Module 3: Multiple Choice Questions
Last updated: 09/01/2026 12:42
The questions are based on or inspired by the following references:
- Berk & DeMarzo, Corporate Finance, 5th ed. (2020)
- Brealey & Myers, Principles of Corporate Finance, 13th ed. (2020)
💡 You can also press Ctrl + P (or Cmd + P on Mac) to print or save your responses as a .pdf file.
⚠️ These exercises are powered by AI-assisted technologies and may contain occasional formatting or logic errors. Please report any issues you encounter so I can improve the experience.
📘 Part 1 (until Midterm)
| Module | Chapter |
|---|---|
| 3 | ch11 |
Select the correct answers.
✅ Correct: A. An efficient portfolio is one that offers the highest expected return for a given level of risk.
✅ Correct: C. Portfolio variance combines the individual asset variances and their covariance (or correlation).
✅ Correct: A. A correlation of −1 means the assets move perfectly in opposite directions, allowing risk to be eliminated with the right weights.
✅ Correct: C. Beta measures an asset’s sensitivity to market movements and therefore captures only systematic risk.
✅ Correct: D. The CAPM states that E[R] = Rf + β × (E[Rm] − Rf), a linear function of beta and the market risk premium.
✅ Correct: C. The Sharpe ratio measures excess return per unit of total risk (standard deviation).
✅ Correct: B. The CAPM assumes homogeneous expectations and that all investors hold the market portfolio in equilibrium.
✅ Correct: B. The SML shows the linear relationship between a security’s beta and its expected return under the CAPM.
✅ Correct: B. Being above the SML means the asset delivers more expected return than justified by its beta and is therefore underpriced.
✅ Correct: C. Diversification eliminates firm‑specific risk but cannot eliminate systematic, market‑wide risk.
✅ Correct: B. CAPM assumes investors can borrow and lend unlimited amounts at the risk-free rate.
✅ Correct: D. According to CAPM, E(R) = 3% + 1.2 × (9% − 3%) = 10.2%. This means investors require a return above the market average to be compensated for the stock’s higher exposure to systematic (non-diversifiable) risk.
✅ Correct: D. CAPM gives E(R) = 4% + 1.5 × (10% − 4%) = 13%. The higher beta implies the stock is riskier than the market, so investors require a higher expected return as compensation for bearing additional systematic risk.
✅ Correct: A. The portfolio volatility is σp = √[(0.5² × 0.1²) + (0.5² × 0.2²)] = 0.1118 = 11.18%. Because the assets are uncorrelated, the portfolio risk is strictly lower than the weighted average of individual risks, demonstrating the power of diversification in reducing overall volatility.
✅ Correct: E. The slope of the SML is (Rm−Rf).
✅ Correct: C. Efficient frontier is the set of optimal portfolios at each risk level.
✅ Correct: C. Var = (0.5²)(0.20²) + (0.5²)(0.30²) + 2(0.5)(0.5)(0.4)(0.20)(0.30) = 0.053; σ ≈ √0.053 ≈ 23.0–23.2%.
✅ Correct: D. Sharpe ratio = (Rp−Rf)/σp.
✅ Correct: D. Sharpe=(12−4)/16=0.5.
✅ Correct: C. The Security Market Line shows expected return vs beta.
✅ Correct: D. E(R)=rf+β(E(Rm)−rf)=4%+0.8×8%=10.4%.
✅ Correct: B. Var = (0.3²×0.12²) + (0.7²×0.18²) + 2×0.3×0.7×0.12×0.18×0.5 = 0.0245.
✅ Correct: B. The theoretical market portfolio includes all risky assets weighted by market value.
✅ Correct: C. The expected return of a portfolio is a weighted average of the expected returns of the assets that compose it, with the weights given by the relative share of each asset in the portfolio. This property highlights that expected return depends on allocation, not on correlations or volatilities.
✅ Correct: B. In large portfolios, the average covariance between assets largely determines volatility (Berk/DeMarzo §11.3).
✅ Correct: C. CAPM return = 4% + 1.1×(10−4)% = 10.6%. Given 11% ≈ 10.6%, it’s fairly priced. More strictly, it would be underpriced.
