Question

Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 33%. The T-bill rate is 6%. Your client chooses to invest 75% of a portfolio in your fund and 25% in a T-bill money market fund.

a. What is the expected return and standard deviation of your client's portfolio? (Round your answers to 2 decimal places.)

Answer 1

The client's portfolio has an expected return of 14.25% and a standard deviation of 24.75%.

Step-by-step explanation:

The expected return of the client's portfolio can be computed as a weighted average of the returns from the two investments. The risky portfolio has an expected return of 17%, and the T-bill has an expected return of 6%. Since the client invests 75% in the risky portfolio and 25% in T-bills, the expected return is (0.75 × 17%) + (0.25 × 6%) = 12.75% + 1.5% = 14.25%.

As T-bills are risk-free, their standard deviation is zero. The standard deviation of the client's portfolio only comes from the risky investment. Since only 75% of the total portfolio is invested in the risky asset, the portfolio's standard deviation is 0.75 × 33% = 24.75%.