Question

Problem 26-17

Here are data on three hedge funds. Each fund charges its investors an incentive fee of 10% of total returns. Suppose initially that a fund of funds (FF) manager buys equal amounts of each of these funds, and also charges its investors a 10% incentive fee. For simplicity, assume also that management fees other than incentive fees are zero for all funds.

	Hedge Fund 1			Hedge Fund 2			Hedge Fund 3
Start of year value (millions)	$	170		$	170		$	170
Gross portfolio rate of return		15	%		20	%		35	%

a. Compute the rate of return after incentive fees to an investor in the fund of funds. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. Suppose that instead of buying shares in each of the three hedge funds, a stand-alone (SA) hedge fund purchases the same portfolio as the three underlying funds. The total value and composition of the SA fund is therefore identical to the one that would result from aggregating the three hedge funds. Consider an investor in the SA fund. After paying 10% incentive fees, what would be the value of the investor’s portfolio at the end of the year? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)

d. Now suppose that the return on the portfolio held by hedge fund 3 were −35% rather than +35%. Recalculate your answers to parts (a) and (b). (Do not round your intermediate calculations. Negative amount should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)

Answer 1

a) The rate of return after incentive fees to an investor in the fund of funds would be calculated as follows

Weighted average gross rate of return

Name	Value	Weight	Gross Return	Weight x Return
Hedge Fund 1	170	0.33	15%	0.05
Hedge Fund 2	170	0.33	20%	0.07
Hedge Fund 3	170	0.33	35%	0.12
TOTAL	510			0.23

Net return on portfolio = 0.23 - (0.23 * 0.1) = 0.2103 i.e 21.03%

b) Since the stand-alone (SA) hedge fund purchases the same portfolio as the three underlying funds as in (a), the net rate of return would be the same as calculated in (a). The value of the portfolio would be the gross value i.e 510 millions plus the net return on the portfolio.

Therefore, the value of the portfolio at the end of the year is calculated as follows:

=510 millions + (510 millions * 21.03%)

= 617.27 millions

Since the investor's fee is already considered while calculating the net rate of return, there is no requirement for additional calculation for it over here.

c) If the return on hedge fund C is -35% instead of 35%, the answer would be calculated as follows:

Name	Value	Weight	Gross Return	Weight x Return
Hedge Fund 1	170	0.33	15%	0.05
Hedge Fund 2	170	0.33	20%	0.07
Hedge Fund 3	170	0.33	-35%	-0.12
TOTAL	510			0.00

Since the return is 0%, the incentive fee would also be 0%. Therefore both the gross return and net return would be the same i.e 0%.

The value of the portfolio at the end of the year would be the same as at the start of the year, as there is no return on the portfolio. Therefore, the value of the portfolio at the end of the year would be 510 millions.