Evolutionary Intelligence

, Volume 9, Issue 4, pp 125–136 | Cite as

Anatomy of a portfolio optimizer under a limited budget constraint

  • Igor DeplanoEmail author
  • Giovanni Squillero
  • Alberto Tonda
Special Issue


Predicting the market’s behavior to profit from trading stocks is far from trivial. Such a task becomes even harder when investors do not have large amounts of money available, and thus cannot influence this complex system in any way. Machine learning paradigms have been already applied to financial forecasting, but usually with no restrictions on the size of the investor’s budget. In this paper, we analyze an evolutionary portfolio optimizer for the management of limited budgets, dissecting each part of the framework, discussing in detail the issues and the motivations that led to the final choices. Expected returns are modeled resorting to artificial neural networks trained on past market data, and the portfolio composition is chosen by approximating the solution to a multi-objective constrained problem. An investment simulator is eventually used to measure the portfolio performance. The proposed approach is tested on real-world data from New York’s, Milan’s and Paris’ stock exchanges, exploiting data from June 2011 to May 2014 to train the framework, and data from June 2014 to July 2015 to validate it. Experimental results demonstrate that the presented tool is able to obtain a more than satisfying profit for the considered time frame.


Portfolio optimization Multi-layer perceptron Multi-objective optimization Financial forecasting 


