You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two 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?

Question

Quizplus · Accepted Answer

Let x be the proportion of the portfolio invested in the risky portfolio P. Then (1-x) is the proportion invested in the T-bill. 
The expected rate of return of the portfolio is: 
0.11 = x(0.14) + (1-x)(0.05) 
Solving for x, we get: 
x=0.19 
So, 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