Question

1. Consider a portfolio P comprised of two risky assets (A and B) whose returns have a correlation of zero. Risky asset A has an expected return of 10% and standard deviation of 15%. Risky asset B has an expected return of 7% and standard deviation of 11%. Assuming a risk-free rate of 2.5%, what is the standard deviation of returns on the optimal risky portfolio?

a) 9.18%

b) .918%

c) .84%

d) 8.42%

Answer 1

Standard Deviation of a Protfolio = ((Weight A)² * (Variance of A) + (Weight B)² * (Variance of B) + 2 * Weight A * Weight B * Correlation A,B * Standard Deviation of A * Standard Deviation of B)^1/2

Since no info related to Weights is given we assume it to be 50% - 50%

So SD of Portfolio = ((0.5)^{2 *}  (0.15)² + (0.5)^{2 *}  (0.11)² + 2 * 0.5 * 0.5 * 0 * 0.15 * 0.11)^1/2

⁼ (0.25 * 0.0225 + 0.25 * 0.0121)^1/2

= (0.005625 + 0.003025) ^1/2

=(0.008650)^1/2

= 0.0930 or 9.3 %