Abstract
In the presence of skewness, the portfolio selection entails considering competing and conflicting objectives, such as maximizing both its expected returns and skewness, and minimizing its risk for decreasing absolute risk-aversion investors. Since it is unlikely that a portfolio can solve the multiple-objectives problem simultaneously, a portfolio selection must depend on the investor's preference among objectives. This article shows that investor preference can be incorporated into a polynomial goal programming problem from which a portfolio selection with skewness is determined. An inefficient mean-variance portfolio may be optimal in the mean-variance-skewness content. The features of applying polynomial goal programming in portfolio selection are 1) the existence of an optimal solution, 2) the flexibility of the incorporation of investor preference, and 3) the relative simplicity of computational requirements.
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References
Alexander, G. and Resnick, B., “More on Estimation Risk and Simple Rules for Optimal Portfolio Selection,”Journal of Finance 40, 125–133 (1985).
Arditti, F., “Risk and the Required Return on Equity,”Journal of Finance 22, 19–36 (1967).
Arditti, F., “Another Look at Mutual Fund Performance,”Journal of Financial and Quantitative Analysis 6, 909–912 (1971).
Arditti, F. and Levy, H., “Portfolio Efficiency Analysis in Three Moments: The Multiperiod Case,”Journal of Finance 30, 797–809 (1975).
Blume, M., “Portfolio Theory: A Step Toward Its Practical Application,”Journal of Business 43, 152–173 (1975).
Chen, S. and Brown, S., “Estimation Risk and Simple Rules for Optimal Portfolio Selection,”Journal of Finance 38, 1087–1093 (1983).
Elton, E. and Gruber, M.,Modern Portfolio Theory and Investment Analysis, New York, John Wiley & Sons, Inc., 1987.
Elton, E., Gruber, M., and Padberg, M.W., “Simple Criteria for Optimal Portfolio Selection,”Journal of Finance 31, 1341–1357 (1976).
Fiacco, A.V. and McCormick, G.P., “Extension of SUMT for Nonlinear Programming: Equality Constraints and Extrapolation,”Management Science 12, 816–829 (1966).
Fielitz, B., “Further Results on Asymmetric Stable Distributions of Stock Price Changes,”Journal of Financial and Quantitative Analysis 11, 39–55 (1976).
Friend, I. and Blume, M., “Measurement of Portfolio Performance Under Uncertainty,”American Economic Review 60, 561–575 (1970).
Friedman, M. and Savage, L., “The Utility Analysis of Choices Involving Risk,”Journal of Political Economy 6, 279–304 (1948).
Frost, P. and Savarino, J., “An Empirical Bayes Approach to Efficient Portfolio Selection,”Journal of Financial and Quantitative Analysis 21, 293–305 (1986).
Gibbons, M., Ross, S., and Shanken, J., “A Test of the Efficiency of a Given Portfolio,”Econometrica 57, 1121–1152 (1989).
Hanoch, G. and Levy, H., “The Efficiency Analysis of Choices Involving Risk,”Review of Economic Studies 36, 335–345 (1969).
Hanoch, G. and Levy, H., “Efficiency Portfolio Selection with Quadratic and Cubic Utility,”Journal of Business 43, 181–189 (1970).
Hooke, R. and Jeeves, T.A., “Direct Search Solution of Numerical and Statistical Problems,”Journal of the Association of Computing Machinery 8, 212 (1961).
Hwang, C.L., Lai, K.C., Tillman, F., and Kumar, S., “Optimization of System Reliability by Sequential Unconstrained Minimization Technique,”IEEE Transactions On Reliability R-24, 133–135 (1975).
Ingersoll, J., “Multidimensional Security Pricing,”Journal of Financial and Quantitative Analysis 10, 785–798 (1975).
Jacob, N. and Pettit, R.,Investments, second edition, Homewood, IL, Irwin, 1988.
Kane, A., “Skewness Preference and Portfolio Choice,”Journal of Financial and Quantitative Analysis 17, 15–25 (1982).
Kraus, A. and Litzenberger, R., “Skewness Preference and the Valuation of Risk Assets,”Journal of Finance 31, 1085–1094 (1976).
Kroll, Y., Levy, H., and Markowitz, H., “Mean-Variance Versus Direct Utility Maximization,”Journal of Finance 39, 47–61 (1984).
Levy, H., “A Utility Function Depending on the First Three Moments,”Journal of Finance 24, 715–719 (1969).
Markowitz, H., “Portfolio Selection,”Journal of Finance 8, 77–91 (1952).
Roll, R., “A Critique of the Asset Pricing Theory's Tests; Part I: On the Past and Potential Testability of the Theory,”Journal of Financial Economics 4, 129–176 (1977).
Rubinstein, M., “The Fundamental Theorem of Parameter Preference and Security Valuation,”Journal of Financial and Quantitative Analysis 8, 61–69 (1973).
Samuelson, P., “The Fundamental Approximation of Theorem of Portfolio Analysis in Terms of Means, Variances and Higher Moments,”Review of Economic Studies 37, 537–542 (1970).
Simkowitz, M. and Beedles, W., “Diversification in a Three Moment World,”Journal of Financial and Quantitative Analysis 13, 927–941 (1978).
Singleton, J. and Wingender, J., “Skewness Persistence in Common Stock Returns,”Journal of Financial and Quantitative Analysis 13, 335–341 (1986).
Tayi, G. and Leonard, P., “Bank Balance-Sheet Management: An Alternative Multi-Objective Model,”Journal of the Operational Research Society 39, 401–410 (1988).
Tillman, F., Hwang, C.L., and Kuo, W.,Optimization of Systems Reliability, New York, John Wiley & Sons, Inc., 1980, pp. 133–157.
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Lai, TY. Portfolio selection with skewness: A multiple-objective approach. Rev Quant Finan Acc 1, 293–305 (1991). https://doi.org/10.1007/BF02408382
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DOI: https://doi.org/10.1007/BF02408382