  1. 1.
    Abarbanell JS, Bushee BJ (1997) Fundamental analysis, future earnings, and stock prices. J Account Res 35(1):1–24Google Scholar
  2. 2.
    Alexander C (2009) Market risk analysis, value at risk models, vol 4. Wiley, LondonGoogle Scholar
  3. 3.
    Anagnostopoulos K, Mamanis G (2010) A portfolio optimization model with three objectives and discrete variables. Comput Oper Res 37(7):1285–1297MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Anagnostopoulos K, Mamanis G (2011) The mean–variance cardinality constrained portfolio optimization problem: an experimental evaluation of five multiobjective evolutionary algorithms. Expert Syst Appl 38(11):14208–14217Google Scholar
  5. 5.
    Association MF et al (2009) Sound practices for hedge fund managers.
  6. 6.
    Barberis N, Thaler R (2003) A survey of behavioral finance. Handb Econ Finance 1:1053–1128CrossRefGoogle Scholar
  7. 7.
    Beasley JE, Meade N, Chang TJ (2003) An evolutionary heuristic for the index tracking problem. Eur J Oper Res 148(3):621–643MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Bodie Z, Kane A, Marcus AJ (2014) Investments. McGraw-Hill, New YorkGoogle Scholar
  9. 9.
    Borgelt C, Kruse R (2002) Induction of association rules: apriori implementation. In: Compstat. Physica-Verlag, HD, pp 395–400Google Scholar
  10. 10.
    Branke J, Scheckenbach B, Stein M, Deb K, Schmeck H (2009) Portfolio optimization with an envelope-based multi-objective evolutionary algorithm. Eur J Oper Res 199(3):684–693MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Bulkowski TN (2011) Encyclopedia of chart patterns, vol 225. Wiley, LondonGoogle Scholar
  12. 12.
    Cao LJ, Tay FE (2003) Support vector machine with adaptive parameters in financial time series forecasting. IEEE Trans Neural Netw 14(6):1506–1518CrossRefGoogle Scholar
  13. 13.
    Chang TJ, Meade N, Beasley JE, Sharaiha YM (2000) Heuristics for cardinality constrained portfolio optimisation. Comput Oper Res 27(13):1271–1302CrossRefzbMATHGoogle Scholar
  14. 14.
    Coello CAC, Lamont GB, Van Veldhuisen DA (2007) Evolutionary algorithms for solving multi-objective problems. Springer, BerlinzbMATHGoogle Scholar
  15. 15.
    Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  16. 16.
    Deboeck G (1994) Trading on the edge: neural, genetic, and fuzzy systems for chaotic financial markets, vol 39. Wiley, LondonGoogle Scholar
  17. 17.
    Dechow PM, Hutton AP, Meulbroek L, Sloan RG (2001) Short-sellers, fundamental analysis, and stock returns. J Financ Econ 61(1):77–106CrossRefGoogle Scholar
  18. 18.
    Deplano I, Squillero G, Tonda A (2016) Portfolio optimization, a decision-support methodology for small budgets. In: Applications of evolutionary computation. Springer, pp 58–72Google Scholar
  19. 19.
    Devadoss AV, Ligori TAA (2013) Forecasting of stock prices using multi layer perceptron. Int J Comput Algorithm 2:440–449Google Scholar
  20. 20.
    Edwards RD, Magee J, Bassetti W (2007) Technical analysis of stock trends. CRC Press, Boca RatonCrossRefzbMATHGoogle Scholar
  21. 21.
    Fama EF (1970) Efficient capital markets: a review of theory and empirical work. J Finance 25(2):383–417CrossRefGoogle Scholar
  22. 22.
    Fama EF, French KR (2004) The capital asset pricing model: theory and evidence. J Econ Perspect 18:25–46CrossRefGoogle Scholar
  23. 23.
    Fu Tc, Chung Fl, Ng V, Luk R (2001) Pattern discovery from stock time series using self-organizing maps. In: Workshop notes of KDD2001 workshop on temporal data mining, Citeseer, pp 26–29Google Scholar
  24. 24.
    Gabrielsson P, König R, Johansson U (2013) Evolving hierarchical temporal memory-based trading models. Springer, BerlinCrossRefGoogle Scholar
  25. 25.
    Goodfellow I, Bengio Y, Courville A (2016) Deep learning. Book in preparation for MIT Press
  26. 26.
    Graham B, Dodd DL (2008) Security analysis. McGraw-Hill, New YorkGoogle Scholar
  27. 27.
    Grossman S (1976) On the efficiency of competitive stock markets where trades have diverse information. J Finance 31(2):573–585CrossRefGoogle Scholar
  28. 28.
    Grossman SJ, Stiglitz JE (1980) On the impossibility of informationally efficient markets. Am Econ Rev 70(3):393–408Google Scholar
  29. 29.
    Haykin S, Lippmann R (1994) Neural networks, a comprehensive foundation. Int J Neural Syst 5(4):363–364CrossRefzbMATHGoogle Scholar
  30. 30.
    He K, Zhang X, Ren S, Sun J (2015) Delving deep into rectifiers: surpassing human-level performance on imagenet classification. In: Proceedings of the IEEE international conference on computer vision, pp 1026–1034Google Scholar
  31. 31.
    Hochreiter R (2010) Evolutionary multi-stage financial scenario tree generation. In: Applications of evolutionary computation. Springer, pp 182–191Google Scholar
  32. 32.
    Høyland K, Wallace SW (2001) Generating scenario trees for multistage decision problems. Manag Sci 47(2):295–307CrossRefzbMATHGoogle Scholar
  33. 33.
    Ineichen A, Silberstein K (2008) Aimas roadmap to hedge funds. Alternative Investment Management Association, LondonGoogle Scholar
  34. 34.
    Ineichen AM (2002) Absolute returns: the risk and opportunities of hedge fund investing, vol 195. Wiley, LondonGoogle Scholar
  35. 35.
    Jiang ZQ, Zhou WX, Sornette D, Woodard R, Bastiaensen K, Cauwels P (2010) Bubble diagnosis and prediction of the 2005–2007 and 2008–2009 Chinese stock market bubbles. J Econ Behav Organ 74(3):149–162CrossRefGoogle Scholar
  36. 36.
    Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision under risk. Econom J Econom Soc 47(2):263–291Google Scholar
  37. 37.
    Kim D, Kim C (1997) Forecasting time series with genetic fuzzy predictor ensemble. IEEE Trans Fuzzy Syst 5(4):523–535CrossRefGoogle Scholar
