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date: 28 May 2020

Abstract and Keywords

This article focuses on the routine use of robust betas by asset managers and financial data service providers as a complement to least squares (LS) betas. The routine use of robust betas identifies firms and time periods for which there are substantial differences between the two beta estimates. It evaluates the market risk premia based on robust betas that reject one or a very small number of outliers, in comparison with that of LS betas that may be adversely influenced by outliers. The time series of cross-section distributions of paired differences between LS and robust beta estimates of risk is computed, visualized, and analyzed in order to develop an in-depth understanding of the absolute and relative behaviors of robust and LS betas. A natural way to view the increased variability of the robust estimate for the normal distribution is in terms of the reciprocal of the square root of the efficiency. The single-factor model does not capture large percentages of market risk relative to total risk. The standard errors of OLS and robust estimates exhibit considerable variability over time and on average decrease with increasing firm size. The majority of firms in the smallest size group have standard errors that render the betas unreliable in the extreme, and this is the case even for the largest size group of firms during some time periods.

Keywords: least squares betas, robust betas, normal distribution, linear unbiased estimates, robust regression

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