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. 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 theother 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. .
Question: Please compute the manager’s expected payoff 3 under both strategies. (The selfish hedge fund manager will choose whichever strategy maximizes his expected payoff.)
(c) (1 point) 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. Further assume that, if the manager receives the same amount of expected payoff from two strategies, he prefers the one with lower risk. Which strategy would he choose?
(d) (1 point) 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 contracts, induces risk-taking incentives in fund managers?
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