investors for the higher risk (volatility, uncertainty) of equities compared to risk-free government bonds. A is wrong — stocks underperform bonds in many years. B is false. D is a transaction cost, not a risk premium.
Question 873
An investor's budget constraint in portfolio selection states that:
Select an option first.
Correct answer: B — All portfolio weights must sum to one
Explanation: Portfolio weights must sum to 100% (or 1.0) — this is the budget constraint. If you allocate more to some assets, you must allocate less to others. A is a return constraint. C is an optional constraint. D is a real return objective.
Question 874
Which of the following best describes a 'risk premium'?
Select an option first.
Correct answer: B — The extra return above the risk-free rate required for bearing additional risk
Explanation: A risk premium compensates investors for accepting risk beyond the risk-free rate. Examples: equity risk premium, credit risk premium, term premium. A is Rf alone. C is market risk. D is active return.
Question 875
A portfolio of 20 stocks in the same industry:
Select an option first.
Correct answer: C — Remains exposed to industry-specific (systematic to that industry) risk despite having 20 stocks
Explanation: Holding 20 stocks in one industry eliminates some firm-specific risk but retains industry-level systematic risk. Events affecting the whole industry (regulation, commodity prices) still impact all 20 stocks. A confuses quantity with quality of diversification. B and D are wrong.
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Question 876
Which of the following best describes a 'well-diversified portfolio'?
Select an option first.
Correct answer: C — One where unsystematic risk is negligible because holdings are spread across many uncorrelated assets
Explanation: A well-diversified portfolio has eliminated (or nearly eliminated) idiosyncratic risk through broad diversification across many assets with low pairwise correlations. A and B focus on quantity/geography without addressing correlation. D is not diversification — it's selection.
Question 877
In portfolio theory, the 'minimum-variance frontier' refers to:
Select an option first.
Correct answer: B — The set of all minimum-variance portfolios for each level of expected return, including those below the GMVP
Explanation: The minimum-variance frontier includes all portfolios that minimize variance for a given return — even the downward-sloping lower portion (which efficient investors would never choose since higher return is available for same risk). The efficient frontier is just the upper half. A, C, D are subsets or wrong.
Question 878
The risk-free asset in portfolio theory typically refers to:
Select an option first.
Correct answer: B — Short-term government bonds with known, certain return
Explanation: The risk-free asset has zero variance, zero standard deviation, and a known certain return over the investment horizon. Typically modeled as short-term T-bills. A has beta=0 but need not have zero variance. C is wrong. D is wrong — long bonds carry interest rate risk.
Question 879
The 'investment opportunity set' is most accurately described as:
Select an option first.
Correct answer: B — The set of all portfolios that can be formed using available assets, whether efficient or not
Explanation: The investment opportunity set is ALL feasible portfolios from available assets — efficient and inefficient, positive and negative return. It is the entire attainable set. A is the efficient subset. C is with risk-free asset. D is too restrictive.
Question 880
An increase in correlation between two assets in a portfolio will generally:
Select an option first.
Correct answer: B — Reduce portfolio diversification benefit and increase portfolio variance
Explanation: Higher correlation means assets move together more — less offsetting, less diversification. Portfolio variance increases. A is the opposite. C is wrong. D is wrong — correlation doesn't affect individual asset returns.
Question 881
An investor has wealth of $1,000,000 and invests $400,000 in risky Asset A (σ=25%) and $600,000 in the risk-free asset. Portfolio standard deviation is:
Select an option first.
Correct answer: A — 10%
Explanation: σp = wA × σA = (400,000/1,000,000) × 25% = 0.4 × 25% = 10%. The risk-free asset has zero variance. B is Asset A's σ. C would be 60%×25%. D is wrong.
Question 882
Two assets with equal expected returns and equal variances but zero correlation. Equal-weighted portfolio variance equals what fraction of each asset's variance?
Select an option first.
Correct answer: A — One half
Explanation: σp² = (0.5)²σ² + (0.5)²σ² + 0 = 0.25σ² + 0.25σ² = 0.5σ². Portfolio variance = half of each asset's variance. σp = σ/√2. A is correct. B is ¼ (wrong). C ignores diversification. D is wrong.
Question 883
Asset X: σ=30%. Asset Y: σ=30%. ρ=0. Equal-weighted portfolio standard deviation is:
Select an option first.
Correct answer: B — 21.2%
Explanation: σp = σ/√2 = 30/√2 = 30/1.414 = 21.21% ≈ 21.2%. A ignores diversification. C would need σ=21.2%×√2. D doubles standard deviation.
Question 884
Portfolio with 5 equal-weighted assets each with variance 100 and all pairwise correlations = 0.4. Portfolio variance is approximately:
Select an option first.
Correct answer: B — 52
Explanation: For N equal-weighted assets: σp² = (1/N)σᵢ² + (N-1)/N × ρ × σᵢ² = (1/5)×100 + (4/5)×0.4×100 = 20 + 32 = 52. A is just σᵢ²/N (wrong, only valid if ρ=0). C is wrong. D is ρ×σᵢ²×N.
Question 885
Annual returns: Year 1: +25%, Year 2: −20%, Year 3: +10%. Starting with $1,000, what is the ending value?
Select an option first.
Correct answer: A — $1,100
Explanation: $1,000 × 1.25 × 0.80 × 1.10 = $1,000 × 1.10 = $1,100. B uses geometric mean. C and D are wrong.
Question 886
From above, the geometric mean annual return is:
Select an option first.
Correct answer: A — 3.23%
Explanation: $1,000 → $1,100 in 3 years. GR = (1,100/1,000)^(1/3) − 1 = (1.1)^0.333 − 1 = 1.0323 − 1 = 3.23%. B is arithmetic mean: (25-20+10)/3=5%. C and D are wrong.
