Attribution Analysis of Bull/Bear Alphas and Betas with Applications to Downside Risk Management

Abstract

In this research note, we will discuss a specific asymmetrical model and build an attribution framework which allows relating the effects of asymmetry on Alpha and Beta relative to a benchmark model, the single-index model with its symmetric Alpha and Beta. We explain the difference between two models, while in traditional attribution analysis one usually attributes the difference in realized returns between a portfolio and its benchmark. We illustrate how asymmetrical models can be used in ex post portfolio analysis to detect “false” alphas caused by “hidden” asymmetrical betas and how asymmetrical betas can be used in ex ante portfolio construction for the purpose of active downside risk management.

Keywords: Performance Attribution, Bull, Bear, Alpha, Beta, Chow Test, Portfolio Construction