Question

You are considering investing $2,100 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 75% and 25% respectively. X has an expected rate of return of 12%, and Y has an expected rate of return of 9%. To form a complete portfolio with an expected rate of return of 8%, you should invest approximately __________ in the risky portfolio. This will mean you will also invest approximately __________ and __________ of your complete portfolio in security X and Y, respectively.

0%; 75%; 25%

21%; 63%; 16%

50%; 38%; 13%

48%; 36%; 12%

Answer 1

Portfolio return is equal to weighted average return

Let the % invested in risky portfolio be X

(12%*0.75+9%*0.25)*x + 5%(1-x) = 8%

11.25%x +5% -5%x = 8%

X = 0.48

I.e. 48%

Hence, invested in X = 48%*0.75 = 36%

Y = 12%