Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach
This paper proposes a nonparametric efficiency measurement approach for the static portfolio selection problem in mean-variance-skewness space. A shortage function is defined that looks for possible increases in return and skewness and decreases in variance. Global optimality is guaranteed for the resulting optimal portfolios. We also establish a link to a proper indirect mean-variance-skewness utility function. For computational reasons, the optimal portfolios resulting from this dual approach are only locally optimal. This framework permits to differentiate between portfolio efficiency and allocative efficiency, and a convexity efficiency component related to the difference between the primal, non-convex approach and the dual, convex approach. Furthermore, in principle, information can be retrieved about the revealed risk aversion and prudence of investors. An empirical section on a small sample of assets serves as an illustration.
|Date of creation:||Sep 2005|
|Publication status:||Published in Management Science, January 2007, 53(1), pp. 135-149|
|Contact details of provider:|| Postal: 3, rue de la Digue, FR-59000 Lille|
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- Leopold Simar & Paul Wilson, 2000.
"A general methodology for bootstrapping in non-parametric frontier models,"
Journal of Applied Statistics,
Taylor & Francis Journals, vol. 27(6), pages 779-802.
- Simar, L. & Wilson, P.W., 1998. "A General Methodology for Bootstrapping in Nonparametric Frontier Models," Papers 9811, Catholique de Louvain - Institut de statistique.
- Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
- Miles S. Kimball, 1989. "Precautionary Saving in the Small and in the Large," NBER Working Papers 2848, National Bureau of Economic Research, Inc.
- Michael C. Jensen, 1968. "The Performance Of Mutual Funds In The Period 1945–1964," Journal of Finance, American Finance Association, vol. 23(2), pages 389-416, 05.
- Patrick L. Brockett & Yehuda Kahane, 1992. "Risk, Return, Skewness and Preference," Management Science, INFORMS, vol. 38(6), pages 851-866, June.
- William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
- Sharpe, William F., 1967. "Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(02), pages 76-84, June.
- William F. Sharpe, 1965. "Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 39, pages 119-119.
- Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55.
- Jondeau, E. & Rockinger, M., 2004. "Optimal Portfolio Allocation Under Higher Moments," Working papers 108, Banque de France.
- Scott, Robert C & Horvath, Philip A, 1980. " On the Direction of Preference for Moments of Higher Order Than the Variance," Journal of Finance, American Finance Association, vol. 35(4), pages 915-919, September.
- Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," Review of Economic Studies, Oxford University Press, vol. 37(4), pages 537-542.
- Lien, Gudbrand D., 2002. "Non-parametric estimation of decision makers' risk aversion," Agricultural Economics of Agricultural Economists, International Association of Agricultural Economists, vol. 27(1), May.
- Sun, Qian & Yan, Yuxing, 2003. "Skewness persistence with optimal portfolio selection," Journal of Banking & Finance, Elsevier, vol. 27(6), pages 1111-1121, June.
- Chunhachinda, Pornchai & Dandapani, Krishnan & Hamid, Shahid & Prakash, Arun J., 1997. "Portfolio selection and skewness: Evidence from international stock markets," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 143-167, February.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, 09.
- Angus Deaton, 1979. "The Distance Function in Consumer Behaviour with Applications to Index Numbers and Optimal Taxation," Review of Economic Studies, Oxford University Press, vol. 46(3), pages 391-405.
- Lien, Gudbrand, 2002. "Non-parametric estimation of decision makers' risk aversion," Agricultural Economics, Blackwell, vol. 27(1), pages 75-83, May.
- Pogue, G A, 1970. "An Extension of the Markowitz Portfolio Selection Model to Include Variable Transactions' Costs, Short Sales, Leverage Policies and Taxes," Journal of Finance, American Finance Association, vol. 25(5), pages 1005-1027, December.
- Samuelson, Paul A., 1967. "General Proof that Diversification Pays," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(01), pages 1-13, March.
- Kane, Alex, 1982. "Skewness Preference and Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(01), pages 15-25, March.
- Simkowitz, Michael A. & Beedles, William L., 1978. "Diversification in a Three-Moment World," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(05), pages 927-941, December.
- N. J. Jobst & M. D. Horniman & C. A. Lucas & G. Mitra, 2001. "Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 489-501.
- Walter Briec & Kristiaan Kerstens & Jean Baptiste Lesourd, 2001. "Single Period Markowitz Portfolio Selection, Performance Gading and Duality: A Variation on Luenberger'a Shortage Function," Working Papers 0203, Departament Empresa, Universitat Autònoma de Barcelona, revised Apr 2002.
- Markowitz, Harry M, 1991. " Foundations of Portfolio Theory," Journal of Finance, American Finance Association, vol. 46(2), pages 469-477, June.
- Markowitz, Harry M., 1990. "Foundations of Portfolio Theory," Nobel Prize in Economics documents 1990-1, Nobel Prize Committee.
- Arditti, Fred D & Levy, Haim, 1975. "Portfolio Efficiency Analysis in Three Moments: The Multiperiod Case," Journal of Finance, American Finance Association, vol. 30(3), pages 797-809, June.
- Joro, Tarja & Na, Paul, 2006. "Portfolio performance evaluation in a mean-variance-skewness framework," European Journal of Operational Research, Elsevier, vol. 175(1), pages 446-461, November.
- Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
- Morey, Matthew R. & Morey, Richard C., 1999. "Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking," Omega, Elsevier, vol. 27(2), pages 241-258, April. Full references (including those not matched with items on IDEAS)
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