Asset pricing under optimal contracts

We consider the problem of finding equilibrium asset prices in a financial market in which a portfolio manager (Agent) invests on behalf of an investor (Principal), who compensates the manager with an optimal contract. We extend a model from Buffa, Vayanos and Woolley (2014), BVW (2014), by allowing general contracts. We find that the optimal contract rewards Agent for taking specific risk of individual assets and not only the systematic risk of the index by using the quadratic variation of the deviation between the portfolio return and the return of an index portfolio. Similarly to BVW (2014), we find that, in equilibrium, the stocks in large supply have high risk premia, while the stocks in low supply have low risk premia, and this effect is stronger as agency friction increases. However, by using our risk-incentive optimal contract, the sensitivity of the price distortion to agency frictions is of an order of magnitude smaller compared to the price distortion in BVW (2014), where only contracts linear in portfolio value and index are allowed.