PART A Capital Allocation to Risky Assets
. Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $50,000 or $150,000, with equal probabilities of .5. The alternative riskless investment in T-bills pays 5%. (LO 5-3)
a. If you require a risk premium of 10%, how much will you be willing to pay for the portfolio?
b. Suppose the portfolio can be purchased for the amount you found in (a). What will the expected rate of return on the portfolio be?
. Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 18%. T-bills offer a risk-free 7% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to bills?
Please answer the following questions 3 to 7 based on the following assumption: you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%.
. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. (LO 5-3)
a. What is the expected return and standard deviation of your client’s portfolio?
b. Suppose your risky portfolio includes the following investments in the given proportions:
Stock Given Proportions
Stock A 27%
Stock B 33%
Stock C 40%
What are the investment proportions of your client’s overall portfolio, including the position in T-bills?
c. What is the reward-to-volatility ratio ( S ) of your risky portfolio and your client’s overall portfolio?
d. 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.
. Suppose the same client in the previous problem decides to invest in your risky portfolio
a proportion ( y ) of his total investment budget so that his overall portfolio will have an expected rate of return of 15%. (LO 5-3)
a. What is the proportion y?
b. What are your client’s investment proportions in your three stocks and the T-bill fund?
c. What is the standard deviation of the rate of return on your client’s portfolio?
. Suppose the same client as in the previous problem prefers to invest in your portfolio a proportion (y ) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio’s standard deviation will not exceed 20%. (LO 5-3)
a. What is the investment proportion, y?
b. What is the expected rate of return on the overall portfolio?
. Suppose the same client as in the previous problem has the Utility Function: U = E(r) – ½ A σ2. The client has Coefficient of risk aversion A equal to 4. The client prefers to invest in your portfolio a proportion (y) that is the optimal capital allocation.
a. What is the investment proportion, y*?
b. What is the expected rate of return on the overall portfolio?
c. What is the standard deviation of the rate of return on your client’s portfolio?
. You estimate that a passive portfolio invested to mimic the S&P 500 stock index yields an expected rate of return of 13% with a standard deviation of 25%. Draw the CML and your fund’s CAL on an expected return/standard deviation diagram. (LO 5-4)
a. What is the slope of the CML?
b. Characterize in one short paragraph the advantage of your fund over the passive fund.
. Your client (see previous problem) wonders whether to switch the 70% that is invested in your fund to the passive portfolio. (LO 5-4)
a. Explain to your client the disadvantage of the switch.
b. Show your client the maximum fee you could charge (as a percent of the investment in your fund deducted at the end of the year) that would still leave him at least as well off investing in your fund as in the passive one. (Hint: The fee will lower the slope of your client’s CAL by reducing the expected return net of the fee.)
. You manage an equity fund with an expected risk premium of 10% and a standard deviation of 14%. The rate on Treasury bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund.
a. What is the expected return and standard deviation of return on your client’s portfolio? (LO 5-3)
b. What is the reward-to-volatility ratio for the equity fund in the previous problem?
.
You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. Your client’s degree of risk aversion is A = 3.5.
a. What proportion, y, of the total investment should be invested in your fund?
b. What is the expected value and standard deviation of the rate of return on your client’s optimized portfolio?
