You invest $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04. 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 0.11?
A) 53.8% and 46.2%
B) 75% and 25%
C) 62.5% and 37.5%
D) 46.2% and 53.8%
E) Cannot be determined.

Question

Quizplus · Accepted Answer

To achieve an expected return of 0.11, you can use the formula for the expected return of a portfolio: E(Rp) = w1 * E(R1) + w2 * E(R2), where E(Rp) is the expected return of the portfolio, w1 and w2 are the weights of the investments in the risky asset and the risk-free asset respectively, and E(R1) and E(R2) are the expected returns of the risky asset and the risk-free asset respectively. Plugging in the numbers: 0.11 = w1 * 0.17 + (1 - w1) * 0.04. Solving for w1 gives w1 = 0.538 or 53.8%, meaning 46.2% must be invested in the risk-free asset.

You Invest $1,000 in a Risky Asset with an Expected