Question 887
Portfolio: 25% in A (σ=10%), 75% in B (σ=20%), ρ=0.3. Portfolio σ is closest to:
Select an option first.
Correct answer: A — 15.9%
Explanation: σp² = (0.25)²(0.10)²+(0.75)²(0.20)²+2(0.25)(0.75)(0.10)(0.20)(0.3) = 0.000625+0.0225+0.00225 = 0.025375. σp=√0.025375=15.93%≈15.9%. B, C, D are wrong.
Question 888
An investor puts 60% in the market (E(R)=12%, σ=20%) and 40% in the risk-free asset (Rf=4%). The portfolio's expected return and standard deviation are:
Select an option first.
Correct answer: A — E(R)=8.8%, σ=12%
Explanation: E(Rp) = 0.6×12+0.4×4 = 7.2+1.6 = 8.8%. σp = 0.6×20 = 12%. A is correct. B, C, D are wrong.
Question 889
An investor wants a portfolio with 10% standard deviation. The market has σ=20%. Using only the market and risk-free asset, what weight in the market achieves σp=10%?
Select an option first.
Correct answer: A — 50%
Explanation: σp = w_m × σ_m → 10 = w_m × 20 → w_m = 0.50 = 50%. B gives 15%. C gives 5%. D gives 2%.
Question 890
The same investor (w_m=50%, Rf=4%, Rm=12%) expects a portfolio return of:
Select an option first.
Correct answer: A — 8.0%
Explanation: E(Rp) = 0.5×12+0.5×4 = 6+2 = 8.0%. B uses different weights. C and D are wrong.
Question 891
Which of the following return metrics is most useful for comparing managers who take different amounts of risk?
Select an option first.
Correct answer: C — Risk-adjusted return (e.g., Sharpe ratio)
Explanation: Risk-adjusted return (like Sharpe ratio) normalizes for risk, allowing fair comparison between managers with different risk profiles. A and D are raw return measures. B ignores risk completely.
Question 892
An investor who needs to fund a specific expenditure in exactly 3 years should primarily focus on matching:
Select an option first.
Correct answer: B — The portfolio's duration to the liability horizon
Explanation: Liability-driven approaches match asset duration (or cash flows) to specific liabilities. For a 3-year obligation, a 3-year bond (or portfolio with 3-year duration) eliminates interest rate risk. A is a return objective. C is performance optimization. D is market exposure.
Question 893
An investor observes that adding bonds to an equity portfolio reduces portfolio variance below the weighted average of the two variances. The primary reason is:
Select an option first.
Correct answer: B — Bonds and equities often have low or negative correlation
Explanation: The diversification benefit (variance below weighted average) comes from low or negative correlation between bonds and equities. Assets moving differently reduce overall portfolio variance. A is sometimes true but is the wrong explanation. C and D are wrong.
Question 894
A mean-variance optimizer is given erroneous expected return estimates. What type of risk does this represent?
Select an option first.
Correct answer: C — Estimation risk / model risk — the model's output is only as good as its inputs
Explanation: Errors in input estimates (expected returns, variances, correlations) lead to unreliable optimization outputs. This is estimation or model risk — the garbage-in-garbage-out problem. A, B, D are financial market risks, not model risks.
Question 895
Which of the following statements about the minimum-variance portfolio is TRUE?
Select an option first.
Correct answer: B — It is located at the leftmost point of the minimum-variance frontier
Explanation: The global minimum-variance portfolio (GMVP) sits at the leftmost point of the parabolic minimum-variance frontier — the portfolio with the absolute lowest achievable variance. A describes the maximum-return portfolio. C is wrong. D is wrong.
Question 896
Real returns are most directly relevant for evaluating investments from the perspective of:
Select an option first.
Correct answer: C — Purchasing power — how much an investor can actually buy with the returns earned
Explanation: Real returns measure what matters most: the actual increase in purchasing power after inflation. An investor earning 6% nominal with 4% inflation earns only 2% real — can buy only 2% more. A, B, D are not the primary reason for using real returns.
Question 897
A portfolio manager wants to increase expected return while keeping portfolio standard deviation constant. Which adjustment is most likely to achieve this?
Select an option first.
Correct answer: C — Replace a low-expected-return asset with a higher-expected-return asset with similar correlation
Explanation: Swapping a low-return asset for a higher-return one with similar risk and correlation characteristics would increase portfolio expected return (a weighted average) while maintaining similar portfolio standard deviation. A reduces return. B increases risk. D doesn't change composition.
Question 898
An investor holds only one stock. From a portfolio theory perspective, this investor is bearing:
Select an option first.
Correct answer: C — Both systematic and unsystematic risk, but only receiving compensation for systematic risk
Explanation: A single-stock investor bears total risk (systematic + unsystematic) but under CAPM is only compensated for systematic risk. The unsystematic portion earns no premium. A and B are each only half. D is wrong.
Question 899
Which of the following scenarios results in the LOWEST portfolio variance for a two-asset portfolio?
Select an option first.
Correct answer: C — Both assets have moderate variance and ρ=−1.0 with optimal weights
Explanation: Perfect negative correlation (ρ=−1) with optimal weights allows complete variance elimination (σp=0). This is the theoretical minimum. A has high variance and high correlation. B can be very low but not zero unless the risky asset has zero variance. D provides no diversification benefit.
Question 900
The 'excess return' of a portfolio over the risk-free rate is also known as:
Select an option first.
Correct answer: B — The risk premium
Explanation: Excess return = portfolio return − risk-free rate. This is the risk premium earned above the minimum return available (Rf). Alpha (A) is risk-adjusted excess return above CAPM. Active return (C) is return vs. benchmark. Information ratio (D) is active return / TE.
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