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

Author

Listed:
  • Michel Terraza
  • Roman Mestre

    (MRE - Montpellier Recherche en Economie - UM - Université de Montpellier)

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.
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Suggested Citation

  • Michel Terraza & Roman Mestre, 2021. "Adjusted beta based on an empirical comparison of OLS ‐ CAPM and the CAPM with EGARCH errors," Post-Print hal-04058231, HAL.
    • Handle: RePEc:hal:journl:hal-04058231
    DOI: 10.1002/ijfe.1977
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    1. is not listed on IDEAS
    2. Pankaj Agrrawal & Faye W. Gilbert & Jason Harkins, 2022. "Time Dependence of CAPM Betas on the Choice of Interval Frequency and Return Timeframes: Is There an Optimum?," JRFM, MDPI, vol. 15(11), pages 1-18, November.
    3. Roman Mestre, 2019. "Time-Frequency Multi-Betas Model-An Application with Gold and Oil -," Cahiers de recherche 19-05, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.

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