Optimal Impact Portfolios with General Dependence and Marginals

Abstract

We develop a mathematical framework for constructing optimal impact portfolios and quantifying their financial performance by characterizing the returns of impact-ranked assets using induced order statistics and copulas. The distribution of induced order statistics can be represented by a mixture of order statistics and uniformly distributed random variables, where the mixture function is determined by the dependence structure between residual returns and impact factors---characterized by copulas---and the marginal distribution of residual returns. This representation theorem allows us to explicitly and efficiently compute optimal portfolio weights under any copula. This framework provides a systematic approach for constructing and quantifying the performance of optimal impact portfolios with arbitrary dependence structures and return distributions.

Keywords: Impact Investing; Environmental, Social, and Governance (ESG); Induced Order Statistics; Copula; Representation Theorem; Portfolio Theory

JEL Classification: C10, C20, G11, G12