Optimal Contracts in Portfolio Delegation: The Case of Complete Markets

摘要

The optimal contracts are characterized when the underlying state variable is not contractible and the shareholders must rely on the final wealth of the portfolio to design compensation schemes for the mutual-fund managers. It is shown herein that finding the optimal contracts can be converted into solving second-order nonlinear ordinary differential equations. In general, an optimal contract is an increasing, nonlinear function of the final wealth, the shape of which depends on the risk aversions of the principal and the agent, the state price density function, the principal’s initial wealth and the agent’s reservation utility level. The conditions under which option-like pays are optimal are also presented. Various numerical examples are presented to show the features of the optimal contracts. In addition, the optimal contracts are compared with Pareto optimal contracts. We show that, in general, there is an efficiency loss for the optimal contracts unless the utility functions of both the principal and the agent exhibit linear risk tolerance with identical cautiousness.