Module 3: Multiple Choice Questions

For students

Last updated: 19/09/2025 16:36

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)

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💡 You can also press Ctrl + P (or Cmd + P on Mac) to print or save your responses as a .pdf file.

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⚠️ 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.

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📘 Part 1 (until Midterm)

Module	Chapter	Slides	T/F	MCQ	Numeric	Long
3	ch11	🎞️	✅	❓	🔢	📝

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Q1.

Which of the following statements best describes an efficient portfolio?

A. A portfolio that maximizes return for a given level of risk
B. A portfolio with the lowest variance regardless of return
C. A portfolio that holds only a single risky asset
D. A portfolio that invests equal amounts in all available assets
E. A portfolio that minimizes beta

✅ Correct: A. An efficient portfolio is one that offers the highest expected return for a given level of risk.

Q2.

The variance of a two‑asset portfolio depends on:

A. Only the variances of the individual assets
B. Only the covariance between the assets
C. Both the variances of the individual assets and the covariance between them
D. The average return of the portfolio
E. None of the above

✅ Correct: C. Portfolio variance combines the individual asset variances and their covariance (or correlation).

Q3.

If the correlation between two assets is −1, combining them in a portfolio:

A. Eliminates all risk if the weights are properly chosen
B. Has no effect on the portfolio’s risk
C. Doubles the portfolio’s expected return
D. Increases the portfolio’s variance above either asset’s variance
E. Makes the assets perfectly positively correlated

✅ Correct: A. A correlation of −1 means the assets move perfectly in opposite directions, allowing risk to be eliminated with the right weights.

Q4.

Which measure captures only the systematic risk of a stock?

A. Standard deviation
B. Variance
C. Beta
D. Arithmetic mean
E. Sharpe ratio

✅ Correct: C. Beta measures an asset’s sensitivity to market movements and therefore captures only systematic risk.

Q5.

In the Capital Asset Pricing Model (CAPM), the expected return of a security is:

A. Equal to the risk‑free rate
B. Inversely proportional to its beta
C. Equal to the average return of the market portfolio
D. A linear function of the security’s beta and the market risk premium
E. Independent of the security’s beta

✅ Correct: D. The CAPM states that E[R] = Rf + β × (E[Rm] − Rf), a linear function of beta and the market risk premium.

Q6.

The Sharpe ratio of a portfolio is defined as:

A. The portfolio’s excess return divided by its variance
B. The portfolio’s beta divided by its return
C. The portfolio’s excess return divided by its standard deviation
D. The portfolio’s return divided by its beta
E. The portfolio’s variance divided by the market variance

✅ Correct: C. The Sharpe ratio measures excess return per unit of total risk (standard deviation).

Q7.

According to the CAPM assumptions, all investors:

A. Can only buy and hold the risk‑free asset
B. Have homogeneous expectations and hold the same market portfolio
C. Prefer portfolios with the highest idiosyncratic risk
D. Are risk‑neutral
E. Face high transaction costs and taxes

✅ Correct: B. The CAPM assumes homogeneous expectations and that all investors hold the market portfolio in equilibrium.

Q8.

The Security Market Line (SML) depicts the relationship between:

A. Standard deviation and expected return for individual assets
B. Beta and expected return for individual assets
C. Weight and variance for portfolios
D. Correlation and covariance for portfolios
E. Price and earnings per share

✅ Correct: B. The SML shows the linear relationship between a security’s beta and its expected return under the CAPM.

Q9.

If an asset lies above the Security Market Line, it is considered:

A. Overpriced and should be sold
B. Underpriced and offers a higher return for its level of risk
C. Efficient and lies on the efficient frontier
D. A risk‑free asset
E. A candidate for short selling only

✅ Correct: B. Being above the SML means the asset delivers more expected return than justified by its beta and is therefore underpriced.

Q10.

Diversification primarily reduces:

A. Systematic risk
B. Market risk
C. Idiosyncratic (unsystematic) risk
D. The risk‑free rate
E. Beta

✅ Correct: C. Diversification eliminates firm‑specific risk but cannot eliminate systematic, market‑wide risk.

Q11.

Which of the following is an assumption of CAPM? A. Investors have heterogeneous expectations
B. Investors can borrow and lend at the risk-free rate
C. Markets are always inefficient
D. Taxes and transaction costs are large
E. Investors only care about skewness

✅ Correct: B. CAPM assumes investors can borrow and lend unlimited amounts at the risk-free rate.

Q12.

An equity analyst is evaluating a company’s stock using the Capital Asset Pricing Model (CAPM). The stock has a beta of 1.2, reflecting its sensitivity relative to the market portfolio. The risk-free rate is currently 3% per year, while the expected market return is 9%. Based on CAPM, what is the stock’s expected return, and how should it be interpreted in terms of compensation for bearing systematic risk? A. 9.0% — equal to the market return, suggesting no additional risk premium.
B. 10.0% — slightly above the market return, indicating only marginal additional risk.
C. 10.2% — higher than the risk-free rate, but still lower than what the beta implies.
D. 10.2% — equal to 3% + 1.2 × (9% − 3%), showing the stock is expected to yield more than the market due to its above-average beta.
E. 12.0% — a clear overestimation of return if CAPM is applied correctly.

✅ 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.

Q13.

