Relative performance evaluation for dynamic contracts in a large competitive market

Abstract

In this article, we develop a novel dynamic model to study the role and effect of relative performance evaluation (RPE) in a delegated portfolio management framework, where a non-zero-sum game is introduced among managers in addition to the hierarchical Stackelberg game between the shareholders and managers. The characterization of the optimal contracts in the generic finite-population case commonly involves a complicated system of coupled nonlinear equations for which the existence of a solution may not be established. Alternatively, an approximation of the large population case is still viable. Indeed, we derive an analytically tractable mean field equilibrium as the population size goes to infinity and conclude that: (1) it is the risk sharing between shareholders and managers and the presence of correlated investment opportunities across firms that lead to the inclusion of RPE in contracts; (2) these contracts incorporating RPE, in return, trigger the managers to invest more in the correlated assets with the desire to reduce the volatility of compensation payments. To this end, we echo the finding that the incorporation of RPE increases the systemic risk, which was first observed in Albuquerque et al. (Rev. Financ. Stud. 32(11): 4304–4342, 2019). In addition, we show that the systemic risk increases with the aggregate Sharpe Ratios of securities and the risk seeking appetites of managers.