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

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  • Michel Terraza
  • Roman Mestre

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.

Suggested Citation

  • Michel Terraza & Roman Mestre, 2021. "Adjusted beta based on an empirical comparison of OLS ‐CAPM and the CAPM with EGARCH errors," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 3588-3598, July.
    • Handle: RePEc:wly:ijfiec:v:26:y:2021:i:3:p:3588-3598
    DOI: 10.1002/ijfe.1977
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    References listed on IDEAS

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    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Schwert, G William & Seguin, Paul J, 1990. "Heteroskedasticity in Stock Returns," Journal of Finance, American Finance Association, vol. 45(4), pages 1129-1155, September.
    3. Eugene F. Fama, 1968. "Risk, Return And Equilibrium: Some Clarifying Comments," Journal of Finance, American Finance Association, vol. 23(1), pages 29-40, March.
    4. Roman Mestre & Michel Terraza, 2018. "Time-Frequency Analysis of capm: Application to the cac 40," Managing Global Transitions, University of Primorska, Faculty of Management Koper, vol. 16(2 (Summer), pages 141-157.
    5. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    6. Bera, Anil & Bubnys, Edward & Park, Hun, 1988. "Conditional Heteroscedasticity in the Market Model and Efficient Estimates of Betas," The Financial Review, Eastern Finance Association, vol. 23(2), pages 201-214, May.
    7. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    8. Ali BENDOB & Mohamed CHIKHI & Fatma BENNACEUR, 2017. "Testing the CAPM-GARCH Models in the GCC-Wide Equity Sectors," Asian Journal of Economic Modelling, Asian Economic and Social Society, vol. 5(4), pages 413-430, December.
    9. Ali BENDOB & Mohamed CHIKHI & Fatma BENNACEUR, 2017. "Testing the CAPM-GARCH Models in the GCC-Wide Equity Sectors," Asian Journal of Economic Modelling, Asian Economic and Social Society, vol. 5(4), pages 413-430.
    10. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    11. Thomas J. Fisher & Colin M. Gallagher, 2012. "New Weighted Portmanteau Statistics for Time Series Goodness of Fit Testing," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 777-787, June.
    12. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. 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.
    2. 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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