IDEAS home Printed from https://ideas.repec.org/a/eee/jeborg/v209y2023icp185-199.html
   My bibliography  Save this article

Semivariance below the maximum: Assessing the performance of economic and financial prospects

Author

Listed:
  • Courtois, Olivier Le
  • Xu, Xia

Abstract

This paper examines the ordering of economic and financial prospects using a rescaled semivariance below the maximum (SVBMax). This indicator is consistent with stochastic dominance (SD) until order three, but is distinct from any expected utility framework, both in terms of construction and in terms of economic implications, despite an apparent formal similarity with the quadratic expected utility framework. SVBMax is able to deal with economic puzzles such as the restaurant puzzle or Rabin’s paradox. SVBMax also provides a consistent alternative performance measure to popular measures such as the Sharpe ratio, the Omega ratio, or lower partial moments with exogenous thresholds. Compared to almost stochastic dominance, SVBMax is devoid of the drawbacks associated with the determination of violation areas. SVBMax can also replace the Aumann-Serrano and Foster-Hart riskiness indicators, which do not conform to third order SD. Further, SVBMax can provide a way of reaching an optimal diversification of stock portfolios. Besides, we also show that SVBMax is consistent with mean-variance-skewness preferences.

Suggested Citation

  • Courtois, Olivier Le & Xu, Xia, 2023. "Semivariance below the maximum: Assessing the performance of economic and financial prospects," Journal of Economic Behavior & Organization, Elsevier, vol. 209(C), pages 185-199.
    • Handle: RePEc:eee:jeborg:v:209:y:2023:i:c:p:185-199
    DOI: 10.1016/j.jebo.2023.03.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167268123000677
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jebo.2023.03.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. R. G. Vickson, 1975. "Stochastic Dominance Tests for Decreasing Absolute Risk Aversion. I. Discrete Random Variables," Management Science, INFORMS, vol. 21(12), pages 1438-1446, August.
    2. Patrick L. Brockett & Yehuda Kahane, 1992. "Risk, Return, Skewness and Preference," Management Science, INFORMS, vol. 38(6), pages 851-866, June.
    3. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
    4. Thierry Post & Yi Fang & Miloš Kopa, 2015. "Linear Tests for Decreasing Absolute Risk Aversion Stochastic Dominance," Management Science, INFORMS, vol. 61(7), pages 1615-1629, July.
    5. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    6. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-824, December.
    7. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785-814.
    8. Xu Guo & Cuizhen Niu & Wing-Keung Wong, 2019. "Farinelli and Tibiletti ratio and stochastic dominance," Risk Management, Palgrave Macmillan, vol. 21(3), pages 201-213, September.
    9. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    10. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    11. Farinelli, Simone & Tibiletti, Luisa, 2008. "Sharpe thinking in asset ranking with one-sided measures," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1542-1547, March.
    12. Quiggin, John, 1994. "Regret Theory with General Choice Sets," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 153-165, March.
    13. Bawa, Vijay S., 1978. "Safety-First, Stochastic Dominance, and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(2), pages 255-271, June.
    14. Bali, Turan G. & Demirtas, K. Ozgur & Levy, Haim & Wolf, Avner, 2009. "Bonds versus stocks: Investors' age and risk taking," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 817-830, September.
    15. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    16. Porter, R Burr, 1974. "Semivariance and Stochastic Dominance: A Comparison," American Economic Review, American Economic Association, vol. 64(1), pages 200-204, March.
    17. Kadan, Ohad & Liu, Fang, 2014. "Performance evaluation with high moments and disaster risk," Journal of Financial Economics, Elsevier, vol. 113(1), pages 131-155.
    18. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.
    19. Whitmore, G A, 1970. "Third-Degree Stochastic Dominance," American Economic Review, American Economic Association, vol. 60(3), pages 457-459, June.
    20. Vickson, R. G., 1975. "Stochastic Dominance for Decreasing Absolute Risk Aversion," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(5), pages 799-811, December.
    21. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    22. Thierry Post & Miloš Kopa, 2017. "Portfolio Choice Based on Third-Degree Stochastic Dominance," Management Science, INFORMS, vol. 63(10), pages 3381-3392, October.
    23. James Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 491-524, December.
    24. James E. Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster-Greer-Thorbecke (FGT) Poverty Measures: Twenty-Five Years Later," Working Papers 2010-14, The George Washington University, Institute for International Economic Policy.
    25. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    26. 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.
    27. Thierry Post & Haim Levy, 2005. "Does Risk Seeking Drive Stock Prices? A Stochastic Dominance Analysis of Aggregate Investor Preferences and Beliefs," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 925-953.
