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Spanning Tests for Markowitz Stochastic Dominance

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  • Stelios Arvanitis
  • Olivier Scaillet
  • Nikolas Topaloglou

Abstract

We derive properties of the cdf of random variables defined as saddle-type points of real valued continuous stochastic processes. This facilitates the derivation of the first-order asymptotic properties of tests for stochastic spanning given some stochastic dominance relation. We define the concept of Markowitz stochastic dominance spanning, and develop an analytical representation of the spanning property. We construct a non-parametric test for spanning based on subsampling, and derive its asymptotic exactness and consistency. The spanning methodology 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, we find evidence that equity management through base assets can outperform the market, for investors with Markowitz type preferences.

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  • Stelios Arvanitis & Olivier Scaillet & Nikolas Topaloglou, 2018. "Spanning Tests for Markowitz Stochastic Dominance," Papers 1810.10800, arXiv.org.
    • Handle: RePEc:arx:papers:1810.10800
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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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    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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