An investor applies the Capital Asset Pricing Model (CAPM) to evaluate a stock. The stock has a beta of 1.5, the risk-free rate is 4%, and the expected market return is 10%. According to CAPM, what is the expected return on this stock, and how does it reflect the risk–return tradeoff? A. 10% — equal to the market return, implying no compensation for additional risk.
B. 11% — slightly above the market, underestimating the effect of beta.
C. 12% — consistent with a moderate level of risk above the market.
D. 13% — equal to 4% + 1.5 × (10% − 4%), reflecting the higher expected return required for above-average systematic risk.
E. 15% — overstated relative to CAPM, exaggerating the risk premium.

✅ 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.

Q14.

An investor constructs a two-asset portfolio with equal weights in Asset A and Asset B. Asset A has a volatility (σA) of 10%, while Asset B has a volatility (σB) of 20%. The correlation between the two assets’ returns is zero, meaning they are uncorrelated. Using portfolio theory, what is the resulting volatility of the portfolio, and what does this outcome imply about the benefits of diversification? A. 11.18% — lower than the simple average of the two volatilities, illustrating risk reduction through diversification.
B. 12.00% — only slightly reduced relative to the higher volatility asset.
C. 13.00% — indicating partial diversification but still dominated by the riskier asset.
D. 14.14% — equal to the root mean square of the two volatilities without accounting for weights.
E. 15.00% — essentially the average of the two risks, implying no diversification benefit.

✅ 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.

Q15.

The slope of the Security Market Line equals: A. Variance of the market
B. Standard deviation of the market
C. Risk-free rate
D. Sharpe ratio
E. Market risk premium

✅ Correct: E. The slope of the SML is (Rm−Rf).

Q16.

Which statement about the efficient frontier is TRUE? A. It includes only risk-free portfolios
B. It excludes diversification benefits
C. It represents optimal portfolios for each risk level
D. It shifts randomly over time
E. It includes only individual stocks

✅ Correct: C. Efficient frontier is the set of optimal portfolios at each risk level.

Q17.

Two risky assets A and B have σ(A)=20%, σ(B)=30%, and Corr(A,B)=0.4. You form a 50–50 portfolio. What is the portfolio volatility? A. 20.0%
B. 22.4%
C. 23.2%
D. 25.0%
E. 26.0%

✅ 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%.

Q18.

Which ratio measures excess return per unit of total risk? A. Treynor ratio
B. Beta
C. Alpha
D. Sharpe ratio
E. Jensen’s measure

✅ Correct: D. Sharpe ratio = (Rp−Rf)/σp.

Q19.

If E(R)=12%, Rf=4%, σ=16%, Sharpe ratio=? A. 0.25
B. 0.40
C. 0.45
D. 0.50
E. 0.75

✅ Correct: D. Sharpe=(12−4)/16=0.5.

Q20.

Which line shows expected return vs beta? A. Capital Market Line
B. Efficient frontier
C. Security Market Line
D. Indifference curve
E. Isoquant

✅ Correct: C. The Security Market Line shows expected return vs beta.

Q21.

Under CAPM, a stock with β=0.8, risk-free rate 4%, and market expected return 12% should have what expected return? A. 9.0%
B. 9.6%
C. 10.0%
D. 10.4%
E. 12.0%

✅ Correct: D. E(R)=rf+β(E(Rm)−rf)=4%+0.8×8%=10.4%.

Q22.

A portfolio has 30% in Asset X (σ=12%), 70% in Asset Y (σ=18%), correlation=0.5. What is the portfolio variance? A. 0.0220
B. 0.0245
C. 0.0260
D. 0.0270
E. 0.0300

✅ Correct: B. Var = (0.3²×0.12²) + (0.7²×0.18²) + 2×0.3×0.7×0.12×0.18×0.5 = 0.0245.

Q23.

In the CAPM framework, the market portfolio: A. Contains only government bonds
B. Is the combination of all risky assets in the economy
C. Is chosen arbitrarily by investors
D. Contains only large-cap stocks
E. Is equivalent to the risk-free asset

✅ Correct: B. The theoretical market portfolio includes all risky assets weighted by market value.

Q24.

In modern portfolio theory, the expected return of a portfolio is a fundamental concept used to guide investment decisions. Which of the following statements best describes how the expected return of a portfolio is determined? A. It is equal to the risk-free rate plus the weighted average volatility of the assets in the portfolio.
B. It is calculated as the geometric average of individual asset returns, adjusted for portfolio beta.
C. It is the weighted average of the expected returns of the individual assets, with weights corresponding to their proportion in the portfolio.
D. It is determined by multiplying the portfolio’s total volatility by the market risk premium.
E. It is estimated by adding each asset’s alpha to the overall market return.

✅ 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.

Q25.

Which statement about diversification is MOST accurate? A. Adding any stock always lowers portfolio volatility.
B. For large portfolios, average covariance dominates variance in determining volatility.
C. Portfolio variance is the weighted average of individual variances only.
D. If Corr=0, diversification has no effect.
E. Diversification eliminates systematic risk.

✅ Correct: B. In large portfolios, the average covariance between assets largely determines volatility (Berk/DeMarzo §11.3).

Q26.

