A Review of Goal Programming for Portfolio Selection

Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 638)


Goal Programming (GP) is the most widely used approach in the field of multiple criteria decision making that enables the decision maker to incorporate numerous variations of constraints and goals, particularly in the field of Portfolio Selection (PS). This paper gives a brief review of the application of GP and its variants to Portfolio Selection and analysis problems. The paper firstly discusses the Multi-Criteria Decision Analysis in PS context in which GP is introduced as an important approach to PS Problems. An overview of performance measurement in portfolio selection context is also provided. Amongst the concluding remarks many issues in PS that may be addressed by GP such as multi-period, different measures of risk, and extended factors influencing portfolio selection are listed.


  1. Artikis P (2002) Evaluation of equity mutual funds operating in the Greek financial market. J Manag Finance 28:27–42Google Scholar
  2. Artzner P, Delbaen F, Eber J-M, Heath D (1999) Coherent measures of risk. J Math Finance 9:203–228CrossRefGoogle Scholar
  3. Abdelaziz F, Aouni B, El Fayedh R (2007) Multi-objective stochastic programming for portfolio selection. Eur J Oper Res 177: 1811–1823CrossRefGoogle Scholar
  4. Alexander G, Resnick B (1985) Using linear and goal programming to immunize bond portfolios. J Banking Finance, Elsevier 9:35–54CrossRefGoogle Scholar
  5. Allen J, Bhattacharya S, Smarandache F (2003) Fuzziness and funds allocation in portfolio optimisation. Int J Soc Econ: 30(5):619–632CrossRefGoogle Scholar
  6. Balbas A, Balbas R, Mayoral S (2009) Portfolio choice and optimal hedging with general risk functions: a simplex-like algorithm. Eur J Oper Res 192:603–620CrossRefGoogle Scholar
  7. Bilbao A, Arenas M, Jimenez M, Gladish B, Rodriguez M (2006) An extension of sharpe’s single-index model: portfolio selection with expert betas. J Oper Res Soc 57:1442–1451CrossRefGoogle Scholar
  8. Bilbao A, Arenas M, Rodriguez M, Antomil J (2007) On constructing expert betas for single-index model. Eur J Oper Res 183:827–847CrossRefGoogle Scholar
  9. Booth G, Dash G (1977) Bank portfolio management using non-linear goal programming. Finan Rev 14:59–69CrossRefGoogle Scholar
  10. Byrne P, Lee S (1994) Real estate portfolio analysis using a spreadsheet optimizer. J Property Finance 5(4):19–31CrossRefGoogle Scholar
  11. Callin S (2008) Portable alpha theory and practice: what investors really need to know. Wiley, Hoboken, NJGoogle Scholar
  12. Chang C-T (2007) Efficient structures of achievement functions for goal programming models. Asia Pac J Oper Res 24(6):755–764CrossRefGoogle Scholar
  13. Charnes A, Cooper W, Ferguson R (1955) Optimal estimation of executive compensation by linear programming. J Manag Sci 1(1):138–151CrossRefGoogle Scholar
  14. Chow G (1995) Portfolio selection based on return, risk, and relative performance. Financ Anal J March–April:54–60Google Scholar
  15. Christiansen J, Varnes C (2008) From models to practice: decision making at portfolio meetings. Int J Qual Reliab Manag, 25(1):87–101CrossRefGoogle Scholar
  16. Corrado C, Jordan B (2005) Fundamentals of investments: valuations & management, 3rd edn. McGraw-Hill/Irwin, New YorkGoogle Scholar
  17. Cremers J-H, Kritzman M, Page S (2005) Optimal hedge fund allocations. J Portfolio Manage Spring:70–81Google Scholar
  18. Cresson J, Cudd R, Lipscomb T (2002) The early attraction of S&P 500 index funds: is perfect tracking performance an illusion? J Manag Finance 28:1–8Google Scholar
