Delegated portfolio management with socially responsible investment constraints

We consider the problem of how to establish compensation for a portfolio man- ager who is required to restrict the investment set, for example, because of socially responsible screening. This is a problem of Delegated Portfolio Management where the reduction of investment opportunities to the subset of sustainable assets involves a loss in expected earnings for the portfolio manager, compensated by the investor through an extra bonus on the realized return. Under simple assumptions on the investor, manager and market, we compute the optimal bonus as a function of the managers risk aversion and expertise, and of the impact of portfolio restriction on the mean-variance e cient frontier