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Stochastic dominance and risk measure: A decision-theoretic foundation for VaR and C-VaR

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  • Ma, Chenghu
  • Wong, Wing-Keung

Abstract

Is it possible to obtain an objective and quantifiable measure of risk backed up by choices made by some specific groups of rational investors? To answer this question, in this paper we establish some behavior foundations for various types of VaR models, including VaR and conditional-VaR, as measures of downside risk. In this paper, we will establish some logical connections among VaRs, conditional-VaR, stochastic dominance, and utility maximization. Though supported to some extents with unanimous choices by some specific groups of expected or non-expected-utility investors, VaRs as profiles of risk measures at various levels of risk tolerance are not quantifiable - they can only provide partial and incomplete risk assessments for risky prospects. We also include in our discussion the relevant VaRs and several alternative risk measures for investors; these alternatives use somewhat weaker assumptions about risk-averse behavior by incorporating a mean-preserving-spread. For this latter group of investors, we provide arguments for and against the standard deviation versus VaR and conditional-VaRs as objective and quantifiable measures of risk in the context of portfolio choice.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 207 (2010)
Issue (Month): 2 (December)
Pages: 927-935

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Handle: RePEc:eee:ejores:v:207:y:2010:i:2:p:927-935

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Web page: http://www.elsevier.com/locate/eor

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Keywords: Decision analysis Risk analysis Risk attributes Utility Stochastic dominance;

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  1. Alexander, Gordon J. & Baptista, Alexandre M., 2002. "Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1159-1193, July.
  2. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
  3. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  4. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  5. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  6. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
  7. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
  8. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
  9. Johannes Leitner, 2005. "A Short Note On Second-Order Stochastic Dominance Preserving Coherent Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 649-651.
  10. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151.
  11. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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Citations

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Cited by:
  1. Guorui Bian & Michael McAleer & Wing-Keung Wong, 2010. "Robust Estimation and Forecasting of the Capital Asset Pricing Model," Working Papers in Economics 10/66, University of Canterbury, Department of Economics and Finance.
  2. Fathi Abid & Pui Lam Leung & Mourad Mroua & Wing Keung Wong, 2014. "International Diversification Versus Domestic Diversification: Mean-Variance Portfolio Optimization and Stochastic Dominance Approaches," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 7(2), pages 45-66, May.
  3. Bai, Zhidong & Li, Hua & Wong, Wing-Keung, 2013. "The best estimation for high-dimensional Markowitz mean-variance optimization," MPRA Paper 43862, University Library of Munich, Germany.
  4. Lean, Hooi Hooi & McAleer, Michael & Wong, Wing-Keung, 2010. "Market efficiency of oil spot and futures: A mean-variance and stochastic dominance approach," Energy Economics, Elsevier, vol. 32(5), pages 979-986, September.
  5. Zhidong Bai & Hua Li & Michael McAleer & Wing-Keung Wong, 2012. "Stochastic Dominance Statistics for Risk Averters and Risk Seekers: An Analysis of Stock Preferences for USA and China," Documentos de Trabajo del ICAE 2012-13, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  6. Eric S. Fung & Kin Lam & Tak-Kuen Siu & Wing-Keung Wong, 2011. "A Pseudo-Bayesian Model for Stock Returns In Financial Crises," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 4(1), pages 43-73, December.
  7. Basu, Sanjay, 2011. "Comparing simulation models for market risk stress testing," European Journal of Operational Research, Elsevier, vol. 213(1), pages 329-339, August.
  8. Guo, Xu & Lam, Kin & Wong, Wing-Keung & Zhu, Lixing, 2012. "A New Pseudo-Bayesian Model of Investors' Behavior in Financial Crises," MPRA Paper 42535, University Library of Munich, Germany.
  9. Leung, Pui-Lam & Ng, Hon-Yip & Wong, Wing-Keung, 2012. "An improved estimation to make Markowitz’s portfolio optimization theory users friendly and estimation accurate with application on the US stock market investment," European Journal of Operational Research, Elsevier, vol. 222(1), pages 85-95.
  10. Alessandra Cillo & Philippe Delquié, 2013. "Mean-Risk Analysis with Enhanced Behavioral Content," Working Papers 498, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  11. Wong, Wing-Keung & Phoon, Kok Fai & Lean, Hooi Hooi, 2008. "Stochastic dominance analysis of Asian hedge funds," Pacific-Basin Finance Journal, Elsevier, vol. 16(3), pages 204-223, June.
  12. Bai, Zhidong & Phoon, Kok Fai & Wang, Keyan & Wong, Wing-Keung, 2013. "The performance of commodity trading advisors: A mean-variance-ratio test approach," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 188-201.
  13. Guorui Bian & Michael McAleer & Wing-Keung Wong, 2013. "Robust Estimation and Forecasting of the Capital Asset Pricing Model," Tinbergen Institute Discussion Papers 13-036/III, Tinbergen Institute.
  14. Broll, Udo & Wong, Wing-Keung & Wu, Mojia, 2013. "Banking Firm and Two-Moment Decision Making," MPRA Paper 51687, University Library of Munich, Germany.

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