  38. 38.
    Kimoto T, Asakawa K, Yoda M, Takeoka M (1990) Stock market prediction system with modular neural networks. In: 1990 IJCNN international joint conference on neural networks, 1990. IEEE, pp 1–6Google Scholar
  39. 39.
    Koller T, Goedhart M, Wessels D (2015) Valuation: measuring and managing the value of companies, 6th edn. Wiley, LondonGoogle Scholar
  40. 40.
    Laboissiere LA, Fernandes RA, Lage GG (2015) Maximum and minimum stock price forecasting of Brazilian power distribution companies based on artificial neural networks. Appl Soft Comput 35:66–74CrossRefGoogle Scholar
  41. 41.
    Lo AW (2004) The adaptive markets hypothesis: market efficiency from an evolutionary perspective. J Portf Manag. Accessed 28 Aug 2016
  42. 42.
    Loginov A, Heywood MI (2013) On the utility of trading criteria based retraining in forex markets. Springer, BerlinCrossRefGoogle Scholar
  43. 43.
    Lohpetch D, Corne D (2010) Outperforming buy-and-hold with evolved technical trading rules: daily, weekly and monthly trading. In: Applications of evolutionary computation. Springer, pp 171–181Google Scholar
  44. 44.
    Markowitz H (1952) Portfolio selection. J Finance 7(1):77–91Google Scholar
  45. 45.
    Markowitz HM (1968) Portfolio selection: efficient diversification of investments, vol 16. Yale university press, New HavenGoogle Scholar
  46. 46.
    Matz L, Neu P (2006) Liquidity risk measurement and management: a practitioner’s guide to global best practices, 408th edn. Wiley, LondonCrossRefGoogle Scholar
  47. 47.
    Merton RC (1973) An intertemporal capital asset pricing model. Econom J Econom Soc 41(5):867–887Google Scholar
  48. 48.
    Michalak K (2015) Selecting best investment opportunities from stock portfolios optimized by a multiobjective evolutionary algorithm. In: Proceedings of the 2015 on genetic and evolutionary computation conference. ACM, pp 1239–1246Google Scholar
  49. 49.
    Michalak K, Filipiak P, Lipinski P (2013) Usage patterns of trading rules in stock market trading strategies optimized with evolutionary methods. Springer, BerlinCrossRefGoogle Scholar
  50. 50.
    Neri F (2011) Learning and predicting financial time series by combining natural computation and agent simulation. In: Applications of evolutionary computation. Springer, pp 111–119Google Scholar
  51. 51.
    Nguyen D, Widrow B (1990) Improving the learning speed of 2-layer neural networks by choosing. In: Initial values of the adaptive weights, international joint conference of neural networks, pp 21–26Google Scholar
  52. 52.
    Oberlechner T (2001) Importance of technical and fundamental analysis in the European foreign exchange market. Int J Finance Econ 6(1):81–93CrossRefGoogle Scholar
  53. 53.
    Otero FE, Kampouridis M (2014) A comparative study on the use of classification algorithms in financial forecasting. In: Applications of evolutionary computation. Springer, pp 276–287Google Scholar
  54. 54.
    Pascanu R, Gulcehre C, Cho K, Bengio Y (2013) How to construct deep recurrent neural networks. arXiv preprint arXiv:13126026
  55. 55.
    Rather AM, Agarwal A, Sastry V (2015) Recurrent neural network and a hybrid model for prediction of stock returns. Expert Syst Appl 42(6):3234–3241CrossRefGoogle Scholar
  56. 56.
    Ross SA (1976) The arbitrage theory of capital asset pricing. J Econ Theory 13(3):341–360MathSciNetCrossRefGoogle Scholar
  57. 57.
    Shefrin H, Statman M (2000) Behavioral portfolio theory. J Financ Quant Anal 35(02):127–151CrossRefGoogle Scholar
  58. 58.
    Sheppard K (2010) Financial econometrics notes. University of Oxford, OxfordGoogle Scholar
  59. 59.
    Shiller RJ (1999) Human behavior and the efficiency of the financial system. Handb Macroecon 1:1305–1340CrossRefGoogle Scholar
  60. 60.
    Shiller RJ (2003) From efficient markets theory to behavioral finance. J Econ Perspect 17(1):83–104CrossRefGoogle Scholar
  61. 61.
    Simon HA (1955) A behavioral model of rational choice. Q J Econ 69(1):99–118Google Scholar
  62. 62.
    Simon HA (1982) Models of bounded rationality: empirically grounded economic reason, 3rd edn. MIT Press, CambridgeGoogle Scholar
  63. 63.
    Srikant R, Vu Q, Agrawal R (1997) Mining association rules with item constraints. KDD 97:67–73Google Scholar
  64. 64.
    Swisher P, Kasten GW (2005) Post-modern portfolio theory. J Financ Plann Denver 18(9):74Google Scholar
  65. 65.
    Tapia MGC, Coello CAC (2007) Applications of multi-objective evolutionary algorithms in economics and finance: a survey. In: IEEE congress on evolutionary computation, vol 7, pp 532–539Google Scholar
  66. 66.
    Trippi RR, Turban E (1992) Neural networks in finance and investing: using artificial intelligence to improve real world performance. McGraw-Hill, New YorkGoogle Scholar
  67. 67.
    Tversky A, Kahneman D (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertain 5(4):297–323CrossRefzbMATHGoogle Scholar
  68. 68.
    Vassiliadis V, Thomaidis N, Dounias G (2011) On the performance and convergence properties of hybrid intelligent schemes: application on portfolio optimization domain. In: Applications of evolutionary computation. Springer, pp 131–140Google Scholar
  69. 69.
    Ye Y, Chiang CC (2006) A parallel apriori algorithm for frequent itemsets mining. In: Fourth international conference on software engineering research, management and applications, 2006. IEEE, pp 87–94Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Liverpool John Moores UniversityLiverpoolUnited Kingdom
  2. 2.Politecnico di TorinoTorinoItaly
  3. 3.UMR GMPA, AgroParisTech, INRAUniversité Paris-SaclayThiverval-GrignonFrance

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