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Adjusted beta based on an empirical comparison of OLS ‐CAPM and the CAPM with EGARCH errors

Michel Terraza and Roman Mestre

International Journal of Finance & Economics, 2021, vol. 26, issue 3, 3588-3598

Abstract: This paper empirically investigates the differences between the systematic risk estimated by OLS and it simultaneous estimation with a GARCH errors. The systematic risk of an asset is estimated by the beta coefficient of the market line. According to the OLS hypothesis, the estimators are robust and residuals are white noise process. However various papers show the existence of statistical anomalies (stylized facts) in residuals (heteroskedasticity, autocorrelation and non‐normality) rejecting the BLUE properties of estimators. In order to considerate these anomalies to modelize the hazard in residuals regression, we use ARCH processes class that has proved it efficiency in finance. We estimate simultaneously the parameters of the market line and those of the GARCH process for the 30 perennial equities listed in CAC40 for the daily period 2005 to 2015 and we compare them each other. We select the E‐GARCH model providing the best residuals characteristics and we note significant differences with the OLS Betas particularly for equities with betas greater than 1. On this base, we estimate a linear relationship between the OLS Betas and the E‐GARCH Betas considering this break to modelize the differences between these two kinds of Betas. By this way, Investors can quickly adjust the Beta with this tool without completely reestimating them with GARCH.

Date: 2021
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