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Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection

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Abstract

In standard portfolio theory, an investor is typically taken as having one stochastic objective, to maximize the random variable of portfolio return. But in this paper, we focus on investors whose purpose is to build, more broadly, a “suitable portfolio” taking additional concerns into account. Such investors would have additional stochastic and deterministic objectives that might include liquidity, dividends, number of securities in a portfolio, social responsibility, and so forth. To accommodate such investors, we develop a multiple criteria portfolio selection formulation, corroborate its appropriateness by examining the sensitivity of the nondominated frontier to various factors, and observe the conversion of the nondominated frontier to a nondominated surface. Furthermore, multiple criteria enable us to provide an explanation as to why the “market portfolio,” so often found deep below the nondominated frontier, is roughly where one would expect it to be with multiple criteria. After commenting on solvability issues, the paper concludes with the idea that what is the “modern portfolio theory” of today might well be interpreted as a projection onto two-space of a real multiple criteria portfolio selection problem from higher dimensional space.

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References

  • Arenas Parra, M., A. Bilbao Terol, and M.V. Rodríguez Uría. (2001). “A Fuzzy Goal Programming Approach to Portfolio Selection.” European Journal of Operational Research, 133(2), 287–297.

    Article  Google Scholar 

  • Ballestero, E. (1998). “Approximating the Optimum Portfolio for an Investor with Particular Preferences.” Journal of the Operational Research Society, 49(9), 998–1000.

    Article  Google Scholar 

  • Ballestero, E. and D. Plà-Santamaría. (2003). “Portfolio Selection on the Madrid Exchange: A Compromise Programming Model.” International Transactions in Operational Research, 10(1), 33–51.

    Article  Google Scholar 

  • Ballestero, E. and C. Romero. (1996). “Portfolio Selection: A Compromise Programming Solution.” Journal of the Operational Research Society, 47(11), 1377–1386.

    Article  Google Scholar 

  • Bana e Costa, C.A. and J.O. Soares. (2001). “Multicriteria Approaches for Portfolio Selection: An Overview.” Review of Financial Markets, 4(1), 19–26.

    Google Scholar 

  • Bana e Costa, C.A. and J.O. Soares. (2004). “A Multicriteria Model for Portfolio Management.” European Journal of Finance, 10(3), 198–211.

    Article  Google Scholar 

  • Belton, V. and T.J. Stewart. (2002). Multiple Criteria Decision Analysis: An Integrated Approach. Boston: Kluwer.

    Google Scholar 

  • Bodie, Z., A. Kane and A.J. Marcus. (2004). Essentials of Investments, 5th edn. Boston: McGraw-Hill Irwin.

    Google Scholar 

  • Bouri, G., J.M. Martel and H. Chabchoub. (2002). “A Multi-criterion Approach for Selecting Attractive Portfolio.” Journal of Multi-Criteria Decision Analysis, 11(3), 269–277.

    Article  Google Scholar 

  • Caballero, R., E. Cerdá, M.M. Muñoz, L. Rey, and I.M. Stancu-Minasian. (2001). “Efficient Solution Concepts and Their Relations in Stochastic Multiobjective Programming.” Journal of Optimization Theory and Applications, 110(1), 53–74.

    Article  Google Scholar 

  • Chang, T.-J., N. Meade, J.E. Beasley, and Y.M. Sharaiha. (2000). “Heuristics for Cardinally Constrained Portfolio Optimisation.” Computers & Operations Research, 27(13), 1271–1302.

    Article  Google Scholar 

  • Chunhachinda, P., K. Dandapani, S. Hamid, and A.J. Prakash. (1997). “Portfolio Selection and Skewness Evidence from International Stock Markets.” Journal of Banking & Finance, 21, 143–167.

    Article  Google Scholar 

  • Colson, G. and Ch. DeBruyn. (1989). “An Integrated Multiobjective Portfolio Management System.” Mathematical and Computer Modelling, 12(10–11), 1359–1381.

    Article  Google Scholar 

  • Deb, K. (2001). Multi-Objective Optimization using Evolutionary Algorithms. New York: John Wiley.

    Google Scholar 

  • Dominiak, C. (1997). “An Application of Interactive Multiple Objective Goal Programming on the Warsaw Stock Exchange.” In R. Caballero, F. Ruiz, and R.E. Steuer (eds.), Lecture Notes in Economics and Mathematical Systems, Vol. 455, Berlin: Springer-Verlag, pp. 66–74.

  • Doumpos, M., M. Spanos, and C. Zopounidis. (1999). “On the Use of Goal Programming Techniques in the Assessment of Financial Risks.” Journal of Euro-Asian Management, 5(1), 83–100.

    Google Scholar 

  • Ehrgott, M., K. Klamroth, and C. Schwehm. (2004). “An MCDM Approach to Portfolio Optimization.” European Journal of Operational Research, 155(3), 752–770.