    28. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    29. Loomes, Graham & Sugden, Robert, 1987. "Some implications of a more general form of regret theory," Journal of Economic Theory, Elsevier, vol. 41(2), pages 270-287, April.
    30. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
    31. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    32. David E. Bell, 1982. "Regret in Decision Making under Uncertainty," Operations Research, INFORMS, vol. 30(5), pages 961-981, October.
    33. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    34. Thierry Post & Valerio Potì, 2017. "Portfolio Analysis Using Stochastic Dominance, Relative Entropy, and Empirical Likelihood," Management Science, INFORMS, vol. 63(1), pages 153-165, January.
    35. Antonella Basso & Paolo Pianca, 1997. "Decreasing Absolute Risk Aversion and Option Pricing Bounds," Management Science, INFORMS, vol. 43(2), pages 206-216, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Thierry Post & Miloš Kopa, 2017. "Portfolio Choice Based on Third-Degree Stochastic Dominance," Management Science, INFORMS, vol. 63(10), pages 3381-3392, October.
    2. Hildebrandt, Patrick & Knoke, Thomas, 2011. "Investment decisions under uncertainty--A methodological review on forest science studies," Forest Policy and Economics, Elsevier, vol. 13(1), pages 1-15, January.
    3. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.
    4. W. Wong & R. Chan, 2008. "Prospect and Markowitz stochastic dominance," Annals of Finance, Springer, vol. 4(1), pages 105-129, January.
    5. Kolokolova, Olga & Le Courtois, Olivier & Xu, Xia, 2022. "Is the index efficient? A worldwide tour with stochastic dominance," Journal of Financial Markets, Elsevier, vol. 59(PB).
    6. Schuhmacher, Frank & Auer, Benjamin R., 2014. "Sufficient conditions under which SSD- and MR-efficient sets are identical," European Journal of Operational Research, Elsevier, vol. 239(3), pages 756-763.
    7. Wong, Wing-Keung, 2007. "Stochastic dominance and mean-variance measures of profit and loss for business planning and investment," European Journal of Operational Research, Elsevier, vol. 182(2), pages 829-843, October.
    8. Jia Liu & Zhiping Chen & Giorgio Consigli, 2021. "Interval-based stochastic dominance: theoretical framework and application to portfolio choices," Annals of Operations Research, Springer, vol. 307(1), pages 329-361, December.
    9. Kaplanski, Guy & Kroll, Yoram, 2002. "VaR Risk Measures versus Traditional Risk Measures: an Analysis and Survey," MPRA Paper 80070, University Library of Munich, Germany.
    10. Chan, Raymond H. & Chow, Sheung-Chi & Guo, Xu & Wong, Wing-Keung, 2022. "Central moments, stochastic dominance, moment rule, and diversification with an application," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    11. Raymond H. Chan & Ephraim Clark & Xu Guo & Wing-Keung Wong, 2020. "New development on the third-order stochastic dominance for risk-averse and risk-seeking investors with application in risk management," Risk Management, Palgrave Macmillan, vol. 22(2), pages 108-132, June.
    12. Hooi Hooi Lean & Michael McAleer & Wing-Keung Wong, 2010. "Market Efficiency of Oil Spot and Futures: A Stochastic Dominance Approach," CIRJE F-Series CIRJE-F-705, CIRJE, Faculty of Economics, University of Tokyo.
    13. Lean, H.H. & McAleer, M.J. & Wong, W.-K., 2010. "Investor preferences for oil spot and futures based on mean-variance and stochastic dominance," Econometric Institute Research Papers EI 2010-37, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    14. Daskalaki, Charoula & Skiadopoulos, George & Topaloglou, Nikolas, 2017. "Diversification benefits of commodities: A stochastic dominance efficiency approach," Journal of Empirical Finance, Elsevier, vol. 44(C), pages 250-269.
    15. Antonella Basso & Paolo Pianca, 1997. "On the relative efficiency of nth order and DARA stochastic dominance rules," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(4), pages 207-222.
    16. Unser, Matthias, 2000. "Lower partial moments as measures of perceived risk: An experimental study," Journal of Economic Psychology, Elsevier, vol. 21(3), pages 253-280, June.
    17. Post, Thierry & Karabatı, Selçuk & Arvanitis, Stelios, 2018. "Portfolio optimization based on stochastic dominance and empirical likelihood," Journal of Econometrics, Elsevier, vol. 206(1), pages 167-186.
    18. Thierry Post & Iňaki Rodríguez Longarela, 2021. "Risk Arbitrage Opportunities for Stock Index Options," Operations Research, INFORMS, vol. 69(1), pages 100-113, January.
    19. Andrey Lizyayev, 2012. "Stochastic dominance efficiency analysis of diversified portfolios: classification, comparison and refinements," Annals of Operations Research, Springer, vol. 196(1), pages 391-410, July.
    20. Christodoulakis, George & Mohamed, Abdulkadir & Topaloglou, Nikolas, 2018. "Optimal privatization portfolios in the presence of arbitrary risk aversion," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1172-1191.

    More about this item

    Keywords

    Semivariance below the maximum; Stochastic dominance; DARA; Quasi-complete ranking; Utility function; Diversification;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • 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:jeborg:v:209:y:2023:i:c:p:185-199. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jebo .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.