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.

We examine the contagion of investment ideas in a multiperiod setting in which investors are more likely to transmit their ideas to other investors after experiencing higher payoffs in one of two investment styles with different return distributions. We show that heterogeneous investment styles are able to coexist in the long run, implying a greater diversity than traditional theory predicts. We characterize the survival and popularity of styles in relation to the distribution of security returns. In addition, we demonstrate that psychological effects such as conformist preference can lead to oscillations and bubbles in the choice of style. These results offer empirically testable predictions, and provide new insights into the persistence of the wide range of investment strategies used by individual investors, hedge funds, and other professional portfolio managers.

How does a firm’s market power in existing products affect its incentives to innovate? We explore this fundamental question using granular project-level and firm-level data from the pharmaceutical industry, focusing on a particular mechanism through which incumbent firms maintain their market power: “reverse payment” or “pay-for-delay” agreements to delay the market entry of competitors. We first show that when firms are unfettered in their use of “pay-for-delay” agreements, they reduce their innovation activities in response to the potential entry of direct competitors. We then examine a legal ruling that subjected these agreements to antitrust litigation, thereby reducing the incentive to enter them. After the ruling, incumbent firms increased their net innovation activities in response to competitive entry. These effects center on firms with products that are more directly affected by competition. However, at the product therapeutic area level, we find a reduction in innovation by new entrants after the ruling in response to increased competition. Overall, these results are consistent with firms having reduced incentives to innovate when they are able to maintain their market power, highlighting a specific channel through which this occurs.

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.

Due to the “boundary effect” bias, PoS estimates in the most recent years are inflated. To address this issue, we compute a bias-adjustment factor using historical data and multiply the PoS in recent years by this factor.

We propose a quantitative framework for assessing the financial impact of any form of impact investing, including socially responsible investing (SRI), environmental, social, and governance (ESG) objectives, and other non-financial 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 propose a quantitative measure for the financial reward, or cost, of impact investing compared to passive index benchmarks. We illustrate our approach with applications to biotech venture philanthropy, divesting from “sin” stocks, investing in ESG, and “meme” stock rallies such as GameStop in 2021.

We collect tax return data from all 311,222 public NPOs in the United States over the 2009-2017 period to study the asset allocation choices and investment returns of their endowment funds. One in nine public NPOs have endowment funds. The majority of funds allocate their assets conservatively to low-risk assets, and as a result, earn an average annual return of 5.3%. There is substantial heterogeneity in investment returns across funds. Large funds significantly outperform small funds across all return measures and nonprofit sectors. Endowments in NPO sectors devoted to public and societal benefit, the environment, and the arts are among the top performers. High returns among higher education endowments are explained by size, while hospital endowments significantly underperform. Higher investment returns are associated with better governance, more highly paid management, lower discretionary spending, and lower investment management fees. Lastly, when faced with volatile contributions, endowment funds hold more cash and invest more conservatively.

In this paper, we create machine learning (ML) models to forecast home equity credit risk for individuals using a real-world dataset and demonstrate methods to explain the output of these ML models to make them more accessible to the end-user. We analyze the explainability of these models for various stakeholders: loan companies, regulators, loan applicants, and data scientists, incorporating their different requirements with respect to explanations. For loan companies, we generate explanations for every model prediction of creditworthiness. For regulators, we perform a stress test for extreme scenarios. For loan applicants, we generate diverse counterfactuals to guide them with steps to reverse the model's classification. Finally, for data scientists, we generate simple rules that accurately explain 70-72% of the dataset. Our work is intended to accelerate the adoption of ML techniques in domains that would benefit from explanations of their predictions.

With multimorbidity becoming the norm rather than the exception, the management of multiple chronic diseases is a major challenge facing healthcare systems worldwide. Using a large, nationally representative database of electronic medical records from the United Kingdom spanning the years 2005 to 2016 and consisting over 4.5 million patients, we apply statistical methods and network analysis to identify comorbid pairs and triads of diseases and identify clusters of chronic conditions across different demographic groups. Unlike many previous studies, which generally adopt cross-sectional designs, we examine temporal changes in the patterns of multimorbidity. In addition, we perform survival analysis to examine the impact of multimorbidity on mortality.

We assess the potential financial impact of future gene therapies by identifying the 109 late-stage gene therapy clinical trials currently underway, estimating the prevalence and incidence of their corresponding diseases, developing novel mathematical models of the increase in quality-adjusted life years for each approved gene therapy, and simulating the launch prices and the expected spending of these therapies over a 15-year time horizon. The results of our simulation suggest that an expected total of 1.09 million patients will be treated by gene therapy from January 2020 to December 2034. The expected peak annual spending on these therapies is $25.3 billion, and the total spending from January 2020 to December 2034 is $306 billion. We decompose their annual estimated spending by treated age group as a proxy for U.S. insurance type, and consider the tradeoffs of various methods of payment for these therapies to ensure patient access to their expected benefits.