Sustainable Investment: ESG Impacts on Large Portfolio

This paper investigates the impact of environmental, social, and governance (ESG) constraint on a regularized mean-variance (MV) portfolio optimization problem in a large-dimensional setting, in which a positive definite regularization matrix is imposed on the sample covariance matrix. We first derive the asymptotic results for the out-of-sample (OOS) Sharpe ratio (SR) of the proposed portfolio, which help quantify the impact of imposing an ESG-level constraint as well as the effect of estimation error arising from the sample mean estimation of the assets' ESG score. Furthermore, to study the influence of the choices of the regularization matrix, we develop an estimator for the OOS Sharpe ratio. The corresponding asymptotic properties of the Sharpe ratio estimator are established based on random matrix theory. Simulation results show that the proposed estimators perform close to the corresponding oracle level. Moreover, we numerically investigate the impact of various forms of regularization matrices on the OOS SR, which provides useful guidance for practical implementation. Finally, based on OOS SR estimator, we propose an adaptive regularized portfolio which uses the best regularization matrix yielding the highest estimated SR (among a set of candidates) at each decision node. Empirical evidence based on the S\&P 500 index demonstrates that the proposed adaptive ESG-constrained portfolio achieves a high OOS SR while satisfying the required ESG level, offering a practically effective approach for sustainable investment.