Efficiency analysis of classic risk minimizing portfolios

Abstract

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 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 the 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. It is empirically documented that only Pearson measure in Markowitz model identified a portfolio that can be of interest for at least one risk averse investor. Moreover, a portfolio based on Kendall measure is very poor (at least in terms of SSD efficiency).