The impact of a winner takes all tournament on managers’ strategies and asset mispricing

We investigate the asset’s price and the portfolio choices of the managers in the equilibrium generated by a winner takes all contest in a financial market with cash and a risky asset. The manager’s payoff consists in the value of the portfolio at the maturity and a prize, which is assigned according to the ranking based on the absolute performance. Our analysis focuses on the one-periodical game between an infinite number of identical managers. We found the existence of three regions where we can find the possible equilibria: according to the region the equilibrium can predict an overvalued, a valued as much as the fundamental value or an undervalued price of the asset. Then, the model allows for mispricing. We study the equilibria according to the parameters and the type of distribution of the risky asset, finding that only the latter is relevant to characterize the type of equilibrium. We find that the absolute value of mispricing is increasing with the tournament incentive: the inefficiency in pricing financial assets is increasing in managers’ competition concern. Finally, we explore the case of elimination contest and beat the market tournament finding similar results.