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

We study a continuous-time principal-agent problem where the risk-neutral agent can pri-vately and meaningfully choose both the drift and volatility of a cash ow, while the risk-neutral principal only continuously observes the managed cash ows 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 con ict between the principal and the agent on their preferred volatility choices, but to avoid inefficient termination and compensation from excess diffusion, this rst 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 sensi-tivity " (RAS) effect. In a delegated portfolio management context, our model suggests outside investors should prefer investment funds with the characteristics: (i) the investment fund has an \internal fund " available only to management, or equivalently, a \ agship fund " that is closed to new outside investors; (ii) the \external fund " for the outside investors closely tracks the investment strategy and value of the internal fund; and (iii) has dynamic incentive fee schemes