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) by allowing general contracts, and by allowing the portfolio manager to invest privately in individual risky assets or the index. To alleviate the effect of moral hazard, Agent is optimally compensated by benchmarking to the index, which, however, may incentivize him to be too much of a "closet indexer". To counter those incentives, the optimal contract rewards Agent for taking specific risk of individual assets in excess of the systematic risk of the index, by rewarding the deviation between the portfolio return and the return of an index portfolio, and the deviation's quadratic variation