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Title: Simultaneous estimations of the parameters regression with Realized-GARCH errors Authors:  Hisseine Saad Mahamat - University of Montpellier (France) [presenting]
Roman Mestre - University of Montpellier (France)
Michel Terraza - lameta (France)
Abstract: The systematic risk of an equity (measured with the Beta) is estimated by the market line equation. According to the OLS hypothesis, the estimation is robust and residuals are normally white-noise process. However, various papers show that the BETA estimator cannot be BLUE because there are many statistical anomalies in the residuals (heteroskedasticity, autocorrelation and non-normality) proving then that the the model does not hold. The Beta value can be different and the estimation more robust if we re-estimate it by taking into consideration the heteroskedastic nature of the residuals. We base our calculation on the Societe Generale risk premium (a French Bank Equity) and CAC40 premium (French Stockmarket Index) for the daily period from 2005-2015. We use a new GARCH process; called Realized-GARCH, to model the errors variance and we include it in the Market line estimation. The asymmetric nature of the GARCH is also tested; in order to compare the result with other GARCH process such as EGARCH, GJR-GARCH. To select the best GARCH process to correct the Beta estimation, we compare the result about the Beta value and the residuals characteristics. We find that the Beta value with GARCH errors is different and the residuals characteristics are better.