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:

• σ_A = 55%

• σ_B = 85%

• Covariance_A,B = 0.9

• W_A = 70%

• W_B = 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?

          ER_Portfolio                                σ_Portfolio

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 Deviation_{2-Stock Portfolio} = [(w₁² × σ₁²) + (w₂² × σ₂²) + (2 × w₁ × w₂ σ₁σ₂ × ρ_1,2)].

C)   Required Return_nominal = [(1 + Risk Free Rate_real) × (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:

• σ_A = 55%

• σ_B = 85%

• Covariance_A,B = 0.9

• W_A = 70%

• W_B = 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 = [W_A²σ_A² + W_B²σ_B² + 2W_AW_Bσ_Aσ_Br_A,B]

Since σ_Aσ_Br_A,B = Cov_A,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?

          ER_Portfolio                                σ_Portfolio

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 Return_Portfolio = (w_T-bills × ER_T-bills) + (w_Stocks × ER_Stocks)
= (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, σ_1,2 = [(w₁²)(σ₁²) + (w₂²)(σ₂²) + 2w₁w₂ σ₁ σ₂ρ_1,2]^1/2, reduces to: σ_1,2 = [(w_Stocks)(σ_Stocks)] = 0.80 × 0.0324^1/2 = 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 + 2W₁W₂σ₁σ₂r_1,2], 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 Deviation_{2-Stock Portfolio} = [(w₁² × σ₁²) + (w₂² × σ₂²) + (2 × w₁ × w₂ σ₁σ₂ × ρ_1,2)].

C)   Required Return_nominal = [(1 + Risk Free Rate_real) × (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.

thanks

thansk

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