Question

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 11% and a standard deviation of return of 18.0%. Stock B has an expected return of 7% and a standard deviation of return of 3%. The correlation coefficient between the returns of A and B is 0.50. The risk-free rate of return is 5% Find the proportion of the optimal risky portfolio that should be invested in stock A. What is the Sharpe Ratio of the optimal portfolio?

Answer 1

Optimal risk portfolio refers to a portfolio on efficient frontier which optimal combination of risky assets in such way that it provides highest return for every unit of risk.

following information provided in question -

Expected Return of A (R_A) = 0.11

Standard Deviation of A () = 0.18

Expected Return of B (R_B) = 0.07

Standard Deviation of A () = 0.03

Correlation of A & B (r_AB) = 0.5

Risk Free rate (r_f) = 0.05

We calculate the optimal weight of stock in optimal risky portfolio with following formula -

Thus, the proportion of Stock-A in optimal portfolio would be 33.51%

Expected Return of Portfolio (R_p)

Standard deviation of Portfolio ()

Sharpe Ratio of Portfolio