Investment dynamics of fund managers under evolutionary games

We investigate the investment behavior of fund managers in financial markets according to evolutionary dynamics. We consider both the absolute and relative portfolio returns in the payoff gradient, to which the fund managers respond, and find the equilibrium proportion of risky investment. Compared to the case where only relative performance affects the payoff gradient, we find that, as the absolute performance affects the managers’ belief, the equilibrium of long and short positions increases. If short sales are not allowed, negative excess returns will force the managers to stay out of the market until the excess return becomes positive. Furthermore, we use a quadratic function to depict the relative performance. The quadratic setting captures the exaggerated sentiments of winners and losers arising from certain behavioral biases, and leads to a lower speed of convergence, which implies that herding decelerates and the managers are likely to adhere longer to their own strategies.