Green Portfolio Optimization: Penalties for Brown Investments

Abstract

In sustainable portfolio management, categorizing assets as “brown“ or “green“ based solely on ESG ratings can be misleading. A positive ESG score does not inherently indicate environmental responsibility unless it is evaluated relative to a meaningful benchmark. We propose a rescaled ESG rating system that measures each asset’s environmental standing relative to a threshold set by policymakers, reflecting the urgency of the current climate crisis. In this system, assets are assigned positive scores if they exceed the threshold (green) and negative scores if they fall below it (brown), enhancing the interpretability of sustainability metrics in portfolio construction. However, a challenge arises when aggregating these scores into an overall portfolio rating. Under sustainable portfolio optimization developed in [11], short positions in brown assets, otherwise effectively betting against polluting companies, can paradoxically improve the portfolio’s sustainability score. This creates a misleading incentive structure. To address this, we introduce a constraint that prohibits short positions in brown assets, ensuring that such investments do not positively impact the portfolio’s sustainability rating. While this restriction better aligns with environmental objectives, it also introduces complexity into the optimization process. To resolve this, we present an intuitive algorithm inspired by the active set method, which we refer to as Green Portfolio Optimization, capable of handling these constraints efficiently even in high-dimensional settings.