A stock has an expected return of 11%. Risk-free rate = 4%, beta = 1.1, market portfolio return = 10%. According to CAPM, the stock is: A. Overpriced (return < required)
B. Underpriced (return > required)
C. Fairly priced
D. Price cannot be judged
E. Price depends on dividends

✅ 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.

Q27.

A portfolio is 120% long the market index and −20% in the risk-free asset (borrowing at rf). If E(Rm)=11% and rf=3%, what is the portfolio’s expected return? A. 11.0%
B. 12.0%
C. 12.4%
D. 13.0%
E. 12.6%

✅ Correct: E. Along the CML, E(R)=rf+x(E(Rm)−rf)=3%+1.2×8%=12.6%.

Q28.

Two stocks have identical expected returns but different betas (βA=0.7, βB=1.3). Under CAPM, which is TRUE? A. Stock B should have a higher required return; if both have the same E(R), B would have a negative alpha.
B. Stock A must be overpriced.
C. Both have zero alpha by construction.
D. Required returns are identical if Corr=0.
E. A has higher systematic risk.

✅ 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.

Q29.

In mean-variance analysis, efficient portfolios are those that: A. Maximize variance for a given return
B. Minimize return for a given risk
C. Maximize return for a given risk
D. Offer the highest beta
E. Lie below the minimum variance frontier

✅ Correct: C. Efficient portfolios maximize expected return for a given level of risk.

Q30.

Which of the following best describes the Security Market Line (SML) in the CAPM framework? A. It plots expected return versus variance of returns.
B. It shows the risk–return tradeoff of efficient portfolios only.
C. It plots expected return versus total risk (σ).
D. It plots expected return versus beta, showing required returns for any security.
E. It is identical to the Capital Market Line (CML).

✅ Correct: D. The SML graphs expected return against beta, applying to all securities (not only efficient portfolios).

Q31.

If an investor adds a risk-free asset to a portfolio of risky securities, the efficient frontier becomes: A. A concave curve below the original frontier.
B. Unchanged, since risk-free assets add no diversification benefits.
C. A straight line tangent to the frontier, improving risk–return tradeoff.
D. A parabola through the origin.
E. Vertical, showing zero risk.

✅ Correct: C. Adding borrowing/lending at rf yields the Capital Market Line, a straight line tangent to the efficient frontier.

Q32.

In performance evaluation, the concept of “alpha” is widely used to measure the value added by a portfolio manager beyond passive exposure to systematic risk. Which of the following statements best captures the meaning of alpha in the context of asset pricing models such as CAPM? A. Alpha represents the portion of return explained by the sensitivity of the asset to the market portfolio (beta).
B. Alpha measures the abnormal return earned by a portfolio or security, beyond what would be predicted by its exposure to systematic risk.
C. Alpha is the risk-free rate used as the baseline in the CAPM equation.
D. Alpha is the market risk premium that compensates investors for holding risky assets.
E. Alpha is the weighted average cost of capital (WACC) adjusted for the firm’s leverage.

✅ 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.

Q33.

The Sharpe ratio measures: A. Return per unit of unsystematic risk
B. Excess return per unit of total risk
C. Excess return per unit of beta
D. Excess return per unit of variance
E. Return relative to risk-free rate

✅ Correct: B. Sharpe ratio = (Rp−Rf)/σp.

Q34.

If two assets are perfectly negatively correlated (ρ = −1): A. The portfolio is risk-free
B. The portfolio variance is minimized, possibly zero
C. Portfolio variance is maximum
D. Portfolio expected return falls to zero
E. Diversification has no effect

✅ Correct: B. Perfect negative correlation allows construction of a risk-free portfolio.

Q35.

Suppose Stock X has β=1.4, rf=2%, and expected market return=9%. According to CAPM, what is the expected return on X? A. 9.8%
B. 11.8%
C. 12.6%
D. 13.0%
E. 14.5%

✅ Correct: B. E(R)=2%+1.4×(9%−2%)=2%+9.8%=11.8%.

Q36.

Which of the following is TRUE about the Security Market Line (SML)? A. It shows expected return vs. total risk
B. It has slope equal to the Sharpe ratio
C. All assets lie on or below it in equilibrium
D. It is steeper than the CML
E. Its slope equals the market risk premium

✅ Correct: E. The SML slope = (Rm−Rf).

Q37.

Asset A (σ=15%) and Asset B (σ=25%) are uncorrelated, with equal weights. What is portfolio standard deviation? A. 12.0%
B. 15.0%
C. 17.7%
D. 20.0%
E. 22.5%

✅ Correct: C. σp = √[(0.5²×0.15²)+(0.5²×0.25²)] = 17.7%.

Q38.

A stock with β=1.25 is expected to move how relative to the market? A. About 25% more than the market, both up and down.
B. About 25% less than the market, both up and down.
C. 125% more in up markets only.
D. 125% more in down markets only.
E. Moves are unrelated to the market.

✅ Correct: A. Beta measures sensitivity: β=1.25 ⇒ returns vary ~25% more than the market, in both directions.

Q39.

If the market risk premium is 8%, then the risk premium of a stock with β=1.7 must be: A. 8%
B. 10%
C. 13.6%
D. 12.0%
E. Cannot be determined without rf.

✅ Correct: C. Risk premium = β×(Rm−rf)=1.7×8%=13.6%.

Q40.

