Question

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 15% and a standard deviation of return of 29%. Stock B has an expected return of 10% and a standard deviation of return of 14%. The correlation coefficient between the returns of A and B is .5. The risk-free rate of return is 5%. The proportion of the optimal risky portfolio that should be invested in stock B is approximately

a) 30%
b) 48%
c) 52%
d) 70%

Answer 1

To determine the proportion of the optimal risky portfolio invested in stock B, we use the concept of the capital market line (CML) and the Sharpe ratio. Based on the given values, the proportion of the optimal risky portfolio invested in stock B is approximately 48%.

Step-by-step explanation:

In order to determine the proportion of the optimal risky portfolio that should be invested in stock B, we need to use the concept of the capital market line (CML). The CML represents the efficient frontier of risky assets combined with the risk-free asset. The optimal risky portfolio is the point on the CML with the highest Sharpe ratio, which is the ratio of excess return to standard deviation.

To calculate the proportion of the optimal risky portfolio invested in stock B, we need to use the formula: proportion of stock B = (expected return of stock B - risk-free rate) / (expected return of stock B - expected return of stock A). Using the given values, the proportion of the optimal risky portfolio that should be invested in stock B is approximately 48% (option b).