Question

You are considering investing $1,400 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 4% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 18%, and Y has an expected rate of return of 14%. To form a complete portfolio with an expected rate of return of 9%, 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. Show all calculation

a. 0%; 60%; 40%

b.50%; 30%; 20%

c.40%; 24%; 16%

d. 32%; 42%; 26%

Answer 1

Correct option is > c. 40%; 24%; 16%

Working:

.

Risky portfolio is X and Y and if we invest only in risk portfolio what would we earn? ;

Expected return of risky portfolio = 0.6*18%+0.4*14% = 16.40%

.

Now, we should find out if we invest in Portfolio P, then weight applies to risk less asset will be “W” and risky asset will be “1-W”

Portfolio return = W*(Risk free rate) + (1-W)*(Risky portfolio return)

9% = W*4% + (1-W)*16.4%

9% = W*4% + 16.4%-W*16.4%

-7.4% = -12.4%*W

W = 59.68%

Hence, W-1 = 1-59.68% = 40.32% approx. (round it to 40%)

Therefore, 40% goes to risky portfolio X and Y.

Now, we can allocate internally to risky portfolio i.e.

60%*40% for X = 24%

40%*40% for Y = 16%

You are considering investing $1,400 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 4% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 18%, and Y has an expected rate of return of 14%. To form a complete portfolio with an expected rate of return of 9%, you should invest approximately 40% in the risky portfolio. This will mean you will also invest approximately 24% and 16% of your complete portfolio in security X and Y, respectively.