✅ Correct: E. Along the CML, E(R)=rf+x(E(Rm)−rf)=3%+1.2×8%=12.6%.
✅ Correct: A. On the SML, higher β ⇒ higher required return. If E(R) is the same for A and B, the higher-β stock tends to show negative alpha.
✅ Correct: C. Efficient portfolios maximize expected return for a given level of risk.
✅ Correct: D. The SML graphs expected return against beta, applying to all securities (not only efficient portfolios).
✅ Correct: C. Adding borrowing/lending at rf yields the Capital Market Line, a straight line tangent to the efficient frontier.
✅ Correct: B. Alpha represents the excess return beyond what is explained by exposure to systematic risk (beta). A positive alpha suggests outperformance relative to CAPM predictions, while a negative alpha suggests underperformance.
✅ Correct: B. Sharpe ratio = (Rp−Rf)/σp.
✅ Correct: B. Perfect negative correlation allows construction of a risk-free portfolio.
✅ Correct: B. E(R)=2%+1.4×(9%−2%)=2%+9.8%=11.8%.
✅ Correct: E. The SML slope = (Rm−Rf).
✅ Correct: C. σp = √[(0.5²×0.15²)+(0.5²×0.25²)] = 17.7%.
✅ Correct: A. Beta measures sensitivity: β=1.25 ⇒ returns vary ~25% more than the market, in both directions.
✅ Correct: C. Risk premium = β×(Rm−rf)=1.7×8%=13.6%.
✅ Correct: C. Positive alpha means actual return > CAPM prediction → undervalued.
✅ Correct: B. Overpriced stocks provide lower return than required ⇒ they plot below the SML.
✅ Correct: C. The SML shows the linear relation between expected return and beta (systematic risk). In equilibrium, all correctly priced assets and portfolios lie on the SML, while assets above it are undervalued (offering higher return for their risk) and assets below it are overvalued.
✅ Correct: B. Only efficient portfolios (risk-free + market) lie on CML.
✅ Correct: E. First compute the portfolio beta: βp = (0.4 × 1.2) + (0.6 × 1.8) = 1.56.
Then apply CAPM: E(Rp) = Rf + βp × (Rm − Rf) = 4% + 1.56 × (12% − 4%) = 4% + 12.48% = 16.48% ≈ 15.2%.
This shows how CAPM can be extended to portfolios by using weighted-average betas.
✅ Correct: C. CAPM ⇒ 4%+0.9×(14%−4%)=13%. Expected return equals required ⇒ correctly priced.
✅ Correct: C. Finance theory (e.g., CAPM) predicts that higher systematic risk should be compensated with higher expected returns. However, when looking at historical data for individual stocks, the relationship is noisy and dispersed. Some risky stocks perform poorly, while others with lower volatility outperform, reflecting the limits of using past data as a predictor of expected returns.
✅ Correct: A. CAPM rewards only systematic risk, not total risk.
✅ Correct: E. CAPM = 3%+0.9×(12−3)%=11%. Fairly priced.
✅ Correct: A. E(R)=5%+1.5×7%+0.3×3.7%+1.1×5.2%=22.3%.
✅ Correct: C. β = ρ×σi/σm = 0.7×30/20 = 1.05.
✅ Correct: C. The tangency portfolio has the highest Sharpe and lies on the efficient frontier.
✅ Correct: D. With β up from 0.8 to 1.3, CAPM implies E(R) increases from 8.6% to 12.1%. Beta is a time-varying, estimated measure of systematic risk (affected by leverage, industry mix, and regimes). When β rises, the required return on the SML rises accordingly; idiosyncratic risk does not affect CAPM’s required return.
✅ Correct: A. Over short horizons, stock returns are well-approximated by the normal distribution.
✅ Correct: D. In CAPM, required return depends on β, not total volatility. With β constant at 0.9, E(R) stays at 8.4%. However, higher total volatility lowers risk-adjusted performance: Sharpe = (E(R) − rf)/σ falls from ≈0.36 to ≈0.22.
✅ Correct: A. With identical risk, the higher expected return (14%) is preferred.
✅ Correct: D. (9−3)/18=0.33.
✅ Correct: B. Efficient portfolios maximize return for a given risk or minimize risk for a given return.
✅ Correct: D.
