This article analyzes the dynamic portfolio choice implications of strategic interaction among money managers. The strategic interaction emerges as the managers compete for money flows displaying empirically documented convexities. A manager gets money flows increasing with performance, and hence displays relative performance concerns, if her relative return is above a threshold; otherwise she receives no (or constant) flows and has no relative concerns. We provide a tractable formulation of such strategic interaction between two risk averse managers in a continuous-time setting, and solve for their equilibrium policies in closed-form. When the managers' risk aversions are considerably different, we do not obtain a Nash equilibrium as the managers cannot agree on who loses (getting no flows) in some states. We obtain equilibria, but multiple, when the managers are similar since they now care only about the total number of losing states. We recover a unique equilibrium, however, when a sufficiently high threshold makes the competition for money flows less intense. The managers' unique equilibrium policies are driven by chasing and contrarian behaviors when either manager substantially outperforms the opponent, and by gambling behavior when their performances are close to the threshold. Depending on the stock correlation, the direction of gambling for a given manager may differ across stocks, however the two managers always gamble strategically in the opposite direction from each other in each individual stock. JEL Classifications: G11, G20, D81, C73, C61.

This paper analyzes the dynamic portfolio choice implications of strategic interaction among money managers who compete for fund flows. We study such interaction between two risk‐averse managers in continuous time, characterizing analytically their unique equilibrium investments. Driven by chasing and contrarian mechanisms when one is well ahead, they gamble in the opposite direction when their performance is close. We also examine multiple and mixed‐strategy equilibria. Equilibrium policy of each manager crucially depends on the opponent's risk attitude. Hence, client investors concerned about how a strategic manager may trade on their behalf should also learn competitors' characteristics.

Absent much theory, empirical works often rely on the following informal reasoning when looking for evidence of a mutual fund tournament: If there is a tournament, interim winners have incentives to decrease their portfolio volatility as they attempt to protect their lead, while interim losers are expected to increase their volatility so as to catch up with winners. We consider a rational model of a mutual fund tournament in the presence of short-sale constraints and find the opposite-interim winners choose more volatile portfolios in equilibrium than interim losers. Several empirical works present evidence consistent with our model, however based on the above informal argument they appear to conclude against the tournament behavior. We argue that this conclusion is unwarranted. We also demonstrate that tournament incentives lead to differences in interim performance for otherwise identical managers, and that midyear trading volume is inversely related to midyear stock return.

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