  19. Daniel K, Grinblatt M, Titman S, Wermers R (1997) Measuring mutual fund performance with characteristic-based benchmarks. J Finance 52:1035–1058CrossRefGoogle Scholar
  20. Dash G, Kajiji N (2005) A nonlinear goal programming model for efficient asset-liability management of property-liability insurers. J Infor 43(2):135–156Google Scholar
  21. Davies R, Kat H, Lu S (2005) Fund of hedge funds portfolio selection: a multiple objective approach. SSRN 1–31Google Scholar
  22. Deng X-T, Li Z-F, Wang S-Y (2005) A minimax portfolio selection strategy with equilibrium. Eur J Oper Res 166:278–292CrossRefGoogle Scholar
  23. Deng X-T, Wang S-Y, Xia Y-S (2000) Criteria, models and strategies in portfolio selection. J Adv Model Optim (AMO) 2(2):79–103Google Scholar
  24. Elton E, Gruber M (1974) On the optimality of some multiperiod portfolio selection criteria. J Bus 2:231–243CrossRefGoogle Scholar
  25. Fama E (1996) Multifactor portfolio efficiency and multifactor asset pricing. J Financ Quant Anal 31:441–465CrossRefGoogle Scholar
  26. Frankfurter G, Phillip H (1980) Portfolio selection: an analytic approach for selecting securities from a large universe. J Financ Quant Anal 15:357–377CrossRefGoogle Scholar
  27. Gladish B, Jones D, Tamiz M, Terol B (2007) An interactive three-stage model for mutual funds portfolio selection. Int J Manag Sci OMEGA 35:75–88CrossRefGoogle Scholar
  28. Hu W, Kercheval A (2007) Portfolio Optimization for Skewed-t Returns. Working paperGoogle Scholar
  29. Inuiguchi M, Ramik J (2000) Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. J Fuzzy Set Syst 111:3–28CrossRefGoogle Scholar
  30. Jensen M (1968) The performance of mutual funds in the period 1945–1964. J Finance 23:389–416CrossRefGoogle Scholar
  31. Jobst N, Horniman M, Lucas C, Mitra G (2001) Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints. J Quant Finance 1:1–13Google Scholar
  32. Kim J, Kim Y, Shin K (2005) An algorithm for portfolio optimization problem. Informatica 16(1):93–106Google Scholar
  33. Konno H (2003) Portfolio optimization of small scale fund using mean-absolute deviation model. Int J Theor Appl Finance 6:403–418CrossRefGoogle Scholar
  34. Konno H, Kobayashi K (1997) An integrated stock-bond portfolio optimization model. J Econ Dynam Contr 21:1427–1444CrossRefGoogle Scholar
  35. Konno H, Koshizuka T (2005) Mean-absolute deviation model. IIE Trans 37:893–900CrossRefGoogle Scholar
  36. Konno H, Yamazaki H (1991) Mean-absolute deviation portfolio optimization and its applications to Tokyo stock market. J Manag Sci 37:519–531CrossRefGoogle Scholar
  37. Kooros S, McManis B (1998) Multiattribute optimization model for strategic investment decisions. Can J Admin Sci 15(2):152–164CrossRefGoogle Scholar
  38. Kosmidou K, Zopounidis C (2004) Combining goal programming model with simulation analysis for bank asset liability management. J INFOR 42(3):175–187Google Scholar
  39. Kritzman M (2003) The portable financial analyst: what practitioners need to know, 2nd edn. Wiley, New YorkGoogle Scholar
  40. Kumar P, Philippatos G (1979) Conflict resolution in investment decisions: implementation of goal programming methodology for dual-purpose funds. Decis Sci 10:562–576CrossRefGoogle Scholar
  41. Kumar P, Philippatos G, Ezzell J (1978) Goal programming and selection of portfolio by dual-purpose funds. J Finance 33:303–310CrossRefGoogle Scholar
  42. Lee S, Byrne P (1998) Diversification by sector, region or function? a mean absolute deviation optimization. J Property Valuation Invest 16(1):38–56CrossRefGoogle Scholar
  43. Lee S, Chesser D (1980) Goal programming for portfolio selection. J Portfolio Manage 6:22–26CrossRefGoogle Scholar
