You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio,P,constructed with 2 risky securities,X and Y.The weights of X and Y in P are 0.60 and 0.40,respectively.X has an expected rate of return of 0.14 and variance of 0.01,and Y has an expected rate of return of 0.10 and a variance of 0.0081.If you want to form a portfolio with an expected rate of return of 0.10,what percentages of your money must you invest in the T-bill,X,and Y,respectively if you keep X and Y in the same proportions to each other as in portfolio P?
A) 0.25;0.45;0.30
B) 0.19;0.49;0.32
C) 0.32;0.41;0.27
D) 0.50;0.30;0.20
E) cannot be determined

Question

Quizplus · Accepted Answer

To form a portfolio with an expected rate of return of 0.10, we need to find the weights of each asset in the portfolio. Let the weight of the T-bill be w_t, and the weight of the risky portfolio be w_p. Then we have:

0.05w_t + 0.10w_p = 0.10

Since the weights of X and Y in P are 0.60 and 0.40 respectively, we can write:

w_p = 0.60w_x + 0.40w_y

where w_x is the weight of X in the portfolio and w_y is the weight of Y in the portfolio. We also know that w_x + w_y = 1.

To find w_x and w_y, we can use the formula for the expected return of P:

E(P) = 0.14*0.60 + 0.10*0.40 = 0.124

Then we have:

0.10 = 0.05w_t + 0.124w_x + 0.0816w_y

And:

1 = w_x + w_y

Solving these equations gives:

w_t = 0.32
w_x = 0.41
w_y = 0.27

So we should invest 32% in the T-bill, 41% in X, and 27% in Y, which is choice C.

You Are Considering Investing $1,000 in a T-Bill That Pays