Chapter 6: Q19C (page 687)

Here are data on three hedge funds. Each fund charges its investors an incentive fee of 20% 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 20% incentive fee. For simplicity, assume also that management fees other than incentive fees are zero for all funds.
a. Compute the rate of return after incentive fees to an investor in the fund of funds.
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 20% incentive fees, what would be the value of the investor’s portfolio at the end of the year?
c. Confirm that the investor’s rate of return in SA is higher than in FF by an amount equal to the extra layer of fees charged by the fund of funds.
d. Now suppose that the return on the portfolio held by hedge fund 3 were 2 30% rather than 1 30%. Recalculate your answers to parts ( a ) and ( b ). Will either FF or SA charge an incentive fee in this scenario? Why then does the investor in FF still do worse than the investor in SA?

Short Answer

Expert verified

a. As below

b. As below

c. As below

d. As below

Step by step solution

Calculation of rate of return ‘a, b, and c’

	Hedge fund 1	Hedge fund 2	Hedge fund 3	Fund of funds	Stand Alone Funds
Start of year value (millions)	$100	$100	$100	$300	$300
Gross portfolio rate of return	20%	10%	30%
End of year value (before fee)	$120	$110	$130		$360
Incentive fee (individual funds)	$4.0	$2.0	$6.0		$12.0
End of year value (after fee)	$116	$108	$124	$348	$348
Incentive fee (Fund of funds)				$9.6
End of year value (Fund of funds)				$338.4
Rate of return (after fee)	16.00%	8.00%	24.00%	12.80%	16.00%

Investors’ rate of return in SA (16.0%) is higher than the FF (12.8%) by an amount equal to the extra layer of fees (16% x 0.2 = 3.2% or 9.6 million) charged by Fund of Funds.

Calculation of rate of return ‘d’

	Hedge fund 1	Hedge fund 2	Hedge fund 3	Fund of funds	Stand Alone Funds
Start of year value (millions)	$100	$100	$100	$300	$300
Gross portfolio rate of return	20%	10%	-30%
End of year value (before fee)	$120	$110	$70		$300
Incentive fee (individual funds)	$4.0	$2.0	$0.0		$0.0
End of year value (after fee)	$116	$108	$70	$294	$300
Incentive fee (Fund of funds)				$0.0
End of year value (Fund of funds)				$294.0
Rate of return (after fee)	16.00%	8.00%	-30.00%	-2.00%	0.00%

Now there is a difference in the end of value of SA and FF because the fund pays an incentive fee to each of component portfolio. In case of any portfolio does better, an incentive fee will be charged. On the other hand the SA charges an incentive fee only if aggregate portfolio does well.