1. Based on the scenarios below,
a. what is the expected return and standard deviation for a risky portfolio with the
proportion of 70% in abc stock and 30% in xyz stock.
b. If you want to allocate you money between this risky portfolio and a T-bill with 5% coupon
rate, your risk aversion coefficient is 4, please calculate the optimal portfolio.
ScenariosProabilityBoomNormalRecession35%@%Holding period returnabcxyz63#"9%-24%-23% 2. Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will
be either $70,000 or $200,000 with equal probabilities of .5. The alternative risk-free investment in T-bills pays 6% per year.
a. If you require a risk premium of 8%, how much will you be willing to pay for the portfolionow? b. Suppose that the portfolio can be purchased for the amount you found in (a). What will be the expected rate of return on the portfolio?
c. Now suppose that you require a risk premium of 12%. What is the price that you will be willing to pay?
d. Comparing your answers to (a) and (c), what do you conclude about the relationship
between the required risk premium on a portfolio and the price at which the portfolio will sell? 3. Draw the indifference curve in the expected return–standard deviation plane
corresponding to a utility level of 5% for an investor with a risk aversion coefficient of 3. 4. 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 chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund.
a. What is the expected value and standard deviation of the rate of return on his
portfolio?
b. What is the reward-to-variability ratio (Slope) 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.
5. 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%.You estimate that a passive portfolio, that is, one invested in a risky portfolio that mimics the S&P 500 stock index, yields an expected rate of return of 13% with a standard deviation of 25%.
a. Draw the CML and your funds’ CAL on an expected return–standard deviation diagram. b. Characterize in one short paragraph the advantage of your fund over the passive fund.
6. 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 chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. There is a passive portfolio, that is, one invested in a risky portfolio that mimics the S&P 500 stock index, yields an expected rate of return of 13% with a standard deviation of 25%.Your client ponders whether to switch the 70% that is invested in your fund to the passive portfolio. a. Explain to your client the disadvantage of the switch.
b. Show him the maximum fee you could charge (as a percentage of the investment in your fund, deducted at the end of the year) that would leave him at least as well off investing in your fund as in the passive one. (Hint: The fee will lower the slope of his CAL by reducing the expected return net of the fee.)