Strategic Asset Allocation with Relative Performance Concerns

Abstract

This article analyzes the dynamic portfolio choice implications of strategic interaction among money managers. The strategic interaction is modelled as managers' having relative performance concerns in their objectives, either due to money flows or behavioral considerations. We provide tractable formulations of relative performance concerns between two risk averse managers in a continuous-time setting, and solve for their equilibrium policies in closed-form. Under a formulation with relative performance concerns smoothly affecting the managers at all levels of wealth, we obtain a unique Nash equilibrium. We demonstrate that much of the novel investment behavior depends on whether a manager is a chaser, increasing investments in response to the other's increasing hers, or a contrarian. The managers are chasers for empirically plausible parameters and increase their optimal risk exposures due to the presence of strategic interaction. We then consider a formulation with asymmetric relative performance concerns, where a manager gets money flows, and hence displays relative concerns, only if her relative return is above a performance threshold. Such relative concerns induce the manager to engage in risk shifting around the threshold, so as to either end up as a winner (getting money flows) or a loser (no flows). Here, we do not always obtain a Nash equilibrium since the managers cannot agree on the winner. For sufficiently similar managers, we obtain equilibria, but multiple, since managers care only about the total number of winning states. We recover a unique equilibrium, however, with a sufficiently high threshold, where the managers' risk aversion prevents them from taking huge gambles, leading both to be losers around the threshold.