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, nonconvex 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.
Volume (Year): 53 (2007)
Issue (Month): 1 (January)
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- Kimball, Miles S, 1990.
"Precautionary Saving in the Small and in the Large,"
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.
- Jondeau, E. & Rockinger, M., 2004.
"Optimal Portfolio Allocation Under Higher Moments,"
108, Banque de France.
- Lien, Gudbrand, 2002. "Non-parametric estimation of decision makers' risk aversion," Agricultural Economics, Blackwell, vol. 27(1), pages 75-83, May.
- 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.
- 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), pages -, May.
- 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.
- Sun, Qian & Yan, Yuxing, 2003. "Skewness persistence with optimal portfolio selection," Journal of Banking & Finance, Elsevier, vol. 27(6), pages 1111-1121, June.
- 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.
- William F. Sharpe, 1965. "Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 39, pages 1-119.
- Markowitz, Harry M, 1991.
" Foundations of Portfolio Theory,"
Journal of Finance,
American Finance Association, vol. 46(2), pages 469-477, June.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- 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.
- 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.
- 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.
- 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.
- Sharpe, William F., 1967. "Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(02), pages 76-84, June.
- 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.
- Patrick L. Brockett & Yehuda Kahane, 1992. "Risk, Return, Skewness and Preference," Management Science, INFORMS, vol. 38(6), pages 851-866, June.
- 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.
- 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.
- William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
- 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.
- Simar, L. & Wilson, P.W., 1998.
"A General Methodology for Bootstrapping in Nonparametric Frontier Models,"
9811, Catholique de Louvain - Institut de statistique.
- 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.
- 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.
- Kane, Alex, 1982. "Skewness Preference and Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(01), pages 15-25, March.
- 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.
- 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.
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