If an asset’s alpha is positive relative to CAPM: A. Asset is fairly priced
B. Asset is overvalued
C. Asset is undervalued
D. Market is inefficient
E. Beta must be zero

✅ Correct: C. Positive alpha means actual return > CAPM prediction → undervalued.

Q41.

If a stock is overpriced according to CAPM, where would it plot relative to the Security Market Line (SML)? A. Above the SML
B. Below the SML
C. On the SML
D. To the left of the origin
E. Cannot be determined

✅ Correct: B. Overpriced stocks provide lower return than required ⇒ they plot below the SML.

Q42.

Which of the following statements is TRUE about the Security Market Line (SML) in the CAPM framework? A. It depicts the relationship between expected return and total risk (standard deviation).
B. Its slope is equal to the Sharpe ratio of the market portfolio.
C. In equilibrium, all correctly priced assets and portfolios should lie on the SML, with mispriced assets appearing above or below it.
D. It is always steeper than the Capital Market Line (CML) because it uses beta instead of total risk.
E. Its slope equals the market risk premium expressed in percentage points, not per unit of beta.

✅ 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.

Q43.

Which of the following lies on the Capital Market Line (CML)? A. Any individual asset
B. Portfolios combining the risk-free asset and the market portfolio
C. Portfolios with only unsystematic risk
D. Portfolios with negative betas
E. Any inefficient portfolio

✅ Correct: B. Only efficient portfolios (risk-free + market) lie on CML.

Q44.

An investor builds a portfolio composed of 40% in Stock A and 60% in Stock B.
- Stock A has a beta of 1.2.
- Stock B has a beta of 1.8.
The risk-free rate is 4% and the expected market return is 12%.

According to CAPM, what is the expected return of the portfolio? A. 13.6%
B. 14.2%
C. 14.6%
D. 15.0%
E. 15.2%

✅ 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.

Q45.

Assume β=0.9, rf=4%, and E(Rm)=14%. If the stock’s expected return is 13%, how is it priced relative to CAPM? A. Overpriced, since required return is 16%.
B. Underpriced, since required return is 8%.
C. Correctly priced, since required return is 13%.
D. Overpriced, since required return is 12%.
E. Underpriced, since required return is 15%.

✅ Correct: C. CAPM ⇒ 4%+0.9×(14%−4%)=13%. Expected return equals required ⇒ correctly priced.

Q46.

Which of the following best reflects the relationship between risk (volatility) and return observed in financial markets when analyzing individual stocks over long periods? A. There is always a strong and exact linear relationship, with higher volatility guaranteeing higher returns.
B. All assets align perfectly with the predictions of CAPM, meaning no stock ever offers returns inconsistent with its beta.
C. While theory suggests a positive relationship between risk and expected return, in practice the data show considerable dispersion, with some high-volatility stocks yielding poor returns and some low-volatility stocks performing well.
D. Investors can always earn abnormal profits by simply selecting the riskiest stocks available in the market.
E. Diversification eliminates all forms of risk, making volatility irrelevant to expected returns in practice.

✅ 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.

Q47.

Which is FALSE about CAPM? A. Investors are rewarded for bearing total risk
B. Only systematic risk is priced
C. Beta measures systematic risk
D. Market portfolio is efficient
E. Alpha measures mispricing

✅ Correct: A. CAPM rewards only systematic risk, not total risk.

Q48.

Stock has E(R)=11%, β=0.9, Rf=3%, Rm=12%. According to CAPM, is it fairly priced? A. Overpriced, since CAPM = 10.2%
B. Underpriced, since CAPM = 12%
C. Overpriced, since CAPM = 11%
D. Underpriced, since CAPM = 9%
E. Fairly priced, since CAPM = 11%

✅ Correct: E. CAPM = 3%+0.9×(12−3)%=11%. Fairly priced.

Q49.

Using the Fama–French three-factor model: rf=5%, βM=1.5, βS=0.3, βB=1.1; market premium=7%, size premium=3.7%, book-to-market premium=5.2%. What is expected return? A. 22.3%
B. 20.9%
C. 18.0%
D. 15.6%
E. 25.0%

✅ Correct: A. E(R)=5%+1.5×7%+0.3×3.7%+1.1×5.2%=22.3%.

Q50.

Investor holds stock with σ=30%, market σ=20%, correlation=0.7. What is the stock’s beta? A. 0.9
B. 1.0
C. 1.05
D. 1.2
E. 1.3

✅ Correct: C. β = ρ×σi/σm = 0.7×30/20 = 1.05.

Q51.

Which portfolio always lies ON the efficient frontier? A. Any randomly chosen portfolio
B. Any individual stock
C. The portfolio with the highest Sharpe ratio
D. The minimum variance portfolio only
E. None of the above

✅ Correct: C. The tangency portfolio has the highest Sharpe and lies on the efficient frontier.

Q52.

An analyst re-estimates a stock’s beta each quarter using a rolling window. The stock’s beta has risen from 0.8 to 1.3 over the past year. With a risk-free rate of 3% and an expected market return of 10%, what is the CAPM-implied expected return now, and what does this imply? A. 8.6% — unchanged, because expected return depends on total volatility rather than beta.
B. 11.0% — a slight increase; only leverage changes non-systematic risk.
C. 12.1% — but the increase reflects higher idiosyncratic (diversifiable) risk.
D. 12.1% — equal to 3% + 1.3 × (10% − 3%); a higher beta raises the required return due to greater exposure to market (systematic) risk.
E. Cannot be determined without size and value factors.

