Continuous-Time Principal-Agent Problem with Drift and Stochastic Volatility Control: With Applications to Delegated Portfolio Management

Abstract

We study a continuous-time principal-agent problem where the agent can privately and meaningfully choose both the drift and volatility of a cash flow, while the principal only continuously observes the managed cash flows over time. Our model contributes a result that is hitherto relatively unexplored in both the continuous-time dynamic contracting and the delegated portfolio management literatures. Firstly, even though there is no direct moral hazard conflict between the principal and the agent on their preferred volatility choices, but to avoid inefficient termination and compensation from excess diffusion, this first best choice is not reached; this is the reverse moral hazard'' effect. Secondly, the dollar incentives the principal gives to the agent critically depends on the volatility choice, endogenous quasi-risk aversion of the principal, and the elasticity to the exogenous factor level; this is the risk adjusted sensitivity'' (RAS) effect. In a delegated portfolio management context, our model suggests outside investors should prefer funds such that: (i) the investment fund has an fund'' available only to management; (ii) the external fund'' for the outside investors closely tracks the value of the internal fund; and (iii) has dynamic incentive fee schemes, and these fees can be interpreted via Black-Scholes greeks''.