You estimate that a passive portfolio, for example, one invested in a risky portfolio that mimics the S&P 500 stock index, offers an expected rate of return of 17% with a standard deviation of 25%. You manage an active portfolio with expected return 15% and standard deviation 36%. The risk-free rate is 6%. Your client's degree of risk aversion is A = 3.1.

Required:

If he chose to invest in the passive portfolio, what proportion, y, would he select?

What is the fee (percentage of the investment in your fund, deducted at the end of the year) that you can charge to make the client indifferent between your fund and the passive strategy affected by his capital allocation decision (i.e., his choice of y)?