The Predictive Effect of ESG Scores on Stock Volatility: A Comparative Study of Polynomial Regression and Machine learning Models

Abstract

This paper investigates the empirical relationship between environmental, social, and governance scores and stock volatility in the context of growing sustainable investment, using data on S and P 500 index constituents from 2019 to 2023. It compares the predictive performance of second order polynomial regression with machine learning techniques including Random Forest classification and regression models as well as a Support Vector Machine regressor, focusing on key measures of goodness of fit such as test R squared, cross validated R squared, and root mean squared error. The results show a pronounced nonlinear and convex relationship in which higher ESG scores are associated with lower stock volatility, although the marginal reduction in volatility diminishes at higher ESG levels, and they indicate that the second order polynomial regression model delivers the best overall fit with a test R squared of 0.3382, clearly outperforming both linear regression and the machine learning models. Feature importance analysis further corroborates that ESG scores account for approximately ninety two percent of the explained variation in volatility when isolating the contribution of each predictor across the statistical and machine learning approaches.