The non-linear ESG premium

We examine if the ESG performance is being priced in the cross-section of stock returns in a non-linear manner. We consider square and cubic forms of ESG scores when estimating the ESG premium. We find that the premiums from ESG, E, and S scores deviate from linearity, the extent of which depends on types of ESG scores and sample periods. We associate the non-linearity with the cross-sectional distribution of ESG scores. We find that investors ESG sentiment interacts with the cross-sectional distribution of ESG scores in driving linear ESG factors. A change in the ESG data provider will also change the characteristic of non-linear ESG factors. However, the non-linearity still exists using the common sample from different data providers. The above finding also applies in the corporate bond market, in the European market and when extending the sample back to 2004.