Question

Need some help with this one, thanks

You are considering investing $2,400 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 8% 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 15%, and Y has an expected rate of return of 12%. To form a complete portfolio with an expected rate of return of 11%, 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.

48%; 36%; 12%

50%; 38%; 13%

27%; 60%; 13%

0%; 75%; 25%

Answer 1

Expected Return on portfolio = Weighted average return

Hence, expected return of P = 15%*75% + 12%*25% = 14.25%

Let x be invested in risky portfolio P

11% = 8%(1-x) + 14.25%*x

11% = 8% - 8%x + 14.25%x

X = 48%

Hence, invested in risky portfolio = 48%

In X = 48%*75% = 36%

Y = 12%

Hence, the answer is

48%; 36%; 12%