    Article  Google Scholar 

  • Elton, E.J., M.J. Gruber, S.J. Brown, and W. Goetzmann. (2002). Modern Portfolio Theory and Investment Analysis, 6th edn. New York: John Wiley.

    Google Scholar 

  • Feinstein, C.D. and M.N. Thapa. (1993). “Notes: A Reformulation of a Mean-Absolute Deviation Portfolio Optimization Model.” Management Science, 39(12), 1552–1553.

    Google Scholar 

  • Gandibleux, X., R. Caballero, and J. Molina. (2006). MOAMP: A Multiobjective Programming Metaheuristic Using an Adaptive Memory Procedure. University of Malaga, Spain: Malaga.

    Google Scholar 

  • Gilli, M. and E. Këllezi. (2000). A Heuristic Approach to Portfolio Optimization. Department of Econometrics, University of Geneva, Switzerland.

    Google Scholar 

  • Guerard, J.B. and A. Mark. (2003). “The Optimization of Efficient Portfolios: The Case for an R&D Quadratic Term.” Research in Finance, 20, 217–247.

    Google Scholar 

  • Hallerbach, W.G. and J. Spronk. (2002a). “A Multidimensional Framework for Financial-economic Decisions.” Journal of Multi-Criteria Decision Analysis, 11(3), 111–124.

    Article  Google Scholar 

  • Hallerbach, W.G. and J. Spronk. (2002b). “The Relevance of MCDM for Financial Decisions.” Journal of Multi-Criteria Decision Analysis, 11(4–5), 187–195.

    Article  Google Scholar 

  • Hirschberger, M., Y. Qi, and R.E. Steuer. (2007). Tri-criterion Quadratic-linear Programming. Department of Banking and Finance, University of Georgia, Athens, in preparation.

  • Hurson, Ch. and N. Ricci. (1998). “Multicriteria Decision Making and Portfolio Management with Arbitrage Pricing Theory.” In C. Zopounidis (ed.), Operational Tools in the Management of Financial Risks. Dordrecht: Kluwer Academic Publishers, pp. 31–55.

  • Hurson, Ch. and C. Zopounidis. (1995). “On the Use of Multi-criteria Decision Aid Methods to Portfolio Selection.” Journal of Euro-Asian Management, 1(2), 69–94.

    Google Scholar 

  • Jog, V., I. Kaliszewski, and W. Michalowski. (1999). “Using Attribute Trade-off Information in Investment.” Journal of Multi-Criteria Decision Analysis, 8(4), 189–199.

    Article  Google Scholar 

  • Konno, H., H. Shirakawa, and H. Yamazaki. (1993). “A Mean-Absolute Deviation-Skewness Portfolio Optimization Model.” Annals of Operations Research, 45, 205–220.

    Article  Google Scholar 

  • Konno, H. and K.-I. Suzuki. (1995). “A Mean-Variance-Skewness Portfolio Optimization Model.” Journal of the Operations Research Society of Japan, 38(2), 173–187.

    Google Scholar 

  • Konno, H. and H. Yamazaki. (1991) “Mean-Absolute Deviation Portfolio Optimization Model and Its Application to Tokyo Stock Market.” Management Science, 37(5), 519–531.

    Article  Google Scholar 

  • Korhonen, P. and J. Karaivanova. (1999). “An Algoithm for Projecting a Reference Direction onto the Nondominated Set of Given Points.” IEEE Transactions on Systems, Man, and Cybernetics, 29(5), 429–435.

    Article  Google Scholar 

  • Korhonen, P. and J. Wallenius. (1988). “A Pareto Race.” Naval Research Logistics, 35(6), 615–623.

    Google Scholar 

  • Lo, A.W., C. Petrov, and M. Wierzbicki. (2003). “It’s 11pm – Do You Know Where Your Liquidity Is? The Mean-Variance-Liquidity Frontier.” Journal of Investment Management, 1(1), 55–93.

    Google Scholar 

  • Lotov, A.B., V.A. Bushenkov, and G.K. Kamenev. (2004). Interactive Decision Maps: Approximation and Visualization of Pareto Frontier. Boston: Kluwer Academic Publishers.

    Google Scholar 

  • Mansini, R., W. Ogryczak, and M.G. Speranza. (2003). “On LP Solvable Models for Portfolio Selection.” Informatica, 14(1), 37–62.

    Google Scholar 

  • Markowitz, H.M. (1952). “Portfolio Selection.” Journal of Finance, 7(1), 77–91.

    Article  Google Scholar 

  • Markowitz, H.M. (1956). “The Optimization of a Quadratic Function Subject to Linear Constraints.” Naval Research Logistics Quarterly, 3, 111–133.

    Google Scholar 

  • Markowitz, H.M. (1959). Portfolio Selection: Efficient Diversification in Investments. New York: John Wiley.

