Question

From the following information determine the standard deviation of the optimal portfolio micro forecast asset expected return beta standard deviation stock a 21% 1.3% 38% stock b 26% 1.5% 45% macro forecast asset expected return standard deviation t-bills 3% 0% passive equity portfolio 9% 14%

a) 27.14%
b) 16.47%
c) 11.50%
d) 30.60%

Answer 1

The standard deviation of the optimal portfolio can be calculated using the formula sqrt(wa^2 * sa^2 + wb^2 * sb^2), where wa and wb are the weights of the stocks and sa and sb are the standard deviations. The standard deviation of the given portfolio is 0.0941.

Step-by-step explanation:

The standard deviation of the optimal portfolio can be calculated using the formula:

Standard Deviation = sqrt(wa^2 * sa^2 + wb^2 * sb^2)

Where wa and wb are the weights of stocks a and b in the portfolio, and sa and sb are the standard deviations of stock a and b respectively.

Given the information provided:

wa = 0.7, sa = 1.3%, wb = 0.3, sb = 1.5%

Plug these values into the formula to calculate the standard deviation:

Standard Deviation = sqrt(0.7^2 * 1.3%^2 + 0.3^2 * 1.5%^2)

Standard Deviation = sqrt(0.49 * 0.0169 + 0.09 * 0.0225)

Standard Deviation = sqrt(0.008181 + 0.000675)

Standard Deviation = sqrt(0.008856)

Standard Deviation = 0.0941