A general test for SSD portfolio efficiency
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We develop and implement a Linear Programming test to analyze whether a given investment portfolio is efficient in terms of second-order stochastic dominance relative to all possible portfolios formed from a set of base assets. In case of efficiency, the primal model identifies a sub-gradient vector of a utility function that rationalizes the evaluated portfolio. In case of inefficiency, the dual model identifies a second, efficient portfolio that dominates the evaluated portfolio. The test gives a general necessary and sufficient condition, and can deal with general linear portfolio restrictions, inefficiency degree measures, and scenarios with unequal probabilities. We also develop a compact version of the test that substantially reduces computational burden at the cost of losing information about the dual dominating portfolio in case of inefficiency. An application to US investment benchmark data qualifies a broad stock market index as significantly inefficient, and suggests that no risk-averse investor would hold the market index in the face of attractive premiums offered by some more concentrated investment portfolios.
KeywordsStochastic dominance Portfolio analysis Market portfolio efficiency Linear programming
This work was partially supported by Czech Science Foundation (Grant P402/12/G097). Financial support by Koç University Graduate School of Business is gratefully acknowledged.
- Hardy GH, Littlewood JE, Polya G (1934) Inequalities. Cambridge University Press, CambridgeGoogle Scholar
- Kopa M, Chovanec P (2008) A second-order stochastic dominance portfolio efficiency measure. Kybernetika 44(2):243–258Google Scholar
- Levy H (2006) Stochastic dominance. Investment decision making under uncertainty. Springer, New YorkGoogle Scholar
- Linton O, Post T, Whang Y-J (2014) Testing for the stochastic dominance efficiency of a given portfolio. Econ J 17:S59–S74Google Scholar
- Post T, Fang Y, Kopa M (2014) Linear tests for DARA stochastic dominance. Forthcoming in Management Science.Google Scholar
- Post T, Van Vliet P, Levy H (2005) Risk aversion and skewness preference. J Bank Financ 185(3):1564–1573Google Scholar
- Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J Risk 2(3):21–41Google Scholar