Application of Chow, Cusum and rolling window in testing stability of systematic risk of companies listed in WIG-ESG in 2019-2022

The aim of the article is to analyze the stability of beta coeffi cients of companies listed in WIG-ESG. There are many studies on the stability of companies' systematic risk, but the literature and research lack an analysis of the stability of the beta coeffi cient for ESG companies. We examined beta coeffi cients for 57 companies listed in WIG-ESG, established for sets of daily rates of return between September 3, 2019, to June 6, 2022 (period including COVID-19 crisis and asset price infl ation, Russian invasion of Ukraine). We estimate the beta coeffi cient for the whole as a result of which we obtain the average value of the beta coeffi cient over the entire analyzed period, and subperiods with fi xed length rolling window, resulting in a time series of beta coeffi cients. To assess beta stability, we used the Chow test with the F statistic, the Cusum test based on generalized fl uctuations test framework, and the Wald-Wolfowitz runs test of randomness around the mean for the time series beta coeffi cients obtained in the rolling window. The considered tests argue for the instability of the time series of beta coeffi cients in most of the companies tested: 93% short-term instability cases confi rmed by the Chow test, 100% short-term instability cases confi rmed by the Wald-Wolfowitz runs test. The paper is an initial attempt to bridge the gap that presently exists between the theoretical and empirical literature on the stability of ESG companies' systematic risk. It cannot be ruled out (hypothesis) that the beta coeffi cient for companies listed in the WIG-ESG index is/will be stable over longer periods of time.