Question

You manage a risky portfolio with expected rate of return of 14% and a standard deviation of 30%. The risk-free rate is 4%. A client chooses to invest 70% of her wealth in your portfolio and 30% in the T-bill money market fund. What is the expected value and standard deviation of the rate of return on her portfolio?

Answer 1

The expected value of the client's investment return is 11%, with a portfolio standard deviation of 21%.

Step-by-step explanation:

The expected value of the portfolio's return can be calculated using a weighted average of the returns from the risky portfolio and the risk-free T-bill money market fund.

To calculate the expected return, you would multiply the proportion of the total investment in each component by its expected return and add them together. In this case, it's (0.70 * 14%) + (0.30 * 4%), which equals 11%. The standard deviation of the return, however, only applies to the risky part of the portfolio, since the T-bill's standard deviation is zero. Therefore, the standard deviation of the overall portfolio is 0.70 * 30%, which equals 21%.