Kybernetika 46 no. 3, 488-500, 2010

Measuring of second-order stochastic dominance portfolio efficiency

Miloš Kopa


In this paper, we deal with second-order stochastic dominance (SSD) portfolio efficiency with respect to all portfolios that can be created from a considered set of assets. Assuming scenario approach for distribution of returns several SSD portfolio efficiency tests were proposed. We introduce a $\delta$-SSD portfolio efficiency approach and we analyze the stability of SSD portfolio efficiency and $\delta$-SSD portfolio efficiency classification with respect to changes in scenarios of returns. We propose new SSD and $\delta$-SSD portfolio efficiency measures as measures of the stability. We derive a non-linear and mixed-integer non-linear programs for evaluating these measures. Contrary to all existing SSD portfolio inefficiency measures, these new measures allow us to compare any two $\delta$-SSD efficient or SSD efficient portfolios. Finally, using historical US stock market data, we compute $\delta$-SSD and SSD portfolio efficiency measures of several SSD efficient portfolios.


stability, stochastic dominance, SSD portfolio efficiency measure


91B28, 91B30