Reading 50: An Introduction to Portfolio Management - LOS following, style, black, class

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1.Which of the following equations is INCORRECT?

A)   Required Return_nominal = [(1 + Risk Free Rate_real)*(1 + Expected Inflation)*(1 + Risk Premium)] - 1.

B)   Beta = (Cov_{i, mkt}) / (σ²_mkt).

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

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

2.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)   0.54

C)   0.39

D)   0.30

3．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)   +0.50.

B)   +0.30.

C)   +1.00.

D)   0.00.

4．As the correlation between the returns of two assets becomes lower, the risk reduction potential becomes:

A)   smaller.

B)   unaffected.

C)   greater.

D)   decreased by the same level.

5．Assets A (with a variance of 0.25) and B (with a variance of 0.40) are perfectly positively correlated. If an investor creates a portfolio using only these two assets with 40 percent invested in A, the portfolio standard deviation is closest to:

A)   0.5795.

B)   0.3400.

C)   0.3742.

D)   0.7616.

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答案和详解如下：

1.Which of the following equations is INCORRECT?

A)   Required Return_nominal = [(1 + Risk Free Rate_real)*(1 + Expected Inflation)*(1 + Risk Premium)] - 1.

B)   Beta = (Cov_{i, mkt}) / (σ²_mkt).

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

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

The correct answer was D)

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.

2.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)   0.54

C)   0.39

D)   0.30

The correct answer was A)

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

s ² = [W_A²s_A² + W_B²s_B² + 2W_AW_Bs_As_Br_A,B]

Since s_As_Br_A,B = Cov_A,B, then

s ² = [(0.7² * 0.55²) + (0.3² * 0.85²) + (2 * 0.7 * 0.3 * )9.0] = [0.14822 + 0.06502 + 0.378] = 0.59124, or approximately 0.59.

3．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)   +0.50.

B)   +0.30.

C)   +1.00.

D)   0.00.

The correct answer was C)

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

4．As the correlation between the returns of two assets becomes lower, the risk reduction potential becomes:

A)   smaller.

B)   unaffected.

C)   greater.

D)   decreased by the same level.

The correct answer was C)

Perfect positive correlation (r = +1) of the returns of two assets offers no risk reduction, whereas perfect negative correlation (r = -1) offers the greatest risk reduction.

5．Assets A (with a variance of 0.25) and B (with a variance of 0.40) are perfectly positively correlated. If an investor creates a portfolio using only these two assets with 40 percent invested in A, the portfolio standard deviation is closest to:

A)   0.5795.

B)   0.3400.

C)   0.3742.

D)   0.7616.

The correct answer was A)

The portfolio standard deviation = [(0.4)²(0.25) + (0.6)²(0.4) + 2(0.4)(0.6)1(0.25)^.5(0.4)^.5]^.5 = .5795