Spanning Tests for Markowitz Stochastic Dominance

52 Pages Posted: 2 Feb 2018

See all articles by Stelios Arvanitis

Stelios Arvanitis

Athens University of Economics and Business - Department of Economics

O. Scaillet

University of Geneva GSEM and GFRI; Swiss Finance Institute; University of Geneva - Research Center for Statistics

Nikolas Topaloglou

Athens University of Economics and Business

Date Written: January 31, 2018

Abstract

Using properties of the cdf of a random variable defined as a saddle-type point of a real valued continuous stochastic process, we derive first-order asymptotic properties of tests for stochastic spanning w.r.t. a stochastic dominance relation. First, we define the concept of Markowitz stochastic dominance spanning, and develop an analytical representation of the spanning property. Second, we construct a non-parametric test for spanning via the use of an empirical analogy. The method determines whether introducing new securities or relaxing investment constraints improves the investment opportunity set of investors driven by Markowitz stochastic dominance. In an application to standard data sets of historical stock market returns, we reject market portfolio Markowitz efficiency as well as two-fund separation. Hence there exists evidence that equity management through base assets can outperform the market, for investors with Markowitz type preferences.

Keywords: Saddle-Type Point, Markowitz Stochastic Dominance, Spanning Test, Linear and Mixed integer programming, reverse S-shaped utility

JEL Classification: C12, C14, C44, C58, D81, G11

Suggested Citation

Arvanitis, Stelios and Scaillet, Olivier and Topaloglou, Nikolas, Spanning Tests for Markowitz Stochastic Dominance (January 31, 2018). Swiss Finance Institute Research Paper No. 18-08. Available at SSRN: https://ssrn.com/abstract=3114016 or http://dx.doi.org/10.2139/ssrn.3114016

Stelios Arvanitis (Contact Author)

Athens University of Economics and Business - Department of Economics ( email )

76 Patission Street
GR-10434 Athens
Greece

Olivier Scaillet

University of Geneva GSEM and GFRI ( email )

40 Boulevard du Pont d'Arve
Geneva 4, 1211
Switzerland
+ 41 22 379 88 16 (Phone)
+41 22 389 81 04 (Fax)

HOME PAGE: http://www.scaillet.ch

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

University of Geneva - Research Center for Statistics

Geneva
Switzerland

Nikolas Topaloglou

Athens University of Economics and Business ( email )

76, Patision street
Athens, GR10434
Greece

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