Downside Risk Sensitivity and Conditional Stochastic Dominance in Euro Area Stock Markets

Abstract

This article compares portfolio selection based on the downside risk sensitivity with portfolio selection based on Sharpe or Treynor ratios. Downside risk sensitivity (DRS) is given by an asset pricing model in which the downside and upside market returns are separated variables relative to target return. While CAPM, Sharpe ratios and Treynor ratios are based on symmetric risk aversion in both sides of the expected return of the market portfolio, the assumption underlying downside risk sensitivity is that investors utility functions weight losses more heavily s than gains relative to the target return.

The methodology used consists of making alternate estimations using a downside-upside risk model (DURM) and CAPM. Portfolios based on DRS, Sharpe ratios and Treynor ratios DRS were created and their composition is updated using the output of rolling estimations of the asset pricing models. The ex post returns of portfolios based on the three alternate methods of portfolio selection are evaluated comparatively by conditional Sharpe ratios which provide information about the conditional stochastic dominance between them.

We found that portfolio selection based on downside risk sensitivity gives better protection against losses and better global performance than portfolios based on Sharpe ratios and Treynor ratios.

Keywords: conditional Sharpe ratios, conditional stochastic dominance, downside risk, lower partial moments, Sharpe ratios, Treynor ratios

JEL Classification: F36, G11, G15