Concordance Measures and Second Order Stochastic Dominance - Portfolio Efficiency Analysis

Portfolio selection problem is one of the most important issues within financial risk management and decision making. It concerns both, financial institutions and their regulator/supervisor bodies. A crucial input factor, when the admissible or even optimal portfolio is detected, is the measure of dependency. Although there exists a wide range of dependency measures, a standard assumption is that the (joint) distribution of large portfolios is multivariate normal and that the dependency can be described well by a linear measure of correlation – the Pearson coefficient of correlation is therefore usually utilized. A very challenging question in this context is whether there is some impact of alternative dependency/concordance measures on the efficiency of optimal portfolios. Therefore, the alternative ways of portfolio comparisons were developed, among them a stochastic dominance approach is one of the most popular one. In particular, the definition of second-order stochastic dominance (SSD) relation uses comparisons of either twice cumulative distribution functions or expected utilities. Alternatively, one can define SSD relation using cumulative quantile functions or conditional value at risk. The task of this paper is therefore to examine and analyze the SSD efficiency of min-var portfolios that are selected on the basis of alternative concordance matrices set up on the basis of either Spearman rho or Kendall tau. In order to carry out the analysis the real data of FX rate returns over 2007 and 2008 are used. It is documented that although all portfolios considered were SSD inefficient especially a portfolio based on Kendall measure is very poor (at least in terms of SSD efficiency). Moreover, the inefficiency during the crisis year 2008 was much lower than during one year earlier.