Strategic Asset Allocation in Money Management

Abstract

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.

Difference in interim performance and risk taking with short-sale constraints

“…Loranth and Sciubba (2006) investigate how the riskiness of fund strategies is affected by the (threat of) entry by new funds. Basak and Makarov (2009) study strategic interactions among a small number of top-performing funds.…”

Utility maximization with a given pricing measure when the utility is not necessarily concave

“…This leads to a partially convex (or convex-concave) utility function. Not necessarily concave utility functions also appear in the context of manager compensation [18], portfolio delegation [31], and strategic interaction among money managers [5].…”

“…In the case that U is not concave, problem (1.1) is more involved. There is a broad class of models in which the non-concave problem has been studied by reducing it to the classical concave case; see for instance Aumann and Perles [2], Carpenter [18], Berkelaar et al [8], Larsen [31], Carassus and Pham [15], Rieger [35], Basak and Makarov [5] and Bichuch and Sturm [13]. At the other end of the scale, there are results on the existence of a solution in a number of (incomplete) discrete-time settings where one does not necessarily have a fixed pricing density, but the structure of the setup allows one to optimize directly over the set of strategies; see Benartzi and Thaler [7], Bernard and Ghossoub [10], He and Zhou [23] and Carassus and Rásonyi [16].…”

Fund Tournaments and Asset Bubbles*

“…Consistent with our model, DeMarzo, Kaniel, and Kremer (2008) show that bubbles stem from investors trying to keep up with the Joneses, and Palomino (2005) argues that relative performance concerns lead managers to adopt riskier investment strategies. 4 However, unlike these papers, our model also implies that relative performance concerns may dampen bubbles by leading managers to use safer strategies, depending on the degree of convexity of the flow-performance relationship.…”

“…Our paper is also related to the papers studying the role of relative performance evaluations in financial markets. Basak and Makarov (2012) analyze strategic interactions among fund managers concerned with fund flows. Unlike their paper, we study the managers' investment behavior in bubble periods and the associated persistence of bubbles.…”