The Convexity and Concavity of the Flow-Performance Relationship for Hedge Funds

The shape of the flow-performance relationship in the hedge fund industry is not constant over time, but varies across market conditions. We employ a switching regression approach to explain quarterly hedge fund flows, based on defining two regimes where either inflows or outflows are dominating, combined with a flexible functional form for each of the equations, allowing for a nonlinear impact of past performance at different lags. We characterize the local and global convexities of the relationship by several measures and investigate how they vary over time. Overall, the flow-performance relationship appears flatter at the one quarter horizon than at the four quarter horizon. Moreover, the curve is not uniformly convex or concave. For most periods, the flow-performance relationship is locally convex for a large subset of funds but becoming concave for the top three deciles of performers. The kink in the top part of the curve is more pronounced in periods when aggregate inflows to the industry are high. This effect seems mostly driven by funds that are restricting new inflows, for example due to capacity constraints or decreasing returns to scale. These results are helpful in understanding the incentives of hedge fund managers due to the implications for manager compensation based on performance fees and management fees.