Portfolio Delegation with Limited Liability

We consider the portfolio delegation problem in a world with potentially incomplete contingent claim markets. A principal hires an agent to manage a portfolio. When the agent has limited liability (that is, there is a lower bound on the compensation contract), she may have an incentive to take on excessive risk. With complete markets, the precise nature of the risk the agent may take on is a large short position in the state with lowest probability, and a long position in every other state. Our main result is that, with limited liability and a large number of states, completing the set of markets exacerbates the agency problem and can lead to greater risk-taking by the agent. In this situation, incentive compatibility alone restricts the feasible contract to be either a flat one or one with exactly two compensation levels (equal to the lower and upper bounds on compensation). We examine the effectiveness of Value at Risk compensation schemes in this context. An appropriately set VaR scheme can be effective at controlling the size of the maximum loss suffered by the portfolio. However, in general, we do not expect it to attain the same outcome as the optimal contract