The expected rate of return for stock A, stock B, and stock C are X%, 20%, and 1

Question

The expected rate of return for stock A, stock B, and stock C are X%, 20%, and 14%, respectively. The risk (as measured by standard deviation of returns) of stock A, stock B, and stock C are 43%, 62%, and 52%, respectively. The correlation coefficients of returns between A and B is 0.26, between A and C is 0.19, and between B and C is 0.07. You form a portfolio by investing 22.50% of your wealth in A, 25% of your wealth in B, and remaining wealth in C. The expected return of your portfolio is 14.60%. What is the risk of your portfolio?

Explanation / Answer

Portfolio

A - 22.50% B - 25% C = 100-22.50-35 = 52.50%

Return of portfolio = (x*0.225)+ 0.25*20%+(0.525*14%)

14.60% = 0.225x + 0.1235

0.225x = 0.0225

x = 0.0225/0.225 = 10%

Therefore, Expected rate of return for Stock A = 10%

Portfolio risk is measured using Standard Deviation.

Portfolio standard deviation =Squareroot(weight of A*SD of A+weight of B*SD of B+weight of c*SD of C+2*WeightA*WeightB*SD ofA*SD of B*Correlation coefficient of A and B+2*WeightB*WeightC*SD ofB*SD of C*Correlation coefficient of B and C +2*WeightA*WeightC*SD ofA*SD of C*Correlation coefficient of A and C

=SqRt(0.225*0.43+0.25*0.62+0.525*0.52+2*0.225*0.25*0.43*0.62*0.26+2*0.25*0.525*0.62*0.52*0.07+2*0.225*0.525*0.43*0.52*0.19)

= SqRt(0.53255+0.005924+0.010037)

=SqRt(0.638844)

=0.799 = 0.80

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