Question $2($Hedge fund manager contracts$).$ This question extends lectures

$15-16$ where we briefly talked about hedge fund manager contracts. Our goal here is

to think through how the contract impacts fund managers' incentive to take risks.

Consider a hedge fund with initial assets under management $($AUM$)$ of $$1$ billion;

the fund will operate for a year. The manager is paid by a standard $"2+20"$ hedge

fund contract. That is$,$ at the end of the year, he collects management fees of $2\%$ of

AUM $($as of the start of the year$),$ and if the fund's return is above $0\%($the hurdle

rate$),$ he collects $20\%$ of that in performance fees.

For instance, suppose the fund's return turns out to be $5\%,$ which amounts to

profits of $$1$ billion $5\%=$$$50$ million in dollar terms. The manager then collects

$$50$ million $20\%=$$$10$ million in performance fees, in addition to the $$1$ billion $$

$2\%=$$$20$ million management fees. If the fund's return is below $0\%,$ then the

manager only collects management fees.

$($a$)(1$ point$)$ Please plot a graph that represents the manager's total pay as

a function of the fund's return. Specifically, fund return should be on the

horizontal axis and the manager's total pay is on the vertical axis ${?}^2$ Mark the

axis and values as clearly as possible.

$($b$)(1$ point$)$ Let us now consider the risk$-$taking incentives of the fund manager.

Suppose the manager chooses between these two strategies:

Strategy $1$ yields a sure return of $5\%($no risk$).$

Strategy $2$ yields a $+20\%$ return half of the time and a $-20\%$ return the

other half of the time. Thus, it is a strategy with zero expected returns

and much higher risk.

Because investors like higher returns and dislike risk, strategy $2$ is dominated

by strategy $1-$ that is$,$ it is worse in terms of both risk and returns. Thus, if

the manager chooses strategy $2,$ this is bad for investors.