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Reading 50: An Introduction to Portfolio Management - LOS

Q6. Adding a stock to a portfolio will reduce the risk of the portfolio if the correlation coefficient is less than which of the following?

A)   0.00.

B)   +0.50.

C)   +1.00.

Q7. An investor has a two-stock portfolio (Stocks A and B) with the following characteristics:

  • σA = 55%

  • σB = 85%

  • CovarianceA,B = 0.9

  • WA = 70%

  • WB = 30%

The variance of the portfolio is closest to:

A)   0.59

B)   0.39

C)   0.54

Q8. An investor’s portfolio currently consists of 100% of stocks that have a mean return of 16.5% and an expected variance of 0.0324. The investor plans to diversify slightly by replacing 20% of her portfolio with U.S. Treasury bills that earn 4.75%. Assuming the investor diversifies, what are the expected return and expected standard deviation of the portfolio?

          ERPortfolio                                σPortfolio

 

A)  14.15%                                   2.59%

B)  10.63%                                  2.59%

C)  14.15%                                  14.40%

Q9. What is the variance of a two-stock portfolio if 15% is invested in stock A (variance of 0.0071) and 85% in stock B (variance of 0.0008) and the correlation coefficient between the stocks is –0.04?

A)   0.0020.

B)   0.0026.

C)   0.0007.

Q10. Which of the following equations is least accurate?

A)   Real Risk-Free Rate = [(1 + nominal risk-free rate) / (1 + expected inflation)] − 1.

B)   Standard Deviation2-Stock Portfolio = [(w12 × σ12) + (w22 × σ22) + (2 × w1 × w2 σ1σ2 × ρ1,2)].

C)   Required Returnnominal = [(1 + Risk Free Ratereal) × (1 + Expected Inflation) × (1 + Risk Premium)] − 1.

答案和详解如下:

Q6. Adding a stock to a portfolio will reduce the risk of the portfolio if the correlation coefficient is less than which of the following?

A)   0.00.

B)   +0.50.

C)   +1.00.

Correct answer is C)

Adding any stock that is not perfectly correlated with the portfolio (+1) will reduce the risk of the portfolio.

Q7. An investor has a two-stock portfolio (Stocks A and B) with the following characteristics:

  • σA = 55%

  • σB = 85%

  • CovarianceA,B = 0.9

  • WA = 70%

  • WB = 30%

The variance of the portfolio is closest to:

A)   0.59

B)   0.39

C)   0.54

Correct answer is A)

The formula for the variance of a 2-stock portfolio is:

s2 = [WA2σA2 + WB2σB2 + 2WAWBσAσBrA,B]

Since σAσBrA,B = CovA,B, then

s2 = [(0.72 × 0.552) + (0.32 × 0.852) + (2 × 0.7 × 0.3 × 0.9)] = [0.14822 + 0.06502 + 0.378] = 0.59124, or approximately 0.59.

Q8. An investor’s portfolio currently consists of 100% of stocks that have a mean return of 16.5% and an expected variance of 0.0324. The investor plans to diversify slightly by replacing 20% of her portfolio with U.S. Treasury bills that earn 4.75%. Assuming the investor diversifies, what are the expected return and expected standard deviation of the portfolio?

          ERPortfolio                                σPortfolio

 

A)  14.15%                                   2.59%

B)  10.63%                                  2.59%

C)  14.15%                                  14.40%

Correct answer is C)

Since Treasury bills (T-bills) are considered risk-free, we know that the standard deviation of this asset and the correlation between T-bills and the other stocks is 0. Thus, we can calculate the portfolio expected return and standard deviation.

Step 1: Calculate the expected return
Expected ReturnPortfolio = (wT-bills × ERT-bills) + (wStocks × ERStocks)
= (0.20) × (0.0475) + (1.00-0.20) × (0.165) = 0.1415, or 14.15%.

Step 2: Calculate the expected standard deviation
When combining a risk-free asset and a risky asset (or portfolio or risky assets), the equation for the standard deviation, σ1,2 = [(w12)(σ12) + (w22)(σ22) + 2w1w2 σ1 σ2ρ1,2]1/2, reduces to: σ1,2 = [(wStocks)(σStocks)] = 0.80 × 0.03241/2 = 0.14400, or 14.40%. (Remember to convert variance to standard deviation).

Q9. What is the variance of a two-stock portfolio if 15% is invested in stock A (variance of 0.0071) and 85% in stock B (variance of 0.0008) and the correlation coefficient between the stocks is –0.04?

A)   0.0020.

B)   0.0026.

C)   0.0007.

Correct answer is C)

The variance of the portfolio is found by:

[W12 σ12 + W22 σ22 + 2W1W2σ1σ2r1,2], or [(0.15)2(0.0071) + (0.85)2(0.0008) + (2)(0.15)(0.85)(0.0843)(0.0283)(–0.04)] = 0.0007.

Q10. Which of the following equations is least accurate?

A)   Real Risk-Free Rate = [(1 + nominal risk-free rate) / (1 + expected inflation)] − 1.

B)   Standard Deviation2-Stock Portfolio = [(w12 × σ12) + (w22 × σ22) + (2 × w1 × w2 σ1σ2 × ρ1,2)].

C)   Required Returnnominal = [(1 + Risk Free Ratereal) × (1 + Expected Inflation) × (1 + Risk Premium)] − 1.

Correct answer is B)         

This is the equation for the variance of a 2-stock portfolio. The standard deviation is the square root of the variance. The other equations are correct.

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