Skip to main content
Springer Nature Link
Log in

A numerical evaluation of meta-heuristic techniques in portfolio optimisation

  • Original Paper
  • Published:
Operational Research Aims and scope Submit manuscript

Abstract

Optimal portfolio management under only mean and variance/covariance measures in Markowitz (J Finance 7(1):77–91, 1952; J Polit Econ:152–158, 1952) and Tobin (Rev Econ Stud 25:65–86, 1958; Econometrica 26(1):24–36, 1958) framework, is inefficient in real stock markets, as investors do not have quadratic utility functions, and returns are not normally, independently, and identically distributed. Hence alternative forms of utility functions with further higher moments such as the power utility should be used, but these do not provide closed form solutions towards a good feasible portfolio selection. A variety of innovative heuristics have been put forward recently. Hence implementing empirical data, we test and compare different heuristic techniques for portfolio management with power utility as well as contrasting the differences between power utility maximised portfolios and quadratic utility maximised portfolios.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Adcock CJ (2002) Asset pricing and portfolio selection based on the multivariate skew-student distribution, Non-linear Asset Pricing Workshop, April, Paris

  • Arditti F (1967) Risk and the required return on equity. J Finance 22:19–36

    Article  Google Scholar 

  • Arditti F (1971) Another look at mutual fund performance. J Financial Quant Anal 6(3):909–912

    Article  Google Scholar 

  • Aristotle, Ta Oikonomika (translation G.C. Armstrong as the Oeconomica), in the Loeb Classical Library, (London 1916), vol 287, Harvard University Press, Cambridge, MA

  • Aristotle, Economics, Perseus (Loeb edition, 1935)

  • Arnone S, Loraschi A, Tettamanzi A (1993) A genetic approach to portfolio selection. Neural Netw World Int J Neural Mass-Parallel Comput Inform Syst 3:597–604

    Google Scholar 

  • Arrow KJ (1965a) Uncertainty and the welfare economics of medical care. Am Econ Rev 53(1963):941–973

    Google Scholar 

  • Arrow KJ (1965b) The Theory of Risk version. Aspects of Risk Bearing, Helsinki: Yrjo Jahnssonin Säätio, Lecture 2, Reprinted in Essays in the Theory of Risk Bearing, Markham Publishing Company, Chicago, 1971, 90–109

  • Arrow KJ (1971) Essays on the theory of risk bearing. Markham, Chicago

    Google Scholar 

  • Bernoulli D (1738) “Exposition of a new theory on the measurement of risk”, Comentarii Academiae Scientiarum Imperialis Petropolitanae, as translated and reprinted in 1954. Econometrica 22:23–36

    Article  Google Scholar 

  • Britten-Jones M (2002) Portfolio optimisation and Bayesian regression, Unpublished working paper, London Business School

  • Clerc M, Kennedy J (2002) The particle swarm—explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73

    Article  Google Scholar 

  • Coello Coello CA, Aguirre AH, Zitzler E (2007) Evolutionary multi-objective optimization. Eur J Oper Res 181(3):1617–1619

    Article  Google Scholar 

  • Darwin C (1859) On the origin of species by means of natural selection, or the preservation of favoured races in the struggle for life. John Murray, London

    Google Scholar 

  • de Athayde GM, Flores RG Jr (2004) Finding a maximum skewness Portfolio—a general solution to three moments portfolio choice. J Econ Dyn Control 28(7):1335–1352

    Article  Google Scholar 

  • Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. Found Genetic Algorithms 2:187–202

    Google Scholar 

  • Fama E (1963) Mandelbrot and the Stable Paretan Hypothesis. J Bus 36:420–429

    Article  Google Scholar 

  • Fama E (1965) The behaviour of stock market prices. J Bus 38:34–105

    Article  Google Scholar 

  • Friend I, Blume M (1975) The demand for risky assets. Am Econ Rev: 900–922

  • Haas M (2006) Improved duration-based backtesting of value-at-risk. J Risk 8(2):17–38. Winter 2005–2006

    Google Scholar 

  • Hakansson NH, Ziemba WT (1995) Capital growth theory. In: Jarrow RA, Maksimovic V, Ziemba WT (eds) Handbooks in operations research and management science: finance. North Holland, Amsterdam 9:65–86

