Asset pricing models with errors-in-variables

This paper revisits Fama and French [Fama, Eugene F., French, Kenneth R., (1993) Common risk factors in the returns on stock and bonds. Journal of Financial Economics 33 (1), 3–56] and Carhart [Carhart, Mark M., 1997. On persistence in mutual fund performance. Journal of Finance 52 (1), 57–82] multifactor model taking into account the possibility of errors-in-variables. In their well known paper, Fama and French [Fama, Eugene F., French, Kenneth R., 1997. Industry costs of equity. Journal of Financial Economic 43 (2), 153–193] concluded that estimates of the cost of equity for the three-factor model of FF (1993) were imprecise. We argue that this imprecision is even more severe because of the pervasive effects of measurement errors. We propose Dagenais and Dagenais [Dagenais, Marcel G., Dagenais, Denyse L., 1997. Higher moment estimators for linear regression models with errors in the variables. Journal of Econometrics 76 (1–2), 193–221] higher moments estimator as a solution. Our results show that estimates of the cost of equity obtained with Dagenais and Dagenais estimator differ sharply from popular OLS estimates and shed a new light on performance attribution and abnormal performance (α). Adapting the Generalized Treynor Ratio, recently developed by Hübner [Hübner, Georges, 2005. The generalized treynor ratio. Review of Finance 9 (3), 415–435], we show that the performance of managed portfolios with multi-index models should be revisited in presence of errors-in-variables.