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In: Finance

10. Security A has an expected rate of return of 10% and a standard deviation of...

10. Security A has an expected rate of return of 10% and a standard deviation of 16%. Security B has an expected rate of return of 8% and a standard deviation of 12%. Let A and B are perfectly negatively correlated. The expected return of a risk-free portfolio formed with A and B is

Select one:

a. 10%

b. 9.47%

c. 7.86%

d. 8.86%

Expert Solution

Expected return of A, μ_A = 10%

Standard Deviation of A, σ_A = 16%

Expected return of B, μ_B = 8%

Standard Deviation of B, σ_B = 12%

Correlation coefficient, ρ_(A,B) = -1

Portfolio variance is given by the formula

Where w_A and w_B are weights of the assets in the portfolio

w_B = 1-w_A

For a risk free portfolio, variance = 0

Implies

Solving for w_A using solution for a quadratic equation

w_A = 0.0672 / 0.1568 = 0.428571

w_B = 1- w_A = 1- 0.428571 = 0.571429

Expected return of the risk free portfolio = w_A*μ_A + w_B*μ_B = 0.428571 * 10% + 0.571429 * 8%

= 4.2857% + 4.5714% = 8.8571%

Expected return of the risk free portfolio = 8.86%

Answer is Option d.

jeff jeffy answered 2 years ago

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