IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v217y2020i2p291-311.html
   My bibliography  Save this article

Spanning tests for Markowitz stochastic dominance

Author

Listed:
  • Arvanitis, Stelios
  • Scaillet, Olivier
  • Topaloglou, Nikolas

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 datasets 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.

Suggested Citation

  • Arvanitis, Stelios & Scaillet, Olivier & Topaloglou, Nikolas, 2020. "Spanning tests for Markowitz stochastic dominance," Journal of Econometrics, Elsevier, vol. 217(2), pages 291-311.
  • Handle: RePEc:eee:econom:v:217:y:2020:i:2:p:291-311
    DOI: 10.1016/j.jeconom.2019.12.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407619302519
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    2. 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.
    3. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 735-765.
    4. Reinganum, Marc R., 1981. "A New Empirical Perspective on the CAPM," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(4), pages 439-462, November.
    5. 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.
    6. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    7. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    8. Guggenberger, Patrik & Hahn, Jinyong & Kim, Kyooil, 2008. "Specification testing under moment inequalities," Economics Letters, Elsevier, vol. 99(2), pages 375-378, May.
    9. Basu, Sanjoy, 1983. "The relationship between earnings' yield, market value and return for NYSE common stocks : Further evidence," Journal of Financial Economics, Elsevier, vol. 12(1), pages 129-156, June.
    10. Stelios Arvanitis & Mark Hallam & Thierry Post & Nikolas Topaloglou, 2019. "Stochastic Spanning," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(4), pages 573-585, October.
      • Stelios Arvanitis & Mark Hallam & Thierry Post & Nikolas Topaloglou, 2015. "Stochastic Spanning," Working Papers 201510, Athens University Of Economics and Business, Department of Economics.
    11. Stelios Arvanitis & Mark Hallam & Thierry Post & Nikolas Topaloglou, 2015. "Stochastic Spanning," Working Papers 201510, Athens University Of Economics and Business, Department of Economics.
    12. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1932, October.
    13. 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.
    14. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    15. 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.
    16. Huberman, Gur & Kandel, Shmuel, 1987. "Mean-Variance Spanning," Journal of Finance, American Finance Association, vol. 42(4), pages 873-888, September.
    17. Edwards, Kimberley D., 1996. "Prospect theory: A literature review," International Review of Financial Analysis, Elsevier, vol. 5(1), pages 19-38.
    18. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 335-346.
    19. Manel Baucells & Franz H. Heukamp, 2006. "Stochastic Dominance and Cumulative Prospect Theory," Management Science, INFORMS, vol. 52(9), pages 1409-1423, September.
    20. Fama, Eugene F. & French, Kenneth R., 1997. "Industry costs of equity," Journal of Financial Economics, Elsevier, vol. 43(2), pages 153-193, February.
    21. Moshe Levy & Haim Levy, 2002. "Prospect Theory: Much Ado About Nothing?," Management Science, INFORMS, vol. 48(10), pages 1334-1349, October.
    22. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," Review of Economic Studies, Oxford University Press, vol. 25(2), pages 65-86.
    23. Scaillet, Olivier & Topaloglou, Nikolas, 2010. "Testing for Stochastic Dominance Efficiency," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 169-180.
    24. Thierry Post & Haim Levy, 2005. "Does Risk Seeking Drive Stock Prices? A Stochastic Dominance Analysis of Aggregate Investor Preferences and Beliefs," Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 925-953.
    25. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    26. Carhart, Mark M, 1997. "On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    27. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1931, October.
    28. Yusif Simaan, 1993. "Portfolio Selection and Asset Pricing---Three-Parameter Framework," Management Science, INFORMS, vol. 39(5), pages 568-577, May.
    29. Blume, Marshall E & Friend, Irwin, 1973. "A New Look at the Capital Asset Pricing Model," Journal of Finance, American Finance Association, vol. 28(1), pages 19-33, March.
    30. 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.
    31. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    32. Levy, Haim & Wiener, Zvi, 1998. "Stochastic Dominance and Prospect Dominance with Subjective Weighting Functions," Journal of Risk and Uncertainty, Springer, vol. 16(2), pages 147-163, May-June.
    33. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    34. 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.
    35. Banz, Rolf W., 1981. "The relationship between return and market value of common stocks," Journal of Financial Economics, Elsevier, vol. 9(1), pages 3-18, March.
    36. Arvanitis, Stelios & Topaloglou, Nikolas, 2017. "Testing for prospect and Markowitz stochastic dominance efficiency," Journal of Econometrics, Elsevier, vol. 198(2), pages 253-270.
    37. Post, Thierry & Kopa, Miloš, 2013. "General linear formulations of stochastic dominance criteria," European Journal of Operational Research, Elsevier, vol. 230(2), pages 321-332.
    38. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
    39. Stelios Arvanitis & Nikolas Topalogou, 2017. "Testing for Prospect and Markowitz stochastic dominance efficiency," Working Papers 201701, Athens University Of Economics and Business, Department of Economics.
    40. Haim Levy, 2004. "Prospect Theory and Mean-Variance Analysis," Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 1015-1041.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Saddle-type point; Markowitz stochastic dominance; Spanning test; Linear and mixed integer programming; Reverse S-shaped utility;

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:217:y:2020:i:2:p:291-311. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Haili He). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.