3. Question 3 (Hedge fund contracts and incentives to take risk). This ques- tion is loosely related to lecture 15 which briefly talked about hedge fund manager contracts. Our goal here is to think through how the hedge fund contract impact the fund manager's incentive to take risk. 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 fund's return is above 0% (the hurdle rate), he collects 20% of that in performance fees. For instance, suppose the fund's return is 5%, which amounts to $1 billion 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) 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 manager's total pay is on the vertical axis. Mark the axis and values as 4This type of payoff is often known as call option payoff. It has a head I win, tail I don't lose" 3 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 payoff 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. 3. Question 3 (Hedge fund contracts and incentives to take risk). This ques- tion is loosely related to lecture 15 which briefly talked about hedge fund manager contracts. Our goal here is to think through how the hedge fund contract impact the fund manager's incentive to take risk. 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 fund's return is above 0% (the hurdle rate), he collects 20% of that in performance fees. For instance, suppose the fund's return is 5%, which amounts to $1 billion 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) 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 manager's total pay is on the vertical axis. Mark the axis and values as 4This type of payoff is often known as call option payoff. It has a head I win, tail I don't lose" 3 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 payoff 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