In this talk, I will introduce a quantitative framework for constructing optimal impact portfolios and quantifying their financial performance. We characterize the returns of impact-ranked assets using induced order statistics and copulas. We provide a representation theorem for the distribution of induced order statistics, which allows us to explicitly and efficiently compute optimal portfolio weights under any copula. In addition, we show that portfolio constraints may contain information that is correlated with returns, in which case imposing such constraints can affect performance. Overall, our framework provides a systematic approach for constructing and quantifying the performance of optimal impact portfolios with arbitrary dependence structures and return distributions.

Bio: Ruixun Zhang is an assistant professor and Boya Young Fellow in the Department of Financial Mathematics, School of Mathematical Sciences at Peking University (PKU). He is currently a visiting scholar at Columbia University in the IEOR department in Fall 2024. Ruixun received a PhD in applied mathematics from MIT in 2015, and bachelor degrees in Mathematics and Applied Mathematics, and Economics (double degree) from Peking University in 2011. Ruixun’s research interests include machine learning, green finance, and evolutionary models of financial behavior. His research has appeared in journals such as PNAS, Management Science, and Operations Research. His work has been recognized by the S&P Global ESG Academic Research Award, ICPM Academic Research Award, CEMA Best Paper Award, and CFRI&CIRF Best Paper Award.