Problem $20-19($Static$)$

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.

Required:

a$.$ Compute the rate of return after incentive fees to an investor in the fund of funds. $($Round your percentage answer to $1$ decimal

place.$)$

Rate of return

b$.$ Suppose that instead of buying shares in each of the three hedge funds, a stand$-$alone $($SA$)$ hedge fund purchases the same

portfollo 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? $($Enter your answer In millions.$)$

c$.$ Now suppose that the return on the portfolio held by hedge fund $3$ were $-30\%$ rather than $+30\%.$ Recalculate your answers to parts

$($d$)$ and $($b$).($Negatlve Value should be Indicated by a minus sign. Enter your answer In millions.$)$