Testing downside risk efficiency under market distress

In moments of distress downside risk measures like Lower Partial Moments (LPM) are more appropriate than the standard variance to characterize risk. The goal of this paper is to study how to compare portfolios in these situations. In order to do that we show the close connection between mean-risk efficiency sets and stochastic dominance under distress episodes of the market, and use the latter property to propose a hypothesis test to discriminate between portfolios across risk aversion levels. Our novel family of test statistics for testing stochastic dominance under distress makes allowance for testing orders of dominance higher than zero, for general forms of dependence between portfolios and can be extended to residuals of regression models. These results are illustrated in the empirical application for data from US stocks. We show that mean-variance strategies are stochastically dominated by mean-risk efficient sets in episodes of financial distress.