Question

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 12% with a standard deviation of 25%. You manage an active portfolio with an expected return of 19% and a standard deviation of 32%. The risk-free rate is 7%. Your client's degree of risk aversion is A = 3.3.

a.
If he chose to invest in the passive portfolio, what proportion, y, would he select? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Proportion of y ____%??

b. 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 )? (Do not round intermediate calculations. Round your answer to 1 decimal place. Omit the "%" sign in your response.)

Fee ____% per year ????

Answer 1

Please find the detailed answer as follows:

Step-by-step explanation:

a If the Client Chose to invest in Passive Portfolio,

y = (Rp - Rf) / 0.01*A* \sigma ^{^{^{2}}} = (12 - 7) / 0.01*3.3*252 =24.24

b. Fee (F) that can be charged the fund => (E(r) - Rf - F) / \sigmaa = (E(r) - Rf ) / \sigmab

(19 - 7 - F) / 32 = (12 - 7) / 25

F = 5.6