Journal of Global Optimization

, Volume 57, Issue 2, pp 299–314 | Cite as

A stochastic programming approach to multicriteria portfolio optimization

  • Ceren Tuncer Şakar
  • Murat Köksalan


We study a stochastic programming approach to multicriteria multi-period portfolio optimization problem. We use a Single Index Model to estimate the returns of stocks from a market-representative index and a random walk model to generate scenarios on the possible values of the index return. We consider expected return, Conditional Value at Risk and liquidity as our criteria. With stocks from Istanbul Stock Exchange, we make computational studies for the two and three-criteria cases. We demonstrate the tradeoffs between criteria and show that treating these criteria simultaneously yields meaningful efficient solutions. We provide insights based on our experiments.


Portfolio optimization Stochastic programming Market efficiency Multicriteria Liquidity Conditional value at risk 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abdelaziz F.B., Aouni B., Fayedh R.E.: Multi-objective stochastic programming for portfolio selection. Eur. J. Oper. Res. 177, 1811–1823 (2007)CrossRefGoogle Scholar
  2. Balıbek E., Köksalan M.: A multi-objective multi-period stochastic programming model or public debt management. Eur. J. Oper. Res. 205(1), 205–217 (2010)CrossRefGoogle Scholar
  3. Beale E.M.L.: On minimizing a convex function subject to linear inequalities. J. R. Stat. Soc. (Series B) 17(2), 173–184 (1955)Google Scholar
  4. Bertsimas D., Darnell C., Soucy R.: Portfolio construction through mixed-integer programming at Grantham, Mayo, Van Otterloo and Company. Interfaces 29(1), 49–66 (1999)CrossRefGoogle Scholar
  5. Bertsimas D., Shioda R.: Algorithm for cardinality-constrained quadratic optimization. Comput. Optim. Appl. 43, 1–22 (2009)CrossRefGoogle Scholar
  6. Bodie Z., Kane A., Marcus A.J.: Investments. McGraw-Hill International Edition, New York (2009)Google Scholar
  7. Buguk C., Brorsen W.: Testing weak-form market efficiency: evidence from the istanbul stock exchange. Int. Rev. Financial Anal. 2, 579–590 (2003)CrossRefGoogle Scholar
  8. Campbell J.Y., Lo A.W., MacKinlay A.C.: The Econometrics of Financial Markets. Princeton University Press, Princeton (1997)Google Scholar
  9. Cesarone, F., Scozzari, A., Tardella, F. (2012). A new method for mean-variance portfolio optimization with cardinality constraints. Ann. Oper. Res. doi:  10.1007/s10479-012-1165-7
  10. Chang T.J., Meade N., Beasley J.E., Sharaiha Y.M.: Heuristics for cardinality constrained portfolio optimisation. Comput. Oper. Res. 27, 1271–1302 (2000)CrossRefGoogle Scholar
  11. Dantzig G.B.: Linear programming under uncertainty. Manag. Sci. 1(3&4), 197–206 (1955)CrossRefGoogle Scholar
  12. Dupacova J., Consigli G., Wallace S.W.: Scenarios for multistage stochastic programs. Ann. Oper. Res. 100, 25–53 (2000)CrossRefGoogle Scholar
  13. Ehrgott M., Tenfelde-Podehl D.: Computing nadir values in three objectives. Lecture Notes Econ. Math. Syst. 507, 219–228 (2001)CrossRefGoogle Scholar
  14. Ehrgott M., Klamroth K., Schwehm C.: An MCDM approach to portfolio optimization. Eur. J. Oper. Res. 155, 752–770 (2004)CrossRefGoogle Scholar
  15. Fama E.F., French K.R.: Common risk factors in the returns on stocks and bonds. J. Financial Econ. 33, 3–56 (1993)CrossRefGoogle Scholar
  16. Guastaroba G., Mansini R., Speranza M.G.: On the effectiveness of scenario generation techniques in single-period portfolio optimization. Eur. J. Oper. Res. 192, 500–511 (2009)CrossRefGoogle Scholar
