2. Question 2 (Hedge fund manager contracts). This question extends lectures 15- 16 where we briey 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 prots of $1 billion x 5% = $50 million in dollar terms. The manager then collects $50 million x 20% = $10 million in performance fees, in addition to the $1 billion x 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