**Please show work**

2. 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, 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. "This type of payoff is often known as "call option" payoff. It has a "head I win, tail I don't lose" iure. You may have encountered options in other classes; if you haven't, you likely will encounter m in future investment classes. 2 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? (There is no "absolutely correct" answer. You will receive full credit as long as you provide a sensible answer.) 2. 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, 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. "This type of payoff is often known as "call option" payoff. It has a "head I win, tail I don't lose" iure. You may have encountered options in other classes; if you haven't, you likely will encounter m in future investment classes. 2 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? (There is no "absolutely correct" answer. You will receive full credit as long as you provide a sensible answer.)