✅ 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.

Q53.

Daily stock returns are best approximated by which distribution? A. Normal distribution
B. Lognormal distribution
C. Binomial distribution
D. Uniform distribution
E. Poisson distribution

✅ Correct: A. Over short horizons, stock returns are well-approximated by the normal distribution.

Q54.

A stock’s rolling 12-month volatility rose from 15% to 25% over the past year, while its estimated beta remained roughly constant at β = 0.9. With risk-free rate rf = 3% and expected market return E(Rm) = 9%, which statement is MOST consistent with CAPM and mean–variance analysis now? A. The expected return must rise above 8.4% because higher σ increases the required return in CAPM.
B. The expected return must fall because higher σ reduces beta.
C. The expected return is unchanged and the Sharpe ratio improves as σ rises.
D. The expected return remains 8.4% (= 3% + 0.9 × (9% − 3%)), but the Sharpe ratio worsens as σ rises (from (8.4−3)/0.15 ≈ 0.36 to (8.4−3)/0.25 ≈ 0.22).
E. CAPM provides no implication once volatility changes.

✅ 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.

Q55.

Two stocks (A and B) have equal variance but E(RA)=12% and E(RB)=14%. Which would a nondiversified investor prefer? A. Stock B
B. Stock A
C. Indifferent, same variance
D. Whichever has lower beta
E. Cannot be determined

✅ Correct: A. With identical risk, the higher expected return (14%) is preferred.

Q56.

Market portfolio return=9%, σ=18%. Rf=3%. What is the slope of the CML? A. 0.20
B. 0.25
C. 0.30
D. 0.33
E. 0.40

✅ Correct: D. (9−3)/18=0.33.

Q57.

Portfolios that deliver the highest expected return for a given level of risk are called: A. Dominated portfolios
B. Efficient portfolios
C. Arbitrage portfolios
D. Diversifiable portfolios
E. Passive portfolios

✅ Correct: B. Efficient portfolios maximize return for a given risk or minimize risk for a given return.

Q58.

An investor holds a portfolio with three assets:
- Asset A: weight = 40%, σA = 10%
- Asset B: weight = 30%, σB = 20%
- Asset C: weight = 30%, σC = 15%

The pairwise correlations are: ρAB = 0.2, ρAC = 0.1, ρBC = 0.3.
What is the portfolio’s standard deviation (σp)? A. 11.0%
B. 11.5%
C. 12.0%
D. 12.1%
E. 12.5%

✅ 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.

Q59.

Which of the following is FALSE about the Security Market Line (SML)? A. It plots expected return vs beta
B. Its slope is the market risk premium
C. All correctly priced assets lie on it
D. It is identical to the CML
E. Mispriced assets lie above or below it

✅ Correct: D. The SML differs from the CML.

Q60.

An investor allocates 70% of wealth to stocks and 30% to bonds.
- Expected return of stocks: 14%, volatility = 20%
- Expected return of bonds: 6%, volatility = 8%
- Correlation between stock and bond returns: 0.2

What is the portfolio’s standard deviation (σp)? A. 11.0%
B. 11.5%
C. 14.8%
D. 15.5%
E. 16.0%

✅ 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.

Q61.

Which statement is TRUE about the Capital Market Line (CML)? A. It plots expected return vs beta
B. Its slope equals beta
C. It ignores the risk-free rate
D. It applies to all individual assets
E. It represents efficient portfolios of risk-free asset and the market portfolio

✅ Correct: E. CML shows efficient portfolios mixing risk-free and market portfolio.

Q62.

According to CAPM, the market portfolio is: A. The tangency portfolio when combined with rf
B. Risk-free
C. A portfolio with beta = 0
D. Identical to any efficient portfolio
E. The minimum variance portfolio

✅ Correct: A. In CAPM, the market portfolio is the tangency portfolio combined with the risk‑free asset to form the CML.

Q63.

Have empirical tests generally confirmed the CAPM’s predictions for high‑beta stocks? A. Yes, CAPM accurately explains high‑beta returns.
B. No, many tests show CAPM fails, especially for high‑beta stocks.
C. Only during bull markets.
D. Yes, but only for large‑cap stocks.
E. Empirical evidence is irrelevant to CAPM.

✅ Correct: B. Empirical evidence often rejects strict CAPM predictions, particularly for high‑beta stocks.

Q64.

Which statement best differentiates the Arbitrage Pricing Theory (APT) from the CAPM? A. APT assumes a single systematic risk factor, while CAPM allows many.
B. Both CAPM and APT require the market portfolio to be efficient.
C. CAPM uses regression against multiple factors; APT does not.
D. CAPM explains expected returns with a single beta on the market portfolio, while APT allows multiple factor sensitivities.
E. APT implies all securities lie exactly on the Security Market Line.

✅ Correct: D. CAPM uses one systematic factor (the market), while APT permits several economic factors driving returns.

Q65.

