Optimal Impact Portfolios with General Dependence and Marginals

Abstract

Impact investing typically involves ranking and selecting assets based on a non-financial impact factor, such as the environmental, social, and governance (ESG) score and the prospect of developing a disease-curing drug. We develop a framework for constructing optimal impact portfolios and quantifying their financial performances. Under general bivariate distributions of the impact factor and residual returns from a multi-factor asset-pricing model, the construction and performance of optimal impact portfolios depend critically on the dependence structure (copula) between the two, which reduces to a correlation under normality assumptions. More generally, we explicitly derive the optimal portfolio weights under two widely-used copulas---the Gaussian copula and the Archimedean copula family, and find that the optimal weights depend on the tail characteristics of the copula. In addition, when the marginal distribution of residual returns is skewed or heavy-tailed, assets with the most extreme impact factors have lower weights than non-extreme assets due to their high risk. Our framework requires the estimation of only a constant number of parameters as the number of assets grow, an advantage over traditional Markowitz portfolios. Overall, these results provide a recipe 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); Portfolio Theory; Copula; Heavy Tail

JEL Classification: C10, C20, G11, G12