You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03.
-What percentages of your money must be invested in the risky asset and the risk-free asset,respectively,to form a portfolio with an expected return of 0.08?
A)85% and 15%
B)75% and 25%
C)62.5% and 37.5%
D)57% and 43%
E)cannot be determined

Question

Quizplus · Accepted Answer

Let x be the percentage of the investment in the risky asset and (1-x) be the percentage of the investment in the risk-free asset.
Expected return of the portfolio:
0.11x + 0.03(1-x) = 0.08
0.11x -0.03x + 0.03 = 0.08
0.08x = 0.05
x = 0.625 or 62.5%
Therefore, the percentage of the investment in the risky asset is 62.5% and in the risk-free asset is 37.5%. Thus, the answer is C.

You Invest $100 in a Risky Asset with an Expected