Global versus local beta models: A partitioned distribution approach

Abstract

This study investigates the assumption that stock riskiness, captured by the market global beta, is constant over the market returns domain. To relax this assumption we propose to model stock returns through disjoint truncated normal distributions fit by means of the Minimum Distance Approach. This provides a set of disjoint conditional regions where normality still holds but it allows to decompose the unconditional beta into local ones referred to each region. In the case study we show that this approach, while preserving the simplicity of describing data by normal distributions, significantly improves the accuracy of the fit, compensating the well-known inadequacy of the standard normal distribution to fit returns in the tails. An extensive out of sample returns predictive test shows that the quality of prediction obtained with our methodology globally has similar statistical properties as for the standard global beta, but it outperforms the latter especially when the negative returns' domain is considered.