Value at Risk application to FSD portfolio efficiency testing

The paper deals with efficiency testing of a given portfolio with respect to all other portfolios that can be created from the considered set of assets. The efficiency is based on the first order stochastic dominance (FSD) relation. A necessary and sufficient condition for the first order stochastic dominance criterion is expressed in terms of Value at Risks (VaRs). Consequently a FSD portfolio efficiency test based on VaRs is formulated. Contrary to the usual case, a general discrete distribution of portfolio returns is assumed what makes the test computationally more demanding comparing to the equiprobable scenarios case. Therefore we present a tractable reformulation of this test that turns constraints on VaRs into classical mixed-integer nonlinear programming problem.