Why We Need Robust Alphas (and Betas) -Is it possible to beyond "premium vs. anomaly anomaly" with the statistical method method?

Abstract

OLS (Ordinary Least Square) estimation of sample means and betas can lead to biased estimates of alpha in the presence of certain patterns of heteroscedasticity. There has been discussing on something t o do with background of modern portfolio theory for forecasting risk premium and dealing with anomaly. We demonstrate that those patterns occur in practice, and that a robust estimation process eliminates the bias with some algorithms.