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Consistent tests for risk seeking behavior: A stochastic dominance approach

Author

Listed:
  • Stelios Arvanitis

    (Athens University of Economics and Business)

  • Nikolas Topaloglou

    (Athens University of Economics and Business)

Abstract

We develop non-parametric tests for prospect stochastic dominance Efficiency (PSDE) and Markowitz stochastic dominance efficiency (MSDE) with rejection regions determined by block bootstrap resampling techniques. Under the appropriate conditions we show that they are asymptotically conservative and consistent. We engage into Monte Carlo experiments to assess the nite sample size and power of the tests allowing for the presence of numerical errors. We use them to empirically analyze investor preferences and beliefs by testing whether the value-weighted market portfolio can be considered as efficient according to prospect and Markowitz stochastic dominance criteria when confronted to diversi cation principles made of risky assets. Our results indicate that we cannot reject the hypothesis of prospect stochastic dominance efficiency for the market portfolio. This is supportive of the claim that the particular portfolio can be rationalized as the optimal choice for any S-shaped utility function. Instead, we reject the hypothesis for Markowitz stochastic dominance, which could imply that there exist reverse S-shaped utility functions that do not rationalize the market portfolio.

Suggested Citation

  • Stelios Arvanitis & Nikolas Topaloglou, 2015. "Consistent tests for risk seeking behavior: A stochastic dominance approach," Working Papers 201511, Athens University Of Economics and Business, Department of Economics.
  • Handle: RePEc:aeb:wpaper:201511:y:2015
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    File URL: http://www2.econ.aueb.gr/uploadfiles/AllDP112015
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    References listed on IDEAS

    as
    1. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    2. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    3. Horvath, Lajos & Kokoszka, Piotr & Zitikis, Ricardas, 2006. "Testing for stochastic dominance using the weighted McFadden-type statistic," Journal of Econometrics, Elsevier, vol. 133(1), pages 191-205, July.
    4. Jesus Gonzalo & Jose Olmo, 2014. "Conditional Stochastic Dominance Tests In Dynamic Settings," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 819-838, August.
    5. Davidson, Russell & MacKinnon, James G., 2007. "Improving the reliability of bootstrap tests with the fast double bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3259-3281, April.
    6. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    7. Edwards, Kimberley D., 1996. "Prospect theory: A literature review," International Review of Financial Analysis, Elsevier, vol. 5(1), pages 19-38.
    8. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279-279.
    9. Davidson, Russell & MacKinnon, James G., 2006. "The power of bootstrap and asymptotic tests," Journal of Econometrics, Elsevier, vol. 133(2), pages 421-441, August.
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    11. Levy, Haim, 1982. "Stochastic Dominance Rules for Truncated Normal Distributions: A Note," Journal of Finance, American Finance Association, vol. 37(5), pages 1299-1303, December.
    12. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
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    More about this item

    Keywords

    Non parametric test; prospect stochastic dominance efficiency; Markowitz stochastic dominance efficiency; simplical complex; extremal point; Linear Programming; Mixed Integer Programming; Block Bootstrap; Consistency;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • 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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