  17. Gülpınar N., Rustem B., Settergren R.: Multistage stochastic mean-variance portfolio analysis with transaction costs. Innov. Financ. Econ. Netw. 3, 46–63 (2003)Google Scholar
  18. Haimes Y.Y., Lasdon L.S., Wismer D.A.: On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Trans. Syst. Man Cybern. 1(3), 296–297 (1971)CrossRefGoogle Scholar
  19. Hoyland K., Wallace S.W.: Generating scenario trees for multistage decision problems. Manag. Sci. 47(2), 295–307 (2001)CrossRefGoogle Scholar
  20. Ibrahim K., Kamil A.A., Mustafa A.: Portfolio selection problem with maximum downside deviation measure: a stochastic programming approach. Int. J. Math. Models Methods Appl. Sci. 1(2), 123–129 (2008)Google Scholar
  21. Konno H.: Piecewise linear risk function and portfolio optimization. J. Oper. Res. Soc. 33, 139–156 (1990)Google Scholar
  22. Konno H., Yamazaki H.: Mean absolute deviation portfolio model and its applications to Tokyo stock market. Manag. Sci. 37, 519–531 (1991)CrossRefGoogle Scholar
  23. Lo A.W., MacKinlay A.C.: Stock market prices do not follow random walks: evidence from a simple specification test. Rev. Financ. Stud. 1, 41–66 (1988)CrossRefGoogle Scholar
  24. Markowitz H.: Portfolio Selection: Efficient Diversification of Investments. Wiley, New York (1959)Google Scholar
  25. Michalowski W., Ogryczak W.: Extending the MAD portfolio optimization model to incorporate downside risk aversion. Naval Res. Logist. 48, 186–200 (2001)CrossRefGoogle Scholar
  26. Odabasi A., Aksu C., Akgiray V.: The statistical evolution of prices on the Istanbul stock exchange. Eur. J. Financ. 10, 510–525 (2004)CrossRefGoogle Scholar
  27. Pınar M.Ç.: Robust scenario optimization based on downside- risk measure for multi-period portfolio selection. OR Spectr. 209, 295–309 (2007)Google Scholar
  28. Poterba J., Summers L.: Mean reversion in stock prices: evidence and implications. J. Financ. Econ. 22, 27–59 (1988)CrossRefGoogle Scholar
  29. Rockafellar R.T., Uryasev S.: Optimization of conditional value-at-risk. J. Risk 2(3), 21–41 (2000)Google Scholar
  30. Rockafellar R.T., Uryasev S.: Conditional value-at-risk for general loss distributions. J. Banking Financ. 26, 1443–1471 (2002)CrossRefGoogle Scholar
  31. Sarr, A., Lybek, T. (2002), Measuring Liquidity in Financial Markets. IMF Working Paper, WP/02/232Google Scholar
  32. Seyhun H.N.: Insiders’ profits, costs of trading and market efficiency. J. Financ. Econ. 16(2), 189–212 (1986)CrossRefGoogle Scholar
  33. Skolpadungket, P., Dahal, K., Harnpornchai, N. (2007) Portfolio optimization using multi-objective genetic algorithms. IEEE Congr. Evol. Comput., 516–523Google Scholar
  34. Smith G., Ryoo H.J.: Variance ratio tests of the random walk hypothesis for European emerging stock markets. Eur. J. Financ. 9, 290–300 (2003)CrossRefGoogle Scholar
  35. Steuer R.E., Qi Y., Hirschberger M.: Portfolio optimization: new capabilities and future methods. Zeitschrift für Betriebswirtschaft 76(2), 199–219 (2006)CrossRefGoogle Scholar
  36. Steuer R.E., Qi Y., Hirschberger M.: Suitable-portfolio investors, nondominated frontier sensitivity, and the effect on standard portfolio selection. Ann. Oper. Res. 152, 297–317 (2007)CrossRefGoogle Scholar
  37. Yu L., Wang S., Wu Y., Lai K.K.: A dynamic stochastic programming model for bond portfolio management. Lecture Notes Comput. Sci. 3039(2004), 876–883 (2004)CrossRefGoogle Scholar
  38. Yu L.Y., Ji X.D., Wang S.Y.: Stochastic programming models in financial optimization: a survey. Adv. Model. Optim. 5(1), 1–26 (2003)Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Industrial Engineering DepartmentMiddle East Technical UniversityAnkaraTurkey

Personalised recommendations