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.
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%
Get Answers For Free
Most questions answered within 1 hours.