Consider a hedge fund that only runs for a year, and it has assets under management

(AUM) of $1 billion. 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, and if the funds return is above 0% (the hurdle rate), he collects 20% of

that in performance fees.

For instance, suppose the funds return is 5%, which amounts to $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 funds return is below 0%, then the manager only collects

management fees.

(a) Please plot a graph that represents the managers total pay as a function of

the funds return. Specifically, fund return should be on the horizontal axis

and managers total pay is on the vertical axis.4 Mark the axis and values as clearly as possible.

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

the manager can take one of the two following strategies:

Strategy 1 yields a sure 5% return all the time. Thus, it is a strategy with

no risk.

Strategy 2 yields 20% return half of the time and -20% return the other

half of the time. Thus, it is a strategy with zero expected return and much

higher risk.

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

by strategy 1. That is, it is worse than strategy 1 in terms of both return and

risk. Thus, if the manager chooses strategy 2, this is bad for investors.

Please compute the expected payoff5 of the manager under both strategies.

(c) Recall that hedge fund managers are relatively unconstrained in the strategies

they take. Further, since they do not need to tell investors what strategies

they choose, it is safe to assume that the hedge fund manager in this question

will choose whichever strategies gives him the highest expected payoff. Which

strategy, 1 or 2, will the manager choose?

(d) Now suppose the manager is only compensated with management fees but not

performance fees. In other words, the contract is similar to that used in mutual

funds. Assume that, if manager receives the same amount of expected payoff

from two strategies, he prefers the one with lower risk. Which strategy would

he choose?

(e) What do you learn from this exercise about how the structure of the hedge

fund manager contract, relative to the structure of mutual fund manager con-

tracts, induce risk-taking incentives in fund managers?

There is no absolutely correct answer. You will receive full credit as long as

you say something thoughtful and sensible.