Competition among Portfolio Managers and Asset Specialization

This paper investigates the competition among portfolio managers as they attempt to outperform each other. We provide a tractable dynamic continuous-time model of competition between two risk-averse managers concerned about relative performance. To capture the managers’ asset specialization, we consider two imperfectly correlated risky stocks whereby each manager trades in one of the stocks, and so faces incomplete markets. We show that a unique pure-strategy Nash equilibrium always obtains, and provide the ensuing equilibrium portfolio policies explicitly. We find that competition makes a relatively risk tolerant manager decrease, and a risk intolerant increase, her portfolio risk. Moreover, a higher own risk aversion induces a manager to take more risk when the opponent is advantaged, in that she specializes in the stock with the relatively higher Sharpe ratio. We then explore the link between our two key ingredients, competition and asset specialization, and show that competition can be conducive to asset specialization. In particular, we find that both managers, when relatively risk tolerant, can voluntarily opt for asset specialization and the corresponding loss of diversification to avoid competing on the same turf by trading in the same set of stocks. When they are risk intolerant, however, the no-specialization scenario is more likely. When we consider a client investor of a manager, we show that her preferences for or against asset specialization could well be the opposite to that of her manager. We also examine the potential costs to a client investor, arising as managerial turnover or changing stock characteristics misaligns the client manager’s policy. We find that the client loses more when it is her manager who is replaced than the other manager. In contrast, the client’s losses are the same for a given change in her manager’s stock characteristics as for that in the competitor manager’s stock.