You manage a risky portfolio with expected rate of return of 18% and standard deviation of 28%. The T-bill rate is 8%. a. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. What is the expected value and standard deviation of the rate of return on his portfolio? b. What is the reward-to-volatility ratio (S) of your risky portfolio? Your client’s? c. Draw the CAL of your portfolio on an expected return–standard deviation diagram. What is the slope of the CAL? Show the position of your client on your fund’s CAL. d. Suppose that your client decides to invest in your portfolio a proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 16%. What is the proportion y? What is the standard deviation of the rate of return on your client’s portfolio? e. Suppose that your client prefers to invest in your fund a proportion y that maximizes the expected return on the complete portfolio subject to the constraint that the complete portfolio’s standard deviation will not exceed 18%. What is the investment proportion, y? What is the expected rate of return on the complete portfolio?

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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You manage a risky portfolio with expected rate of return of 18% and standard deviation of 28%. The T-bill rate is 8%. a. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. What is the expected value and standard deviation of the rate of return on his portfolio? b. What is the reward-to-volatility ratio (S) of your risky portfolio? Your client’s? c. Draw the CAL of your portfolio on an expected return–standard deviation diagram. What is the slope of the CAL? Show the position of your client on your fund’s CAL. d. Suppose that your client decides to invest in your portfolio a proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 16%. What is the proportion y? What is the standard deviation of the rate of return on your client’s portfolio? e. Suppose that your client prefers to invest in your fund a proportion y that maximizes the expected return on the complete portfolio subject to the constraint that the complete portfolio’s standard deviation will not exceed 18%. What is the investment proportion, y? What is the expected rate of return on the complete portfolio?

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