Question

The expected return of Asset A and Asset B are 15% and 20% respectively, and the standard deviation of the two assets are 20% and 30% respectively. The correlation coefficient between the two assets is zero. Suppose you form a portfolio using the two assets, and the expected return of your portfolio is 22.5%. Find out the standard deviation of your portfolio.

Answer 1

Soluotion:

Calculation of Weight of each asset

Let the weight of Asset A=Wa

then weight of Asset B=1-Wa

Expected Return of portfolio=Return Of Asset A*Weight of Asset A+Return Of Asset B*Weight of Asset B

22.5%=15%*Wa+20%*(1-Wa)

0.225=.15Wa+.20-.2Wa

Wa=.225/-0.05

=-.5

Weight of Asset B(Wb) is 1.5

Calculation of standard deviation of your portfolio

standard deviation of your portfolio=SQRT[(SDA)^2*(Wa)^2+(SDB)^2*(Wb)^2+(2*SDA*SDB*Wa*Wb*CA,B)]

Where;

SDA=Standard deviation of Asset A

SDB=Standard deviation of Asset B

CA,B=Correlation of Asset A and Asset B

Thus standard deviation of portfolio;

=SQRT[(20)^2*(-0.5)^2+(30)^2*(1.5)^2+(2*20*30*-0.5*1.5*0)]

=SQRT[100+2025+0]

=46.10%