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‘I have not found among my possessions anything which I hold more dear than, or value so much as, my knowledge of the actions of great people, acquired by long experience in contemporary affairs, and a continual study of antiquity.’ The Prince, Machiavelli

We propose a quantitative framework for assessing the financial impact of any form of impact investing, including socially responsible investing; environmental, social, and governance (ESG) objectives; and other nonfinancial investment criteria. We derive conditions under which impact investing detracts from, improves on, or is neutral to the performance of traditional mean-variance optimal portfolios, which depends on whether the correlations between the impact factor and unobserved excess returns are negative, positive, or zero, respectively. Using Treynor–Black portfolios to maximize the risk-adjusted returns of impact portfolios, we derive an explicit and easily computable measure of the financial reward or cost of impact investing as compared with passive index benchmarks. We illustrate our approach with applications to biotech venture philanthropy, a semiconductor research and development consortium, divesting from "sin" stocks, ESG investments, and "meme" stock rallies such as GameStop in 2021. This paper was accepted by Agostino Capponi, finance. Funding: Research funding from the National Key Research and Development Program of China [Grant 2022YFA1007900], the National Natural Science Foundation of China [Grant 12271013], Peking University's Fundamental Research Funds for the Central Universities, and the Massachusetts Institute of Technology Laboratory for Financial Engineering is acknowledged. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.01168. [ABSTRACT FROM AUTHOR]

Biomedicine is experiencing an inflection point in which the origins of many human diseases have been decoded, leading to new treatments and, in some cases, complete cures. Many domain experts acknowledge that the gating factor to innovation is not knowledge, but rather a lack of financial resources to translate theory into practice, the so-called "valley of death" between scientific discovery and the clinical testing that must be done with human subjects before regulators will approve a new drug or medical device. This process of translational medicine is largely an exercise in risk management—organized as a carefully planned sequence of experiments, each one involving a progressively larger number of subjects that may or may not be allowed to continue, depending on the results of the prior experiment. It is, therefore, a natural setting in which to apply modern portfolio theory. The authors describe one such application involving a biotechnology company focused on genetic diseases and the lessons learned from that experience. [ABSTRACT FROM AUTHOR]

Using Induced Order Statistics to Construct Optimal Impact Portfolios with General Dependence and Marginals 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. Our results apply to any joint distribution of impact factors and residual returns, making them broadly applicable to a wide range of contexts. We develop significant extensions of the theory of induced order statistics, with which we are able to characterize the distribution of residual returns of individual assets ranked by the impact factor. Our framework provides a toolkit for practitioners to construct impact portfolios and quantify their performance based on real data. This allows impact investors to achieve higher risk-adjusted returns than those with impact portfolios constructed using simpler heuristics such as negative or positive screening. 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. Funding: Research funding from the China National Key R&D Program [Grant 2022YFA1007900], the China National Natural Science Foundation [Grants 12271013, 72342004], the Fundamental Research Funds for the Central Universities (Peking University), and the MIT Laboratory for Financial Engineering is gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.0400. [ABSTRACT FROM AUTHOR]