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.

$\backslash$table$[[,$Hedge,Hedge,Hedge$],[,$Fund $1,$Fund $2,$Fund $3],[$Start of year value $($millions$),$$$120,$$$120,$$$120$