Question

show work in excel please

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 _________.

Answer 1

Correlation of stock A and stock B = 0.5
SD of Stock A = 29%
SD of stock B = 14%
Covariance of the stock A and stock B = Correlation of (stock A, stock B) * SD of stock A* SD of stock B
= 0.5 * 29 * 14 = 203

Weight of stock A = [Expected Return of the stock A – Risk free rate]* Variance of Stock B – [Expected Return of the Stock B – Risk Free rate]* Covariance of the stock A & stock B/ [Expected Return of the stock A – Risk free rate]* Variance of Stock B + [Expected Return of the stock B – Risk Free rate]* Variance of the stock A – [Expected Return of the stock A – Risk free rate + Expected Return of the stock B – Risk Free rate]* Covariance of the stock A & stock B

= [0.15-0.05]*196 – [0.10-0.05]*203/ [0.15-0.05]*196 + [0.10 – 0.05]* 841 – [0.15- 0.05 + 0.10 – 0.05] * 203

Weights of the stock A = 9.45/ 31.20 = 30% (Approx Weight)

Weight of the stock B = 1- weight of the stock = 1-0.30 = 0.70 Or 70%.

The proportion of optimal risky portfolio invested in stock B is approximately 70%.