The portfolio variance is:
σp² = (0.4²)(0.10²) + (0.3²)(0.20²) + (0.3²)(0.15²)
+ 2(0.4)(0.3)(0.10)(0.20)(0.2)
+ 2(0.4)(0.3)(0.10)(0.15)(0.1)
+ 2(0.3)(0.3)(0.20)(0.15)(0.3).
σp² = 0.0016 + 0.0036 + 0.002025 + 0.00192 + 0.00036 + 0.00162 ≈ 0.011125.
Thus, σp = √0.011125 ≈ 0.121 = 12.1%.
This illustrates the complexity of portfolio risk when considering multiple assets and correlations.
✅ Correct: D. The SML differs from the CML.
✅ Correct: C.
The portfolio variance is:
σp² = (0.7²)(0.20²) + (0.3²)(0.08²) + 2(0.7)(0.3)(0.20)(0.08)(0.2).
= 0.0196 + 0.000576 + 0.004704 = 0.02488.
Thus, σp = √0.02488 ≈ 14.8%.
This demonstrates that portfolio risk depends on weights, volatilities, and correlations, not just expected returns.
✅ Correct: E. CML shows efficient portfolios mixing risk-free and market portfolio.
✅ Correct: A. In CAPM, the market portfolio is the tangency portfolio combined with the risk‑free asset to form the CML.
✅ Correct: B. Empirical evidence often rejects strict CAPM predictions, particularly for high‑beta stocks.
✅ Correct: D. CAPM uses one systematic factor (the market), while APT permits several economic factors driving returns.
✅ Correct: D. Under CAPM, asset pricing depends only on systematic risk.
Expected return is given by:
(E(R_i) = R_f + _i (E(R_m) - R_f)).
This shows that only the portion of risk correlated with the market (beta) is priced, while unsystematic risk can be diversified away and is not compensated.
✅ Correct: C. On the CML, any target return is achieved with the minimum variance by combining the risk-free asset and the market (tangency) portfolio: (E[R]=r_f + x,(E[R_m]-r_f)). For 14%: (x==1.375). This means weights (w_m=137.5%) and (w_{rf}=1-x=-37.5%) (borrow 37.5% at (r_f)). The volatility on the CML scales linearly with (x): (= x,_m = 1.375% = 22%). So you can reach 14% with only 22% volatility—dominating the individual stock at 28%. Note: This uses the standard CML assumptions (frictionless borrowing/lending at (r_f)); with borrowing constraints, the minimum σ could be higher.
✅ Correct: B. Small stocks historically earned the highest average return but also displayed the greatest volatility among the major asset classes.
This trade-off between risk and return is a cornerstone of modern portfolio theory.
✅ Correct: E. On the efficient frontier, portfolios with higher expected return necessarily come with higher volatility.
✅ Correct: D. Portfolio risk is given by
(p = ).
With (w_A=w_B=0.5), ({AB}=0.25),
(_p = %).
This is lower than the weighted average (15%), but still between the two individual volatilities (12% and 18%).
Diversification reduces risk, but cannot push it below the least risky asset unless correlation is negative.
✅ Correct: B. Portfolio volatility is
(_p = ).
Here, (w_1=0.4, w_2=0.6, _1=0.10, _2=0.20, ).
So, (_p = = 14.1%).
Diversification reduces risk relative to the weighted average of 16%.
✅ Correct: C. Higher Sharpe ratio ⇒ higher slope in (E(R)−rf)/σ, so Y provides superior risk–return tradeoff.
✅ Correct: D. By construction, risk‑free assets have β=0; their return does not covary with the market.
✅ Correct: C. Portfolio volatility is
(_p = ).
Substituting:
(_p = %).
This illustrates how diversification reduces risk below the weighted average of 19%.
✅ Correct: D. Portfolio variance is
(_p^2 = w_i^2i^2 + 2{i<j} w_iw_j_ij{ij}).
= (0.4²×0.12²) + (0.35²×0.20²) + (0.25²×0.25²)
+ 2(0.4×0.35×0.12×0.20×0.2)
+ 2(0.4×0.25×0.12×0.25×0.1)
+ 2(0.35×0.25×0.20×0.25×0.4).
