Performance Attribution of Impact Portfolios Based on Induced Order Statistics

Impact portfolios are often evaluated with standard performance-attribution tools. Those tools can misstate the role of environmental, social, and governance (ESG) or another impact characteristic because an ESG ranking also changes exposure to size, value, profitability, investment, beta, and other return drivers. This article develops an attribution framework that is based on induced order statistics (IOS). The method starts from the way that many impact portfolios are actually built: Securities are ranked by an impact variable, and portfolio weights are applied after that ranking. IOS then estimates how much of the portfolio’s expected return is linked to the impact variable itself and how much is linked to other correlated characteristics. Theoretical and simulation results show that IOS is closer to the target contribution ratio than two common benchmarks, especially when firm characteristics change over time or when ESG is correlated with other characteristics. In a US stock application from 2003 to 2018 using MSCI KLD ESG data, IOS assigns a larger ESG contribution than the benchmark methods, suggesting that standard approaches may understate ESG’s role in a long-short green portfolio.