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Spanning Tests for Markowitz Stochastic Dominance

Author

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  • Stelios Arvanitis

    (Athens University of Economics and Business)

  • O. Scaillet

    (University of Geneva and Swiss Finance Institute)

  • Nikolas Topaloglou

    (Athens University of Economics and Business)

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.

Suggested Citation

  • Stelios Arvanitis & O. Scaillet & Nikolas Topaloglou, 2018. "Spanning Tests for Markowitz Stochastic Dominance," Swiss Finance Institute Research Paper Series 18-08, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1808
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    2. Zhou, Zhongbao & Gao, Meng & Xiao, Helu & Wang, Rui & Liu, Wenbin, 2021. "Big data and portfolio optimization: A novel approach integrating DEA with multiple data sources," Omega, Elsevier, vol. 104(C).

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    More about this item

    Keywords

    Saddle-Type Point; Markowitz Stochastic Dominance; Spanning Test; Linear and Mixed integer programming; reverse S-shaped utility;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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