Optimal Contracts in Portfolio Delegation

The optimal contracts in portfolio delegation are characterized when the underlying state variable is not contractible and the principal must rely on the final wealth of portfolios to design compensation schemes for the fund manager. We show that finding the optimal contracts for general utility functions can be converted into solving a second-order nonlinear ordinary differential equation (ODE). Numerical solutions with power utilities 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