  • Hanoch G, Levy H (1969) The efficiency analysis of choices involving risk. Rev Econ Stud 36(3):335–346

    Article  Google Scholar 

  • Harvey CR, Siddique A (2000a) Conditional skewness in asset pricing tests. J Finance 55:1263–1295

    Article  Google Scholar 

  • Harvey CR, Siddique A (2000b) Time-varying conditional skewness and the market risk premium. Res Banking Finance 1:27–60

    Google Scholar 

  • Harvey CR, Liechty JC, Liechty MW, Müller P (2002) Portfolio selection with higher moments: a bayesian decision theoretic approach. Working Paper, Duke University Durham

  • Heppner F, Grenander U (1990) A stochastic nonlinear model for coordinated bird flocks. In: Krasner S (ed) The ubiquity of chaos. AAAS Publications, Washington

    Google Scholar 

  • Herrera F, Lozano M, Verdegay J (1998) Tackling real-coded genetic algorithms: operators and tools for behavioural analysis. Artif Intell Rev 12:265–319

    Article  Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  • Jean WH (1971) The extension of portfolio analysis to three or more parameters. J Financial Quant Anal 6(1):505–515

    Article  Google Scholar 

  • Jondeau E, Rockinger M (2006) Optimal portfolio allocation under higher moments. Eur Financial Manage 12(1):29–55

    Article  Google Scholar 

  • Kallberg JG, Ziemba WT (1983) Comparison of alternative utility functions in portfolio selection problems. Manage Sci 29(11):1257–1276

    Article  Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimisation. In: IEEE Proceedings International Conference on Neural Networks, IEEE service center, vol IV, pp 1942–1948, Piscataway, NJ

  • Kraus A, Litzenberger RH (1976) Skewness preference and the valuation of risky assets. J Finance 31:1085–1100

    Article  Google Scholar 

  • Kon S (1984) Models of stock returns—a comparison. J Finance 39(1):147–165

    Article  Google Scholar 

  • Levy H (1969) A utility function depending on the first three moments. J Finance 24(4):715–719

    Article  Google Scholar 

  • Levy H, Markowitz HM (1979) Approximating expected utility by a function of mean and variance. Am Econ Rev 69:308–317

    Google Scholar 

  • Levy H, Sarnat M (1970) International diversification of investment portfolios. American Economic Review, 60, 668–675, also in (1972) Investment and portfolio Analysis, John Wiley & Sons Inc., New York, and in (1984) Portfolio and investment selection: theory and practice, Prentice Hall International

  • Loukeris N (2008) Radial basis functions networks to hybrid neuro-genetic RBFNs in financial evaluation of corporations. Int J Comput 2(2)

  • Luenberger DG (1993) A preference foundation for log mean-variance criteria in portfolio choice problems. J Econ Dyn Control 17(5/6):887–906

    Article  Google Scholar 

  • Maringer D (2008) Risk preferences and loss aversion in portfolio optimisation. In: Kontoghiorghes EJ, Rustem B, Winker P (eds) Computational methods in financial engineering—essays in honour of Manfred Gilli. Springer, Berlin

  • Maringer D, Parpas P (2007) Global optimisation of higher order moments in portfolio selection. J Global Optim

  • Markowitz HM (1952a) Portfolio selection. J Finance 7(1):77–91

    Article  Google Scholar 

  • Markowitz HM (1952b) The utility of wealth. J Polit Econ 152–158

  • Markowitz HM (1959) Portfolio selection: efficient diversification of investments. Wiley, New York

    Google Scholar 

  • Merton RC (1969) Lifetime portfolio selection under uncertainty: the continuous time case. Rev Econ Stat 51(3):247–257

    Article  Google Scholar 

  • Merton RC (1971) Optimum consumption and portfolio rules in a continuous-time model. J Econ Theor 3:373–413

    Article  Google Scholar 

  • Merton R (1982) On the mathematics and economics assumptions of continuous time models. In: William FS, Cathryn MC (eds) Financial economics: essays in honour of Paul Cootner. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Mills TC (1995) Modelling skewness and kurtosis in the London stock exchange FT-SE index return distributions. Statistician 44(3):323–332

    Article  Google Scholar 

  • Ogryczak W, Vetschera R (2004) Methodological foundations of multi-criteria decision making. Eur J Oper Res 158(2):267–270

