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Downside Risk Efficiency Under Market Distress

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  • Jesús Gonzalo

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  • José Olmo

Abstract

In moments of financial distress downside risk measures like lower partial moments are more appropriate than the standard variance to characterize risk. The goal of this paper is to study how to choose optimal portfolios in these periods. In order to do this we extend the definition of lower partial moments to this environment, derive the corresponding mean-risk dominance set and define the concept of stochastic dominance under distress. The paper shows the close connection between the mean-risk dominance set and the stochastic dominance frontier in these situations. The advantage of using stochastic dominance is that we can readily compare investors' preferences over investment portfolios in a meaningful way regardless their degree of risk aversion. We do this by proposing a hypothesis test. Our novel family of test statistics for testing stochastic dominance under distress makes allowance for testing orders of dominance higher than one, for general forms of dependence between portfolios and can be extended to residuals of regression models. These results are illustrated in an empirical application for data from US stocks. We show that mean- variance strategies are stochastically dominated by meanrisk efficient portfolios in episodes of financial distress.

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we094423.

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Date of creation: Jun 2009
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Handle: RePEc:cte:werepe:we094423

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Keywords: Downside risk; Lower partial moments; Market distress; Mean-risk models; Mean-variance models; Stochastic dominance;

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References

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  1. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
  2. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1932, October.
  3. Oliver Linton1 & Kyungchul Song & Yoon-Jae Whang, 2008. "Bootstrap Tests of Stochastic Dominance with Asymptotic Similarity on the Boundary," PIER Working Paper Archive 08-006, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  4. 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.
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  7. Porter, R Burr, 1974. "Semivariance and Stochastic Dominance: A Comparison," American Economic Review, American Economic Association, vol. 64(1), pages 200-04, March.
  8. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Capital market equilibrium in a mean-lower partial moment framework," Journal of Financial Economics, Elsevier, vol. 5(2), pages 189-200, November.
  9. Bawa, Vijay S., 1978. "Safety-First, Stochastic Dominance, and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(02), pages 255-271, June.
  10. Bawa, Vijay S, 1976. "Admissible Portfolios for All Individuals," Journal of Finance, American Finance Association, vol. 31(4), pages 1169-83, September.
  11. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  12. Harlow, W. V. & Rao, Ramesh K. S., 1989. "Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory and Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(03), pages 285-311, September.
  13. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-93, September.
  14. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  15. De Giorgi, Enrico & Post, Thierry, 2008. "Second-Order Stochastic Dominance, Reward-Risk Portfolio Selection, and the CAPM," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 43(02), pages 525-546, June.
  16. Kaur, Amarjot & Prakasa Rao, B.L.S. & Singh, Harshinder, 1994. "Testing for Second-Order Stochastic Dominance of Two Distributions," Econometric Theory, Cambridge University Press, vol. 10(05), pages 849-866, December.
  17. Hogan, William W. & Warren, James M., 1974. "Toward the Development of an Equilibrium Capital-Market Model Based on Semivariance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(01), pages 1-11, January.
  18. Arzac, Enrique R. & Bawa, Vijay S., 1977. "Portfolio choice and equilibrium in capital markets with safety-first investors," Journal of Financial Economics, Elsevier, vol. 4(3), pages 277-288, May.
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