Which of the following statements best describes how asset pricing is determined under the CAPM framework? A. The expected return of an asset depends only on its own variance, regardless of correlations with the market.
B. Assets are priced according to their total risk, since both systematic and unsystematic risk are equally compensated.
C. An asset’s fair price is determined exclusively by investor demand, without reference to its relation to the market portfolio.
D. The expected return of an asset is determined by the risk-free rate plus a risk premium proportional to its beta, which measures systematic risk relative to the market portfolio.
E. In equilibrium, all assets must offer the same return, regardless of their risk exposure.

✅ 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.

Q66.

You hold a stock with expected return 14% and volatility 28%.
The risk-free rate is 3% and the market portfolio has expected return 11% and volatility 16%.
According to the Capital Market Line (CML), what is the minimum volatility you can achieve while targeting the same 14% expected return as the stock?
A. 18.0%
B. 20.0%
C. 22.0%
D. 24.0%
E. 28.0%

✅ 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.

Q67.

Over the past ninety-six years of U.S. market history, which of the following asset classes offered the highest overall return but also came with the largest fluctuations (volatility)? A. Treasury Bills
B. Small stocks
C. S&P 500 index
D. Corporate bonds
E. Treasury bonds

✅ 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.

Q68.

Consider two portfolios, P and Q, both lying on the efficient frontier. Portfolio P has higher expected return than Q. Which must be true? A. P has lower standard deviation than Q.
B. P and Q must have the same Sharpe ratio.
C. P dominates Q, offering higher return and lower risk.
D. P must have a beta below 1, while Q’s beta exceeds 1.
E. P has higher risk (σ) than Q, otherwise Q would not be on the efficient frontier.

✅ Correct: E. On the efficient frontier, portfolios with higher expected return necessarily come with higher volatility.

Q69.

An investor builds a portfolio with 50% in Asset A (σ=18%) and 50% in Asset B (σ=12%). If the correlation between A and B is 0.25, which statement is correct about the portfolio’s risk relative to its components? A. The portfolio volatility must equal the simple average: 15%.
B. The portfolio volatility is higher than Asset A’s volatility, since A is riskier.
C. The portfolio volatility will be lower than both assets’ volatilities, because correlation is less than 1.
D. The portfolio volatility lies between 12% and 18%, and is reduced below 15% by diversification due to correlation < 1.
E. The portfolio volatility is always equal to the weighted average of component volatilities, regardless of correlation.

✅ 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.

Q70.

Two assets have expected returns of 8% and 14%, with volatilities 10% and 20%, respectively. If an investor allocates 40% to the first and 60% to the second, and their correlation is 0.5, what is the portfolio’s volatility? A. 13.0%
B. 14.1%
C. 15.0%
D. 16.0%
E. 17.0%

✅ 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%.

Q71.

Suppose two portfolios, X and Y, have Sharpe ratios of 0.5 and 0.7 respectively. Which conclusion follows? A. X lies above the Capital Market Line, Y lies on it.
B. Both X and Y are efficient portfolios.
C. Y dominates X, since higher Sharpe ratio means better risk–adjusted return.
D. X must be risk-free, Y must be risky.
E. No conclusion is possible without knowing betas.

✅ Correct: C. Higher Sharpe ratio ⇒ higher slope in (E(R)−rf)/σ, so Y provides superior risk–return tradeoff.

Q72.

Risk‑free U.S. Treasury bills have which beta under CAPM, and why? A. Beta = 1, because they move with the market portfolio.
B. Beta > 0, since they have small inflation risk.
C. Beta < 0, since they hedge market downturns.
D. Beta = 0, since their returns are uncorrelated with the market.
E. Beta undefined, since they are riskless.

✅ Correct: D. By construction, risk‑free assets have β=0; their return does not covary with the market.

Q73.

An investor builds a portfolio with 60% in Asset A (σ = 15%) and 40% in Asset B (σ = 25%). The correlation between A and B is 0.3. What is the portfolio’s volatility? A. 17.0%
B. 17.5%
C. 18.0%
D. 18.5%
E. 19.0%

✅ Correct: C. Portfolio volatility is
(_p = ).
Substituting:
(_p = %).
This illustrates how diversification reduces risk below the weighted average of 19%.

Q74.

An investor forms a portfolio with three assets:
- Asset A: weight = 40%, σ = 12%
- Asset B: weight = 35%, σ = 20%
- Asset C: weight = 25%, σ = 25%

The correlations are ρ(A,B)=0.2, ρ(A,C)=0.1, and ρ(B,C)=0.4.
What is the portfolio’s volatility? A. 14.5%
B. 15.0%
C. 15.5%
D. 16.0%
E. 16.5%

✅ 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.

Q75.

A stock is underpriced relative to CAPM predictions. Where will it plot on the Security Market Line (SML), and what is the implication? A. Above the SML; expected return exceeds required return, implying positive alpha.
B. Below the SML; expected return below required return, implying negative alpha.
C. On the SML; correctly priced with alpha=0.
D. Above the CML; risk-adjusted return equals Sharpe ratio.
E. On the y‑axis, indicating zero systematic risk.

✅ Correct: A. Underpriced stocks plot above the SML, since investors earn more than required for their level of systematic risk (positive alpha).

Q76.

