Question

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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%. Your client's degree of risk aversion is A 3.5 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.) Proportion of y 22.86 % 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.) Fee 4.4 % per year

Answer 1

Part A	Scal = (18% - 8%)/28% = 0.3771
	Scml = (13%-8%)/25%=0.2
Part B	in chart Diagram
Part C	My fund allows an investor to achieve a higher mean for any given standard deviationthan would a a passive strategy i.e. higher expected for any given level of risk.
Part D	With 70% of the funds invested in my portfolio, the clients expected return is 15% per year and standard deviation is 19.6%per year. If he shifts that money to the passive portfolio (which has an expected rate of return of 13% and standard deviation of 25%) his overall expetected return becomes:
	E(rC) = rF + 0.7[E(rM)-rf] = 8+ [0.7*(13-8) = 11.5%
	The Standard Deviation of the complete portfoilio using the passive portfolio would be:
	0.7 *25% = 17.5%
	So the shift entails a decrease in mean from 15 to 11.5 % and a standard decrease in standard deviation from 19.6% to 17.5%. Since both return and deviation decrease, thus the move is not beneficial.