Does the mutual fund industry lose its best managers to hedge funds? We find that mutual funds are able to retain managers with good performance in the face of competition from a growing hedge fund industry. On the other hand, poor performers are more likely to leave the mutual fund industry. A small fraction of these poor performers find jobs with smaller and younger hedge fund companies, especially when the hedge fund industry is growing rapidly. Analogously, a small fraction of the better-performing mutual fund managers are retained by allowing them to manage a hedge fund side-by-side.

Algorithm designers increasingly optimize not only for accuracy, but also for the fairness of the algorithm across pre-defined groups. We study the tradeoff between fairness and accuracy for any given set of inputs to the algorithm. We propose and characterize a fairness-accuracy frontier, which consists of the optimal points across a broad range of preferences over fairness and accuracy. Our results identify a simple property of the inputs, group-balance, which qualitatively determines the shape of the frontier. We further study an information-design problem where the designer flexibly regulates the inputs (e.g., by coarsening an input or banning its use) but the algorithm is chosen by another agent. Whether it is optimal to ban an input generally depends on the designer's preferences. But when inputs are group-balanced, then excluding group identity is strictly suboptimal for all designers, and when the designer has access to group identity, then it is strictly suboptimal to exclude any informative input.