You start with a universe of risky assets whose pairwise correlations are strictly less than 1. You first build efficient portfolios using only 3 assets, and then expand the investable set to 10 assets (same return forecasts and volatilities, correlations unchanged on average). What happens to the mean–variance efficient frontier when the number of available assets increases? A. It shifts outward (up/left): for a given expected return you can attain lower volatility, and for a given volatility you can attain higher expected return.
B. It is unchanged, because adding assets with similar characteristics adds no diversification.
C. It rotates downward: adding assets always increases portfolio variance.
D. It collapses to a single point equal to the average stock’s risk and return.
E. Only the minimum-variance point moves; the rest of the frontier is unaffected.

✅ 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.

Q77.

Which is FALSE about CAPM assumptions? A. Investors are mean-variance optimizers
B. All investors have homogeneous expectations
C. There are no taxes or transaction costs
D. Unlimited borrowing and lending at risk-free rate
E. Market risk can be eliminated through diversification

✅ Correct: E. CAPM assumes systematic risk cannot be diversified away.

Q78.

Two risky assets A and B have the same expected return but different volatilities, σ_A=10% and σ_B=20%. As the correlation ρ between A and B varies from +0.9 down to −1, what happens to the feasible mean–variance set and the minimum-variance portfolio? A. Lower correlation raises expected returns but leaves risk unchanged.
B. As ρ decreases, the set shifts left (more diversification): the minimum achievable σ falls; at ρ = −1 there exists a combination with σ = 0 (e.g., w_A=σ_B/(σ_A+σ_B)).
C. The minimum σ is constant for any ρ; only the frontier’s slope changes.
D. Diversification benefits are identical for all ρ ≠ 1.
E. With ρ = +1 there is a zero-variance combination.

✅ Correct: B. Portfolio variance is ( (R_p)=w^2_A^2+(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 )).

Q79.

Which of the following describes the efficient frontier? A. All possible portfolios
B. Portfolios with minimum risk only
C. Portfolios dominated by others
D. Portfolios with maximum return for given risk
E. Portfolios with maximum risk for given return

✅ Correct: D. Efficient frontier shows best risk-return combinations.

Q80.

Market return=15%, Rf=5%, stock β=0.5. CAPM expected return? A. 10%
B. 11%
C. 12%
D. 13%
E. 14%

✅ Correct: A. 5%+0.5×(15−5)%=10%.

Q81.

Which of the following best explains the role of the risk-free rate in CAPM? A. It measures total volatility
B. It equals the market premium
C. It represents the baseline return investors can earn without risk
D. It measures alpha
E. It equals beta of the market

✅ Correct: C. The risk-free rate is the baseline for all investments in CAPM.

Q82.

Stock β=1.4, Rf=3%, Rm=11%. Expected return? A. 12%
B. 13%
C. 13.5%
D. 14.2%
E. 15%

✅ Correct: D. 3%+1.4×(11−3)%=14.2%.

Q83.

Which statement is TRUE about the efficient frontier? A. It only includes single assets
B. It shows optimal portfolios with maximum return for each risk level
C. It guarantees elimination of market risk
D. It is irrelevant in CAPM
E. It equals the Security Market Line

✅ Correct: B. The efficient frontier represents optimal risk-return trade-offs.

Q84.

Consider the same opportunity set of risky portfolios. Draw Capital Market Lines (CMLs) for different risk-free rates: 3%, 7.5%, 10%, and 15%. Which statement is MOST accurate about how the risk-free rate affects the CML and investors’ expected returns for a given standard deviation? A. A lower risk-free rate makes the CML steeper (higher Sharpe). Thus, for sufficiently large σ (levered positions), the 3% CML delivers the highest expected return for a given σ, even though higher rf gives a higher intercept at σ=0.
B. A higher risk-free rate always makes the CML steeper and dominates for every σ.
C. Changing the risk-free rate only shifts the CML in parallel; the slope is unchanged.
D. The CML slope is independent of the tangency portfolio, so all investors choose the same σ regardless of rf.
E. Raising the risk-free rate does not affect the CML or the optimal risky portfolio.

✅ 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.

Q85.

Which is FALSE about the Security Market Line (SML)? A. It has slope equal to the market risk premium
B. It shows expected return vs beta
C. It applies only to risk-free assets
D. Mispriced assets lie off it
E. Correctly priced assets lie on it

✅ Correct: C. The SML applies to all assets, not just risk-free.

Q86.

A stock has rf=3%, βM=1.2, βS=0.4, βB=0.6. Market premium=7%, size premium=2%, book-to-market premium=3%. Using the Fama–French three-factor model, what is its expected return? A. 11.4%
B. 12.0%
C. 14.2%
D. 15.0%
E. 16.8%

✅ Correct: C. E(R)=3%+1.2×7%+0.4×2%+0.6×3%=3%+8.4%+0.8%+1.8%=14.2%.

Q87.

Which ratio evaluates excess return relative to beta? A. Sharpe ratio
B. Treynor ratio
C. Information ratio
D. Sortino ratio
E. Alpha

✅ Correct: B. Treynor=(Rp−Rf)/β.

Q88.

An investor borrows at rf=4% an amount equal to initial wealth and invests everything in a risky portfolio with E(R)=16%, σ=20%. What are the expected return and volatility of the leveraged portfolio? A. E(R)=24%, σ=30%
B. E(R)=28%, σ=40%
C. E(R)=20%, σ=25%
D. E(R)=32%, σ=50%
E. E(R)=12%, σ=20%

✅ Correct: B. Doubling exposure ⇒ E(R)=2×16%−4%=28%; σ=2×20%=40%.