  44. Lee S, Lerro A (1973) Optimizing the portfolio selection for mutual funds. J Finance 28:1086–1101Google Scholar
  45. Lehmann B, Modest D (1987) Mutual fund performance evaluation: a comparison of benchmarks and benchmarks comparison. J Finance 42:233–265CrossRefGoogle Scholar
  46. Leon T, Liern V, Vercher E (2002) Viability of infeasible portfolio selection problems: a fuzzy approach. Eur J Oper Res 139:178–189CrossRefGoogle Scholar
  47. Levary R, Avery M (1984) On the practical application of weighting equities in a portfolio via goal programming. Opserach 21:246–261Google Scholar
  48. Li D, Ng W-L (2000) Optimal dynamic portfolio selection: multiperiod mean-variance formulation. J Math Finance 10:387–406CrossRefGoogle Scholar
  49. Li J, Xu J (2007) A class of possibilistic portfolio selection model with interval coefficients and its application. J Fuzzy Optim Decis Making, Vol. 6, Springer, pp. 123–137Google Scholar
  50. Mansini R, Ogryczak W, Speranza MG (2007) Conditional value at risk and related linear programming models for portfolio optimization. Ann Oper Res 152:227–256CrossRefGoogle Scholar
  51. Markowitz H (1952) Portfolio selection. J Finance 7:77–91CrossRefGoogle Scholar
  52. Matallin J, Nieto L (2002) Mutual funds as an alternative to direct stock investment. J Appl Financial Econ 743–750Google Scholar
  53. Muhlemann A, Lockett A, Gear A (1978) Portfolio modelling in multiple-criteria situations under uncertainty. Decis Sci 9:612–626CrossRefGoogle Scholar
  54. Ogryczak W (2000) Multiple criteria linear programming model for portfolio selection. J Ann Oper Res, 97:143–162CrossRefGoogle Scholar
  55. Ogryczak W, Ruszczynski A (2002) Dual stochastic dominance and quantile risk measures. J Int Trans Oper Res 9:661–680CrossRefGoogle Scholar
  56. Otten R, Schweitzer M (2002) A comparison between the European and the U.S. mutual fund industry. J Manag Finance 28:14–34Google Scholar
  57. Parra M, Terol A, Uria M (2001) A fuzzy goal programming approach to portfolio selection. Eur J Oper Res 133:287–297CrossRefGoogle Scholar
  58. Pastor L (2000) Portfolio selection and asset pricing models. J Finance 55:179–223CrossRefGoogle Scholar
  59. Pendaraki K, Doumpos M, Zopounidis C (2004) Towards a goal programming methodology for constructing equity mutual fund portfolios. J Asset Manag 4(6):415–428CrossRefGoogle Scholar
  60. Pendaraki K, Zopounidis C, Doumpos M (2005) On the construction of mutual fund portfolios: a multicriteria methodology and an application to the Greek market of equity mutual funds. Eur J Oper Res 163:462–481Google Scholar
  61. Pflug G (2006) Subdifferential representations of risk measures. Math Program 108:339–354CrossRefGoogle Scholar
  62. Prakash A, Chang C, Pactwa T (2003) Selecting a portfolio with skewness: recent evidence from US, European, and Latin American equity markets. J Bank Finance 27:1375–1390CrossRefGoogle Scholar
  63. Raj M, Forsyth M, Tomini O (2003) Fund performance in a downside context. J Invest 12(2):50–63CrossRefGoogle Scholar
  64. Reina L (2005) From subjective expected utility theory to bounded rationality: an experimental investigation on categorization processes in integrative negotiation, in committees’ decision making and in decisions under risk. Doctorate thesis, Technische Universität DresdenGoogle Scholar
  65. Renwick F (1969) Asset management and investor portfolio behaviour: theory and practice. J Finance 24(2):180–205CrossRefGoogle Scholar
  66. Rifai A (1996) A note on the structure of the goal-programming model: assessment and evaluation. Int J Oper Prod Manag 16:40–49CrossRefGoogle Scholar
