Tri-criterion inverse portfolio optimization with application to socially responsible mutual funds

We present a framework for inverse optimization in a Markowitz portfolio model that is extended to include a third criterion. The third criterion causes the traditional nondominated frontier to become a surface. Until recently, it had not been possible to compute such a surface. But by using a new method that is able to generate the nondominated surfaces of tri-criterion portfolio selection problems, we are able to compute via inverse optimization the implied risk tolerances of given funds that pursue an additional objective beyond risk and return. In applying this capability to a broad sample of conventional and socially responsible (SR) mutual funds, we find that after the screening process there appears to be no significant difference between how assets are allocated in socially responsible and conventional mutual funds, which is likely to be different from what most SR investors would expect.