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%. You manage an active portfolio with expected return 18% and standard deviation 28%. The risk-free rate is 8%.
a. Draw the CML and your funds’ CAL on an expected return–standard deviation diagram.
b. What is the slope of the CML?
c. Characterize in one short paragraph the advantage of your fund over the passive fund.
d. Your client ponders whether to switch the 70% that is invested in your fund to the passive portfolio. Explain to your client the disadvantage of the switch.
e. 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.)