  67. Rockafellar R, Uryasev S, Zabarankin M (2006) Generalized deviations in risk analysis. Finance Stochast 10:51–74CrossRefGoogle Scholar
  68. Romero C (1991) Handbook of critical issues in goal programming. Pergamon, OxfordGoogle Scholar
  69. Romero C (2004) A general structure of achievement function for a goal programming model. Eur J Oper Res 153:675–686CrossRefGoogle Scholar
  70. Rostamy A, Azar A, Hosseini S (2003) A mixed integer goal programming (MIGP) model for multi-period complex corporate financing problems. J Finance India 17(2):495–509Google Scholar
  71. Samuelson P (1969) Lifetime portfolio selection by dynamic stochastic programming. Rev Econ Stat 51:239–246CrossRefGoogle Scholar
  72. Sharma H, Ghosh D, Sharma D (2007) Credit union portfolio management: an application of goal interval programming. Acad Bank Stud J 6(1):39–60Google Scholar
  73. Sharma H, Sharma D (2006) A multi-objective decision-making approach for mutual fund portfolio. J Bus Econ Res 4:13–24Google Scholar
  74. Sharpe W (1966) Mutual fund performance. J Bus 39:119–138CrossRefGoogle Scholar
  75. Sharpe W (1985) Investments, 3rd edn. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  76. Steuer R, Qi Y, Hirschberger M (2007) Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection. J Ann Oper Res 152:297–317CrossRefGoogle Scholar
  77. Stone B, Reback R (1975) Constructing a model for managing portfolio revisions. J Bank Res 6:48–60Google Scholar
  78. Sun Q, Yan Y (2003) Skewness persistence with optimal portfolio selection. J Bank Finance 27:1111–1121CrossRefGoogle Scholar
  79. Tamiz M, Hasham R, Fargher K, Jones D (1997) A comparison between goal programming and regression analysis for portfolio selection. Lect Notes Econ Math Syst 448:421–432Google Scholar
  80. Tamiz M, Hasham R, Jones D (1996) A two staged goal programming model for portfolio selection. Lect Notes Econ Math Syst 432:286–299Google Scholar
  81. Tamiz M, Jones D (1995) A review of goal programming and its applications. Ann Oper Res 58:39–53CrossRefGoogle Scholar
  82. Tamiz M, Jones D (1998) Goal programming: recent developments in theory and practice. Int J Manag Syst 14:1–16Google Scholar
  83. Tamiz M, Jones D, Romero C (1998) Goal programming for decision making: an overview of the current state-of-the-art. Eur J Oper Res 111:569–581CrossRefGoogle Scholar
  84. Tektas A, Ozkan-Gunay E, Gunay G (2005) Asset and liability management in financial crisis. J Risk Finance 6(2):135–149CrossRefGoogle Scholar
  85. Treynor J (1965) How to rate management of investment funds. Harv Bus Rev 43:63–73Google Scholar
  86. Uria MV, Caballero R, Ruiz F, Romero C (2002) Decisions aiding: meta-goal programming. Eur J Oper Res 136:422–429CrossRefGoogle Scholar
  87. Wang S, Zhu S (2002) On fuzzy portfolio selection problems. J Fuzzy Optim Decis Making 1(4):361–377CrossRefGoogle Scholar
  88. Watada J (1997) Fuzzy portfolio selection and its application to decision making. Tatra Mountains Math Publ 13:219–248Google Scholar
  89. Wu L, Chou S, Yang C, Ong C (2007) Enhanced index investing based on goal programming”. J Portfolio Manage 33(3):49–56CrossRefGoogle Scholar
  90. Yaghoobi M, Tamiz M (2006) On improving a weighted additive model for fuzzy goal programming problems. Int Rev Fuzzy Math 1:115–129Google Scholar
  91. Zheng L (1999) Is money smart? a study of mutual fund investor’s fund selection ability. J Finance 901–933Google Scholar
  92. Zopounidis C, Doumpos M (2002) Multi-criteria decision aid in financial decision making: methodologies and literature review. J Multi-criteria Decis Anal 11:167–186CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.University of PortsmouthPortsmouthUK

Personalised recommendations