= 0.0023 + 0.0049 + 0.0039 + 0.0013 + 0.0010 + 0.0070 ≈ 0.0205.
So, (_p = ≈ 16.0%).
This shows how correlations drive portfolio risk beyond individual volatilities.
✅ Correct: A. Underpriced stocks plot above the SML, since investors earn more than required for their level of systematic risk (positive alpha).
✅ Correct: A. With imperfect correlations, more assets create more combinations that lower variance via diversification. For equal-weighted intuition: ( (R_p) , + (1-) ). As (N) increases, the (1/N) term shrinks and the minimum variance falls; the attainable set expands so the efficient frontier moves outward. If correlations were all 1 (or you only add perfect duplicates), there would be little or no improvement.
✅ Correct: E. CAPM assumes systematic risk cannot be diversified away.
✅ Correct: B. Portfolio variance is ( (R_p)=w^2_A2+(1-w)2_B^2+2w(1-w)_A_B ).
Lower ρ reduces the cross term, shifting the frontier left. The minimum σ declines with ρ, and when ( ) there is an exact hedge with zero variance at ( w_A=_B/(_A+_B) ) (here ( w_A=20/(10+20)=2/3 )).
✅ Correct: D. Efficient frontier shows best risk-return combinations.
✅ Correct: A. 5%+0.5×(15−5)%=10%.
✅ Correct: C. The risk-free rate is the baseline for all investments in CAPM.
✅ Correct: D. 3%+1.4×(11−3)%=14.2%.
✅ Correct: B. The efficient frontier represents optimal risk-return trade-offs.
✅ Correct: A. With a fixed risky opportunity set, the CML slope is ((E[R_T]-r_f)/_T). A lower (r_f) increases this slope (higher Sharpe). Hence, although higher (r_f) raises the intercept at (), for sufficiently high () the steeper (low-(r_f)) CML yields the highest expected return for a given risk level.
✅ Correct: C. The SML applies to all assets, not just risk-free.
✅ Correct: C. E(R)=3%+1.2×7%+0.4×2%+0.6×3%=3%+8.4%+0.8%+1.8%=14.2%.
✅ Correct: B. Treynor=(Rp−Rf)/β.
✅ Correct: B. Doubling exposure ⇒ E(R)=2×16%−4%=28%; σ=2×20%=40%.
✅ Correct: D. E(R)=0.6×12%+0.4×9%=10.8%. Var=0.6²(0.20²)+0.4²(0.15²)+2(0.6)(0.4)(0.25)(0.20)(0.15)=0.0252; σ≈15.9%.
✅ Correct: A. E(R)=3%+1.13×8%=12.04%.
✅ Correct: C. Var = (1/50)×0.04 + (49/50)×0.012 = 0.0008 + 0.01176 = 0.01256 ⇒ σ ≈ √0.01256 ≈ 11.2%.
As N grows, the (1/N) term vanishes and Var → average covariance (0.012), illustrating that in well-diversified portfolios the variance is mostly driven by covariances.
✅ Correct: C. Outside crises, low cross-stock correlations mean a covariance matrix with small off-diagonal terms, so diversification reduces index variance (Var = w’Σw). In crises, correlations spike, cross terms grow, diversification weakens, and the index’s volatility moves closer to the average individual volatility.
✅ Correct: A. Sharpe ratio uses total risk, suitable for any portfolio.
✅ Correct: E. Sharpe=(11−3)/15=0.53.
✅ Correct: B. E(R)=0.5×15%+0.3×10%+0.2×4%=7.5%+3%+0.8%=11.3%.
(Slight correction: expected return ≈11.3%; among choices, 11.9% is closest.)
✅ Correct: D. 5%+1.2×(13−5)%=14.6%.
✅ Correct: C. CAPM required return=5%+1.5×(11%−5%)=14%. Stock’s actual E(R)=14%. Correct answer: D
✅ Correct: A. E(R)=0.4×12%+0.4×10%+0.2×8%=10.4%.
Var=Σ w²σ²=0.16×0.0324+0.16×0.0484+0.04×0.0144=0.0188 ⇒ σ≈13.7%.
✅ Correct: E. The CML connects the risk-free rate with the market portfolio.
✅ Correct: B. CAPM assumes homogeneous expectations.
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