    Article  Google Scholar 

  • Peiro A (1999) Skewness in financial returns. J Bank Finance 23(6):847–862

    Article  Google Scholar 

  • Pennanen T, Koivu M (2005) Epi-convergent discretizations of stochastic programs via integration quadratures. Numer Math 100(1):141–163

    Article  Google Scholar 

  • Pratt JW (1964) Risk aversion in the small and in the large. Econometrica 32:122–136

    Article  Google Scholar 

  • Premaratne G, Tay AS (2002) How should we interpret evidence of time varying conditional skewness? National University of Singapore

  • Rabin M (2000) Risk aversion and expected-utility theory: a calibration theorem. Econometrica 68(5):1281–1292

    Article  Google Scholar 

  • Rabin M, Thaler RH (2001) Anomalies: risk aversion. J Econ Perspect 15(1):219–232

    Article  Google Scholar 

  • Reynolds CW (1987) Flocks, herds and schools: a distributed behavioural model. Comput Graph 21(4):25–34

    Article  Google Scholar 

  • Samuelson PA (1969) Lifetime portfolio selection by dynamic stochastic programming. Rev Econ Stat 51(3):239–246

    Article  Google Scholar 

  • Samuelson P (1970) The fundamental approximation theorem of portfolio analysis in terms of means, variances and higher moments. Rev Econ Stud 37(4):537–542

    Article  Google Scholar 

  • Sortino FA, Forsey HJ (1996) On the use and misuse of downside risk. J Portfolio Manage 22:35–42

    Article  Google Scholar 

  • Sortino FA, Price LN (1994) Performance measurement in a downside risk framework. J Invest 3(3):50–58

    Google Scholar 

  • Storn R (1996) On the usage of differential evolution for function optimisation, NAFIPS, Berkeley, 519–523

  • Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimisation over continuous spaces. Technical Report TR-95-012, International Computer Science Institute, ftp.icsi.berkeley.edu

  • Streicher F, Ulmer H, Zell A (2004) Comparing discrete and continuous genotypes on the constrained portfolio selection problem, Genetic and Evolutionary Computation Conference

  • Taylor CW, Hare RM, Barnes J (1998) Greek philosophers—Socrates, Plato, and Aristotle. Oxford University Press, New York

    Google Scholar 

  • Tobin J (1958a) Liquidity preference as behaviour towards risk. Rev Econ Stud 25:65–86

    Article  Google Scholar 

  • Tobin J (1958b) Estimation of relationships for limited dependent variables. Econometrica 26(1):24–36

    Article  Google Scholar 

  • Vehviläinen I (2004) Applying mathematical finance tools to the competitive Nordic electricity market, PhD thesis, Helsinki University of Technology

  • Viennet R, Fonteix C, Marc I (1996) Multicriteria optimization using a genetic algorithm for determining a Pareto set. Int J Syst Sci 27(2):255–260

    Article  Google Scholar 

  • Von Neuman J, Morgernsten O (1974) Theory of games and economic behavior. Princeton University Press, New Jersey

    Google Scholar 

  • Wilson O (1975) Sociobiology: the new synthesis. Belknap Press, Cambridge

    Google Scholar 

  • Xenophon, Oikonomikos, (The Estate Manager), Perseus (ed. Marchant, 1921)

Download references

Author information

Authors and Affiliations

  1. School of Undergraduate Studies, Europe, UMUC, University of Maryland, 3501 University Boulevard East, Adelphi, MD, 20783, USA

    N. Loukeris

  2. CCFEA, University of Essex, Wivenhoe Park, Colchester, Essex, CO4 3SQ, UK

    N. Loukeris, D. Donelly, A. Khuman & Y. Peng

Authors
  1. N. Loukeris
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. D. Donelly
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. A. Khuman
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Y. Peng
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to N. Loukeris.

Additional information

We are very thankful for Professor Dietmar Maringer’s, University of Basel, guidance and support throughout this study and greatly appreciate suggestions and intuitions put forward by Professor Sheri Markose, University of Essex.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Loukeris, N., Donelly, D., Khuman, A. et al. A numerical evaluation of meta-heuristic techniques in portfolio optimisation. Oper Res Int J 9, 81–103 (2009). https://doi.org/10.1007/s12351-008-0028-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12351-008-0028-0

Keywords