Multiple objectives in portfolio construction

In this article we attempt to expand the limited framework of single-objective optimisation and broaden Markowitz's market standard, within which the problem of portfolio selection is conventionally addressed. The decision maker's Investment Policy Statement (IPS) is formulated through a multiobjective mixed-integer linear programming model. The model is then solved through the augmented e-constrained (AUGMECON) method, a novel a posteriori Multiobjective Mathematical Programming (MMP) technique. Our purpose for transforming the traditional two-dimension portfolio selection problem into a mixed-integer multiobjective optimisation problem in space is twofold: 1) to incorporate three objective functions in the decision process beyond the mean-variance approach, i.e., an additional measure of return, the portfolio's relative dividend yield, 2) to model even the most complex preferences that the investor may express, regarding specific cardinal constraints. The proposed model is tested through an illustrative application in the Athens Stock Exchange (ASE).

[1]  Jared L. Cohon,et al.  Multiobjective programming and planning , 2004 .

[2]  Lawrence Fisher,et al.  Some Studies of Variability of Returns on Investments in Common Stocks , 1970 .

[3]  John L. Evans,et al.  DIVERSIFICATION AND THE REDUCTION OF DISPERSION: AN EMPIRICAL ANALYSIS , 1968 .

[4]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[5]  Constantin Zopounidis,et al.  Profilio Selection Using the Adelais Multiobjective Linear Programming System , 1998 .

[6]  Matthias Ehrgott,et al.  Constructing robust crew schedules with bicriteria optimization , 2002 .

[7]  E. Elton.  Modern portfolio theory and investment analysis , 1981 .

[8]  Marco Laumanns,et al.  An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method , 2006, Eur. J. Oper. Res..

[9]  Ching-Lai Hwang,et al.  Multiple Objective Decision Making , 1994 .

[10]  P. Pardalos,et al.  On the use of optimization models for portfolio selection: A review and some computational results , 1994 .

[11]  Ralph E. Steuer,et al.  Multiple criteria decision making combined with finance: A categorized bibliographic study , 2003, Eur. J. Oper. Res..

[12]  Constantin Zopounidis,et al.  Multicriteria decision aid in financial management , 1999, Eur. J. Oper. Res..

[13]  Edward H. Jennings,et al.  An Empirical Analysis of Some Aspects of Common Stock Diversification , 1971, Journal of Financial and Quantitative Analysis.

[14]  C. Hwang.  Multiple Objective Decision Making - Methods and Applications: A State-of-the-Art Survey , 1979 .

[15]  J. Martel,et al.  A multi‐criterion approach for selecting attractive portfolio , 2002 .

[16]  Michael J. Brennan,et al.  The Optimal Number of Securities in a Risky Asset Portfolio When There Are Fixed Costs of Transacting: Theory and Some Empirical Results , 1975 .

[17]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[18]  Constantin Zopounidis,et al.  On The Use Of Multicriteria Decision Aid Methods To Portfolio Selection , 1997 .

[19]  John Psarras,et al.  Equity portfolio management within the MCDM frame: a literature review , 2009 .

[20]  Jaap Spronk,et al.  Financial modelling: Where to go? With an illustration for portfolio management , 1997 .

[21]  H. Markowitz.  Portfolio Selection: Efficient Diversification of Investments , 1971 .

[22]  H. Konno,et al.  Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market , 1991 .

[23]  Horst W. Hamacher,et al.  Finding representative systems for discrete bicriterion optimization problems , 2007, Oper. Res. Lett..

[24]  Thomas L. Saaty,et al.  Portfolio selection through hierarchies* , 1980 .

[25]  Sang M. Lee,et al.  Goal programming for portfolio selection , 1980 .

[26]  M. Statman,et al.  How Many Stocks Make a Diversified Portfolio? , 1987, Journal of Financial and Quantitative Analysis.