Heterogeneous managers, distribution picking and competition.

The first chapter of this thesis develops a model where a number of new hedge funds with unknown and varying ability compete to enhance their reputations by registering high performance relative to their peers. The funds’ choice variable is their return distribution, which financial engineering gives them complete control over subject to a constraint on their means that proxies for ability. This approach has the advantage of not requiring knowledge of fund moneymaking strategies. In all equilibria, funds play tail risk in expectation, and increasing the number of competitors causes tail risk and fund failure rates to rise. This is because a higher number of competitors makes it more difficult to stand out with high relative performance. In the second chapter, a variant of the model where the fund with the greatest Bayesian probability of being a high ability type wins the reputational boost is analysed as a robustness check. Funds still play tail risk, but the results from chapter 1 are weakened by the existence a class of equilibria where tail risk does not increase with the number of funds. Some equilibria of this new model correspond to the setting of Foster and Young (2010), with low ability funds mimicking high ability funds. This is because the more rational version is less like a Blotto Game and closer to a pure signalling model. In the last chapter, an incentive bonus scheme (2 and 20) commonly used in the hedge fund industry is added to the model. When funds play probability mass above the bonus threshold, such a scheme raises failure risk compared to the basic model from part 1 under some mild conditions. When financial engineering that enables return manipulation is available and managers are constrained by innate ability, such a bonus scheme gives funds incentives to play probability mass at high return levels at the cost of tail risk. With the bonus scheme, funds play less probability mass at higher variance above the bonus threshold. The model also returns a restriction on the minimum amount of tail risk