Question

Consider two assets, A and B, with the following equally likely rates of return: A will return either 3%, 6%, or 3.5%. B will return either 2.5%, 8%, or 7.5. Asset A 3.0% 6.0% 3.5% Asset B 2.5% 8.0% 7.5% Find the expected rates of return for assets A and B. Which asset would an investor, who cares only about expected return and risk and can choose only one or the other, prefer?

Answer 1

Expected return of Asset A=1/3*(3%+6%+3.5%)=4.167%

Expected return of Asset B=1/3*(2.5%+8%+7.5%)=6.000%

Risk or Standard Deviation of Asset A=sqrt(1/3*(3%-1/3*(3%+6%+3.5%))^2+1/3*(6%-1/3*(3%+6%+3.5%))^2+1/3*(3.5%-1/3*(3%+6%+3.5%))^2)=1.312%

Risk or Standard Deviation of Asset A=sqrt(1/3*(2.5%-1/3*(2.5%+8%+7.5%))^2+1/3*(8%-1/3*(2.5%+8%+7.5%))^2+1/3*(7.5%-1/3*(2.5%+8%+7.5%))^2)=2.4833%

Coefficient of Variation of Asset A=1.312%/4.167%=0.314854812

Coefficient of Variation of Asset B=2.4833%/6%=0.413883333

CHOOSE ASSET A