Mutual funds flows and the "Sheriff of Nottingham" effect

Investors in mutual funds appear to reward disproportionately the best performing funds with large inflows while, at the same time, avoid to withdraw similar amounts from the poorly managed funds. We show that this peculiar flat-convex shape of the flow-performance curve for mutual funds can be generally explained by a model where profit chasing customers punish the bad funds by switching a fraction of their wealth to the best ones ("Sheriff of Nottingham" effect). In the absence of external flows, the model provably produces a constant curve when the standard deviation of excess returns is much larger than the level of the returns. This for the most part explains the apparent insensitivity of flows to below-average returns. The introduction of exogenous injections of money invested in the top funds completes the model and provides a realistic increase in the flows of the funds yielding above-average returns. We finally show by simulation that our results are robust to variations in the values of the parameters of the model.