Statistical Methods in Finance 2018

Dec 17 - 20, 2018


A New Approach to the Estimation of Beta Risk and An Analysis of Stock Market Through Copula Transformation and Winsorization with S&P500 Index as Proxy

by Ravindra Khattree

We consider the problem of reliable estimation of market betas. Estimation using least squares can be very sensitive to underlying assumptions of normality and presence of outliers, while various robust estimation procedures have a certain degree of arbitrariness in their implementation. This is especially of concern since returns for various equities may have very different statistical distributions and this consideration is routinely ignored when ranking stocks or other assets with respect to their beta values. At the same time, different assumptions made on the distributions of different stocks will result in their betas becoming largely incomparable. Our approach is to bring all estimation problems to a common platform through bivariate Gaussian copula transformation where in view of linearity of regression, correlation is a meaningful measure of dependence. We then carry out the estimation of betas by combining it with winsorized relative volatility of the asset. Extensive analysis of US market with S&P500 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 same when assumptions are met. Improvement is realized in upto 53% of the instances.