Suppose you are given the following data.

Asset Expected Return Standard Deviation

A 7% 30%

B 5% 20%

Risk-free 1%

Assets A and B are the only risky assets in the economy. The correlation between assets A and B is 0.25. Suppose that there is a portfolio P (consisting of Assets A and B) which has an expected return of 5.8%. What is the weight of Asset A in the portfolio P?

a. 18.97%

b. 27.61%

c. 12.32%

d. 14.65%

The weight of Asset A in the portfolio P is 18.97%. The right answer is a

Explanation:

In order to calculate the weight of asset A in the portfolio P, we would have to calculate first the weight of stock A and B as follows:

Let weight of Asset A is w,

0.058 = w (0.07) + (1 - w) (0.05)

0.058 = 0.07w + 0.05 - 0.05w

w = 40%

Weight of Stock A = 40%

Weight of Stock B = 60%

Therefore Standard Deviation = [ (0.40) 2 (0.30) 2 + (0.60) 2 (0.20) 2 + 2 (0.40) (0.60) (0.30) (0.20) (0.25) ]1/2

Standard Deviation = 18.97%

The weight of Asset A in the portfolio P is 18.97%