A note on the Pastor et al. (2021) model

In this paper, we revise the asset pricing model of Lubo ˇ s Pˇ astor et al. (2021) by incorpo- ´ rating a penalty component into investors’ utility functions when they invest in firms with lower ESG compliance (brown firms). Our model highlights the dual behavior of investors who gain utility from investing in green firms (fully ESG-compliant) while incurring disutility from holding brown firms. We introduce a formulation where firms’ green characteristics are represented by a vector of ESG scores, with 1 for full compliance and 0 for non-compliance. The penalty is defined as a function of the deviation from full ESG compliance, adjusted for each investor’s ESG preferences. This leads to a modified CAPM equation that reflects both the non-pecuniary benefits of green investments and the penalties for brown investments.