Question

Amelia owns $400,000 of a well-diversified mutual fund. She has additional savings of $100,000 that she has decided to invest in additional risky assets. Her current portfolio has an expected return of 10.5% with standard deviation of returns of 22.0%. The investment she is considering purchasing has an expected return of 12% with a standard deviation of 26.4%. If the correlation of returns between Amelia’s current portfolio and the new investment is .85. Should she add this investment?

Answer 1

Expected return=(400000*10.5%+100000*12%)/500000=10.8000%

Standard deviation=sqrt((4/5*22%)^2+(1/5*26.4%)^2+2*4/5*22%*1/5*26.4%*0.85)=22.2624%

Now Return/Standard deviation=10.8%/22.2624%=0.49

Earlier Return/Standard deviation=10.5%/22%=0.48

As return per unit risk increases, add the new investment