You estimate that a passive portfolio, that is, a risky portfolio that mimics a stock market index such as the S&P 500 index, yields an expected rate of return 10% with a standard deviation of 25%. You manage an active portfolio with expected return 14% and standard deviation 30% .The risk-free interest rate is 5%.

(a) A client of yours holds a portfolio with 60% invested in your fund and 40% in risk-free securities. What are the expected return and standard deviation of your clients portfolio?

bYour client pondersted whether to switch the 60% that is invested in your fund to the passive portfolio. Explain to your client the disadvantage of the switch.

(c) 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 capital allocation line by reducing the expected return net of the fee.)

(d) Is the fee ( percentage of the investment in your fund,deducted at the end of the year) that you chan charge to make the client indifferent between your fund and the passive strategy affected by his degree of risk aversion?