Stochastic orders and multivariate measures of risk contagion

Abstract

Co-risk measures and risk contributions measures are used in portfolio risk analysis to assess and quantify the risk of contagion, given that one or more assets in the portfolio are in distress. In this paper, given two random vectors X and Y that represent two portfolios of n assets (n ≥ 2) and exhibit some kind of positive dependence, we give sufficient conditions based on stochastic orders to compare the risk of contagion of the portfolios. The measures of risk contagion that we consider are the conditional value at risk (CoVaR), the conditional expected shortfall (CoES) and the recently introduced marginal mean excess (MME).