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 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.)

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.