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Stochastic Spanning

Author

Listed:
  • Stelios Arvanitis

    (Athens University of Economics and Business)

  • Mark Hallam

    (Athens University of Economics and Business)

  • Thierry Post

    (Athens University of Economics and Business)

  • Nikolas Topaloglou

    (Athens University of Economics and Business)

Abstract

This study develops and implements methods for analyzing whether introducing new securities or relaxing investment constraints improves the investment opportunity set for risk averse investors. We develop a statistical test procedure for ‘stochastic span- ning’ for two nested polyhedral portfolio sets based on subsampling and Linear Programming. The test is statistically consistent and asymptotically exact for a class of weakly dependent processes. Using this test, we accept market portfolio efficiency but reject two - fund separation in standard data sets of historical stock market returns. The divergence between the test results for the two hypotheses illustrates the role for higher - order moment risk in portfolio choice and challenges representative - investor models of capital market equilibrium.

Suggested Citation

  • Stelios Arvanitis & Mark Hallam & Thierry Post & Nikolas Topaloglou, 2015. "Stochastic Spanning," Working Papers 201510, Athens University Of Economics and Business, Department of Economics.
    • Handle: RePEc:aeb:wpaper:201510:y:2015
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    References listed on IDEAS

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    1. Scaillet, Olivier & Topaloglou, Nikolas, 2010. "Testing for Stochastic Dominance Efficiency," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 169-180.
    2. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    3. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1931, October.
    4. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    5. Post, Thierry & Versijp, Philippe, 2007. "Multivariate Tests for Stochastic Dominance Efficiency of a Given Portfolio," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(2), pages 489-515, June.
    6. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 735-765.
    7. Oliver Linton & Thierry Post & Yoon‐Jae Whang, 2014. "Testing for the stochastic dominance efficiency of a given portfolio," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 59-74, June.
    8. 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.
    9. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    10. Stephen A. Ross, 2005. "Mutual Fund Separation in Financial Theory—The Separating Distributions," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 10, pages 309-356, World Scientific Publishing Co. Pte. Ltd..
    11. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    12. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    13. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1932, October.
    14. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-317, June.
    15. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
    16. Huberman, Gur & Kandel, Shmuel, 1987. "Mean-Variance Spanning," Journal of Finance, American Finance Association, vol. 42(4), pages 873-888, September.
    17. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    18. Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, February.
    19. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-1152, September.
    20. James P. Quirk & Rubin Saposnik, 1962. "Admissibility and Measurable Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(2), pages 140-146.
    21. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
    22. Ali, Mukhtar M., 1975. "Stochastic dominance and portfolio analysis," Journal of Financial Economics, Elsevier, vol. 2(2), pages 205-229, June.
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    Citations

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    Cited by:

    1. Arvanitis, Stelios & Scaillet, Olivier & Topaloglou, Nikolas, 2020. "Spanning tests for Markowitz stochastic dominance," Journal of Econometrics, Elsevier, vol. 217(2), pages 291-311.
    2. Stelios Arvanitis & O. Scaillet & Nikolas Topaloglou, 2020. "Spanning analysis of stock market anomalies under Prospect Stochastic Dominance," Swiss Finance Institute Research Paper Series 20-18, Swiss Finance Institute.
    3. Iñaki R. Longarela, 2016. "A Characterization of the SSD-Efficient Frontier of Portfolio Weights by Means of a Set of Mixed-Integer Linear Constraints," Management Science, INFORMS, vol. 62(12), pages 3549-3554, December.
    4. Duc Khuong Nguyen & Nikolas Topaloglou & Thomas Walther, 2020. "Asset Classes and Portfolio Diversification: Evidence from a Stochastic Spanning Approach," Working Papers 2020-009, Department of Research, Ipag Business School.
    5. Liesiö, Juuso & Kallio, Markku & Argyris, Nikolaos, 2023. "Incomplete risk-preference information in portfolio decision analysis," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1084-1098.
    6. Pinar, Mehmet & Stengos, Thanasis & Topaloglou, Nikolas, 2020. "On the construction of a feasible range of multidimensional poverty under benchmark weight uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 415-427.
    7. Stelios Arvanitis, 2015. "Saddle-Type Functionals for Continuous Processes with Applications to Tests for Stochastic Spanning," Working Papers 201509, Athens University Of Economics and Business, Department of Economics.
    8. Karl Demers-Bélanger & Van Son Lai, 2019. "Diversification Benefits of Cat Bonds: An In-Depth Examination," Working Papers 2019-008, Department of Research, Ipag Business School.
    9. Stelios Arvanitis, 2021. "Stochastic dominance efficient sets and stochastic spanning," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 401-409, June.
    10. Anyfantaki, Sofia & Arvanitis, Stelios & Topaloglou, Nikolas, 2021. "Diversification benefits in the cryptocurrency market under mild explosivity," European Journal of Operational Research, Elsevier, vol. 295(1), pages 378-393.
    11. Kouaissah, Noureddine, 2023. "Robust reward-risk performance measures with weakly second-order stochastic dominance constraints," The Quarterly Review of Economics and Finance, Elsevier, vol. 88(C), pages 53-62.
    12. Pho, Kim Hung & Ly, Sel & Lu, Richard & Hoang, Thi Hong Van & Wong, Wing-Keung, 2021. "Is Bitcoin a better portfolio diversifier than gold? A copula and sectoral analysis for China," International Review of Financial Analysis, Elsevier, vol. 74(C).

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    More about this item

    Keywords

    Portfolio choice; Stochastic Dominance; Spanning; Subsampling; Linear Programming; Asset Pricing.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • 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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