Q89.

Portfolio weights: 60% in Stock A (E(RA)=12%, σA=20%), 40% in Stock B (E(RB)=9%, σB=15%), Corr(A,B)=0.25. What is the portfolio’s expected return and volatility? A. E(R)=10.8%, σ≈16.0%
B. E(R)=11.0%, σ≈15.5%
C. E(R)=10.2%, σ≈14.8%
D. E(R)=10.8%, σ≈15.9%
E. E(R)=11.4%, σ≈17.0%

✅ 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%.

Q90.

Microsoft has β=1.13, rf=3%, market risk premium=8%. According to CAPM, what is its expected return? A. 12.04%
B. 11.5%
C. 13.0%
D. 14.5%
E. 15.6%

✅ Correct: A. E(R)=3%+1.13×8%=12.04%.

Q91.

Consider an equally weighted portfolio of N = 50 stocks. Each stock has variance 0.04 (i.e., σ = 20%) and the average covariance across stocks is 0.012. Using the large-portfolio identity Var(R_p) = (1/N) × average variance + (1 − 1/N) × average covariance, what is the portfolio’s volatility now, and what happens as N → ∞? A. σ_p ≈ 9.8%; as N → ∞, Var → 0.
B. σ_p ≈ 10.4%; as N → ∞, Var → average variance (0.04).
C. σ_p ≈ 11.2%; as N → ∞, Var → average covariance (0.012), so covariances dominate in large portfolios.
D. σ_p ≈ 12.6%; as N → ∞, Var stays constant.
E. σ_p = 20% regardless of N (diversification does not affect volatility).

✅ 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.

Q92.

Over time, the annualized volatility of a broad market index is typically much lower than the weighted-average volatility of its individual constituent stocks. However, during episodes of systemic stress, both volatilities rise and the gap between them narrows. Which mechanism best explains this pattern? A. Idiosyncratic risk increases in crises, strengthening diversification for the index.
B. Changes in the risk-free rate mechanically depress index volatility outside crises.
C. Average pairwise correlations among stocks jump sharply in crises; with higher correlation, diversification benefits shrink and the index volatility converges toward the (higher) average individual volatility.
D. Betas fall to zero in crises, eliminating systematic risk.
E. The difference is solely due to different sampling windows (monthly vs. daily).

✅ 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.

Q93.

Which ratio is most suitable to compare portfolios regardless of diversification? A. Sharpe ratio
B. Treynor ratio
C. Beta
D. Alpha
E. Standard deviation

✅ Correct: A. Sharpe ratio uses total risk, suitable for any portfolio.

Q94.

Portfolio σ=15%, return=11%, Rf=3%. What is the Sharpe ratio? A. 0.4
B. 0.45
C. 0.5
D. 0.55
E. 0.53

✅ Correct: E. Sharpe=(11−3)/15=0.53.

Q95.

A portfolio consists of 50% in Stock A (E(RA)=15%, σA=25%), 30% in Stock B (E(RB)=10%, σB=20%), and 20% in the risk‑free asset (rf=4%). Correlation between A and B is 0.3. What is the portfolio’s expected return? A. 11.0%
B. 11.9%
C. 12.6%
D. 13.2%
E. 14.0%

✅ 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.)

Q96.

Stock β=1.2, Rf=5%, Rm=13%. CAPM expected return? A. 13%
B. 14%
C. 14.2%
D. 14.6%
E. 15%

✅ Correct: D. 5%+1.2×(13−5)%=14.6%.

Q97.

A stock has β=1.5, rf=5%, and is expected to return 14%. If E(Rm)=11%, what is the stock’s alpha relative to CAPM? A. −1.5%
B. −2.0%
C. −2.5%
D. 0%
E. +1.0%

✅ Correct: C. CAPM required return=5%+1.5×(11%−5%)=14%. Stock’s actual E(R)=14%. Correct answer: D

Q98.

You invest 40% in Stock A (E(R)=12%, σ=18%), 40% in Stock B (E(R)=10%, σ=22%), and 20% in Stock C (E(R)=8%, σ=12%). Assume zero correlations among all three risky assets. What is the portfolio’s expected return and approximate volatility? A. E(R)=10.4%, σ≈13.7%
B. E(R)=10.2%, σ≈15.0%
C. E(R)=11.0%, σ≈14.5%
D. E(R)=9.6%, σ≈12.0%
E. E(R)=10.4%, σ≈16.0%

✅ 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%.

Q99.

Which of the following is TRUE about the Capital Market Line (CML)? A. It shows return vs beta
B. It passes through (β=1, Rm)
C. It is identical to SML
D. It cannot be used with risk-free assets
E. It represents risk-return combinations of market portfolio and risk-free asset

✅ Correct: E. The CML connects the risk-free rate with the market portfolio.

Q100.

Which is NOT an assumption of CAPM? A. Investors can borrow/lend at Rf
B. Investors earn different expected returns for same risk
C. Investors are rational
D. Markets are frictionless
E. Homogeneous expectations

✅ Correct: B. CAPM assumes homogeneous expectations.

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