Beta Estimation with Stock Return Outliers : The Case of U.S. Pharmaceutical Companies

Efficient estimation of the equity cost of public corporations is an essential component of computing the required rate of return of real investment projects, and therefore the basis for a rational investment policy. The accepted methodology relies on the CAPM model to define the return risk premium, and the OLS method to estimate the beta risk coefficient required for calculating the premium. This study challenges the use of the OLS method for this task by demonstrating its vulnerability to the impact of stock return outliers caused by large, unpredictable, company-specific events. That impact is verified on a sample of U.S. pharmaceutical companies by comparing the OLS estimation performance with that of our proposed method based on Huber's Robust M (HRM) estimator, a related statistical method that follows a mixed return model identifying regular and outlier return components. Using the HRM-estimated beta as a benchmark, we demonstrate that (1) outliers can substantially bias the OLS beta, (2) the bias is negatively correlated with company size, and (3) the size of the bias is often moderated but not eliminated by extending the estimation period. The latter finding suggests that a robust method like HRM is preferable where estimators ought to represent the behavior of the majority of historical data despite the presence of outliers. The risk of trusting the OLS beta is especially high when estimation must rely on a small sample