A Revisit to Estimation of Beta Risk and an Analysis of Stock Market Through Copula Transformation and Winsorization with S&P 500 Index as Proxy

Abstract

We consider the problem of reliable estimation of market betas. Estimation using least squares can be very sensitive to underlying assumptions of normality and the presence of outliers, whereas various robust estimation procedures have a certain degree of arbitrariness in their implementation. This is especially of concern because returns for various equities may have very different statistical distributions. Our approach is to bring all estimation problems to a common platform through bivariate Gaussian copula transformation where, in view of the linearity of regression, correlation is a meaningful measure of dependence. We then carry out the estimation of betas by combining it with the winsorized relative volatility of the asset. Extensive analysis of the U.S. market with the S&P 500 as proxy indicates that, when the data show departure from assumptions, our approach provides more stable estimates of betas than least squares, and estimates are essentially the same when assumptions are met. Improvement is realized in up to 53% of instances.