Final answer:
The expected rate of return on the client's combined investment portfolio is 11%, and the standard deviation, which represents risk, is 21%. The calculation involves a weighted average of both the risky portfolio and the risk-free investment.
Step-by-step explanation:
You manage a risky portfolio with an 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. We are asked to calculate the expected value and standard deviation of the rate of return on her portfolio.
The expected return of the client's portfolio can be calculated by taking a weighted average of the returns from the risky portfolio and the risk-free T-bill money market fund. This is given by:
Expected Return = (0.70 * 14%) + (0.30 * 4%) = 9.8% + 1.2% = 11%.
To determine the standard deviation of the client's portfolio, we must remember that the standard deviation of the risk-free asset is 0%, as there is no variability in its return. Therefore, the standard deviation of the client's portfolio is simply the standard deviation of the risky portfolio multiplied by the weight of the risky portfolio in the total portfolio: Standard Deviation = 0.70 * 30% = 21%. Therefore, the expected value and standard deviation of the rate of return on her portfolio are 11% and 21%, respectively.