    Google Scholar 

  • Markowitz, H.M. (1999). “The Early History of Portfolio Selection: 1600–1960.” Financial Analysts Journal, 5–16.

  • Markowitz, H.M. and G.P. Todd. (2000). Mean-Variance Analysis in Portfolio Choice and Capital Markets. New Hope, Pennsylvania, Frank J. Fabozzi Associates.

  • Mathworks. (2004). “Optimization Toolbox for Use with Matlab” Version 7.0.1 (R14). Natick, Massachusetts.

  • Michalowski, W. and W. Ogryczak. (2001). “Extending the MAD Portfolio Optimization Model to Incorporate Downside Risk Aversion.” Naval Research Logistics, 48(3), 185–200.

    Article  Google Scholar 

  • Miettinen, K.M. (1999). Nonlinear Multiobjective Optimization. Boston: Kluwer.

    Google Scholar 

  • Ogryczak, W. (2000). Multiple Criteria Linear Programming Model for Portfolio Selection.” Annals of Operations Research, 97, 143–162.

    Article  Google Scholar 

  • Prakash, A.J., C.H. Chang, and T.E. Pactwa. (2003). “Selecting a Portfolio with Skewness: Recent Evidence from US, European, and Latin American Equity Markets.” Journal of Banking & Finance, 27, 1375–1390.

    Article  Google Scholar 

  • Roll, R. (1977). “A Critique of the Asset Pricing Theory’s Tests.” Journal of Financial Economics, 4, 129–176.

    Article  Google Scholar 

  • Spronk, J. and W.G. Hallerbach. (1997). “Financial Modelling: Where to Go? With an Illustration for Portfolio Management.” European Journal of Operational Research, 99(1), 113–127.

    Article  Google Scholar 

  • Steuer, R.E. and E.U. Choo. (1983). “An Interactive Weighted Tchebycheff Procedure for Multiple Objective Programming.” Mathematical Programming, 26(1), 326–344.

    Google Scholar 

  • Steuer, R.E. and P. Na. (2003). “Multiple Criteria Decision Making Combined with Finance: A Categorized Bibliography.” European Journal of Operational Research, 150(3), 496–515.

    Article  Google Scholar 

  • Stone, B.K. (1973). “A Linear Programming Formulation of the General Portfolio Selection Problem.” Journal of Financial and Quantitative Analysis, 8(4), 621–636.

    Article  Google Scholar 

  • Streichert, F., H. Ulmer, and A. Zell. (2003). “Evolutionary Algorithms and the Cardinality Constrained Portfolio Optimization Problem.” In Selected Papers of the International Conference on Operations Research (OR 2003). Berlin: Springer-Verlag, pp. 253–260.

  • Tamiz, M., R. Hasham, D.F. Jones, B. Hesni, and E.K. Fargher. (1996). “A Two Staged Goal Programming Model for Portfolio Selection.” In M. Tamiz (ed.), Lecture Notes in Economics and Mathematical Systems, Vol. 432. Berlin: Springer-Verlag, pp. 386–399.

  • Yu, G.Y. (1997). “A Multiple Criteria Approach to Choosing an Efficient Stock Portfolio at the Helsinki Stock Exchange.” Journal of Euro-Asian Management, 3(2), 53–85.

    Google Scholar 

  • Zeleny, M. (1977). “Multidimensional Measure of Risk: The Prospect Ranking Vector.” In S. Zionts (ed.), Lecture Notes in Economics and Mathematical Systems, Vol. 155. Heidelberg: Springer Verlag, pp. 529–548.

  • Zopounidis, C. and M. Doumpos. (2000). “INVESTOR: A Decision Support System Based on Multiple Criteria for Portfolio Selection and Composition.” In A. Colorni, M. Paruccini, and B. Roy (eds.), A-MCD-A Aide Multi Critere a la Decision—Multiple Criteria Decision Aiding. Brussels: European Commission Joint Research Centre, pp. 371–381.

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Authors and Affiliations

  1. Terry College of Business, University of Georgia, Athens, Georgia, 30602-6253, USA

    Ralph E. Steuer (Sr. Chair of Business)

  2. Hedge Fund Research Institute, International University of Monaco, Principality of Monaco, France

    Yue Qi

  3. Department of Mathematics, University of Eichstätt-Ingolstadt, Eichstätt, Germany

    Markus Hirschberger

Authors
  1. Ralph E. Steuer
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  2. Yue Qi
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  3. Markus Hirschberger
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Correspondence to Ralph E. Steuer.

Additional information

M. Hirschberger: Research conducted while a Visiting Scholar at the Department of Banking and Finance, Terry College of Business, University of Georgia, October 2003–March 2004.

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Steuer, R.E., Qi, Y. & Hirschberger, M. Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection. Ann Oper Res 152, 297–317 (2007). https://doi.org/10.1007/s10479-006-0137-1

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  • DOI: https://doi.org/10.1007/s10479-006-0137-1

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