Question

2. An investor can design a risky portfolio based on two stocks, S and B. Stock...

2. An investor can design a risky portfolio based on two stocks, S and B. Stock S has an expected return of 12% and a standard deviation of return of 25%. Stock B has an expected return of 10% and a standard deviation of return of 20%. The correlation coefficient between the returns of S and B is 0.4. The risk-free rate of return is 5%

a. The proportion of the optimal risky portfolio that should be invested in stock B is approximately __________.

b. The expected return on the optimal risky portfolio is __________.

Homework Answers

Answer #1

(a) Let the proportion invested in Stock S be w1. Hence, proportion invested in Stock B = 1 - w1

Objective is to find the weights to reduce the risk of the portfolio i.e. minimize the variance

Standard Deviation of Stock S = σS = 0.25

Standard Deviation of Stock B = σB = 0.20

Correlation between stocks = CorrSB = 0.4

covariance of portfolio C = w12σS2 + (1-w1)2σB2 + 2w1(1-w1)*CorrSB = w120.252 + (1-w1)20.202 + 2w1(1-w1)*0.4

To minimize the covariance, dC/dw1 = 0

=> 2*0.252w1 - 2*0.202(1-w1) + 0.8(1-w1) - 0.8w1 = 0

=> 0.125w1 - 0.08w1 + 0.8 - 0.8w1 - 0.8w1 = 0

=> w1 = 0.5144

Hence, proportion invested in Stock B = 1- 0.5144 = 0.4856 or 48.56%

(b) Expected Return = w1RS + (1-w1)RB = 0.5144*0.12 + 0.4856*0.10 = 0.1103 or 11.03%

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