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 0.11,what percentages of your money must you invest in the T-bill and P,respectively?
A) 0.25;0.75
B) 0.19;0.81
C) 0.65;0.35
D) 0.50;0.50
E) cannot be determined

Question

Quizplus · Accepted Answer

Let x be the percentage of the investment in the risky portfolio. Then, (1-x) will be the percentage invested in the T-bill.

To find x, we can use the following formula for the expected rate of return of a portfolio:

E(rp) = x*E(rx) + (1-x)*E(ry)

where E(rx) and E(ry) are the expected rates of return for securities X and Y, respectively.

Plugging in the given values, we get:

0.11 = x*0.14 + (1-x)*0.1

Solving for x gives x = 0.19, which means we should invest 19% in the risky portfolio and 81% in the T-bill.

Therefore, the answer is B.

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