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A stochastic programming approach to multicriteria portfolio optimization

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Abstract

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.

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References

  • Abdelaziz F.B., Aouni B., Fayedh R.E.: Multi-objective stochastic programming for portfolio selection. Eur. J. Oper. Res. 177, 1811–1823 (2007)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • Bertsimas D., Shioda R.: Algorithm for cardinality-constrained quadratic optimization. Comput. Optim. Appl. 43, 1–22 (2009)

    Article  Google Scholar 

  • Bodie Z., Kane A., Marcus A.J.: Investments. McGraw-Hill International Edition, New York (2009)

    Google Scholar 

  • Buguk C., Brorsen W.: Testing weak-form market efficiency: evidence from the istanbul stock exchange. Int. Rev. Financial Anal. 2, 579–590 (2003)

    Article  Google Scholar 

  • Campbell J.Y., Lo A.W., MacKinlay A.C.: The Econometrics of Financial Markets. Princeton University Press, Princeton (1997)

    Google Scholar 

  • 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

  • Chang T.J., Meade N., Beasley J.E., Sharaiha Y.M.: Heuristics for cardinality constrained portfolio optimisation. Comput. Oper. Res. 27, 1271–1302 (2000)

    Article  Google Scholar 

  • Dantzig G.B.: Linear programming under uncertainty. Manag. Sci. 1(3&4), 197–206 (1955)

    Article  Google Scholar 

  • Dupacova J., Consigli G., Wallace S.W.: Scenarios for multistage stochastic programs. Ann. Oper. Res. 100, 25–53 (2000)

    Article  Google Scholar 

  • Ehrgott M., Tenfelde-Podehl D.: Computing nadir values in three objectives. Lecture Notes Econ. Math. Syst. 507, 219–228 (2001)

    Article  Google Scholar 

  • Ehrgott M., Klamroth K., Schwehm C.: An MCDM approach to portfolio optimization. Eur. J. Oper. Res. 155, 752–770 (2004)

    Article  Google Scholar 

  • Fama E.F., French K.R.: Common risk factors in the returns on stocks and bonds. J. Financial Econ. 33, 3–56 (1993)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • Hoyland K., Wallace S.W.: Generating scenario trees for multistage decision problems. Manag. Sci. 47(2), 295–307 (2001)

    Article  Google Scholar 

  • 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 

  • Konno H.: Piecewise linear risk function and portfolio optimization. J. Oper. Res. Soc. 33, 139–156 (1990)

    Google Scholar 

  • Konno H., Yamazaki H.: Mean absolute deviation portfolio model and its applications to Tokyo stock market. Manag. Sci. 37, 519–531 (1991)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Markowitz H.: Portfolio Selection: Efficient Diversification of Investments. Wiley, New York (1959)

    Google Scholar 

  • Michalowski W., Ogryczak W.: Extending the MAD portfolio optimization model to incorporate downside risk aversion. Naval Res. Logist. 48, 186–200 (2001)

    Article  Google Scholar 

  • Odabasi A., Aksu C., Akgiray V.: The statistical evolution of prices on the Istanbul stock exchange. Eur. J. Financ. 10, 510–525 (2004)

    Article  Google Scholar 

  • Pınar M.Ç.: Robust scenario optimization based on downside- risk measure for multi-period portfolio selection. OR Spectr. 209, 295–309 (2007)

    Google Scholar 

  • Poterba J., Summers L.: Mean reversion in stock prices: evidence and implications. J. Financ. Econ. 22, 27–59 (1988)

    Article  Google Scholar 

  • Rockafellar R.T., Uryasev S.: Optimization of conditional value-at-risk. J. Risk 2(3), 21–41 (2000)

    Google Scholar 

  • Rockafellar R.T., Uryasev S.: Conditional value-at-risk for general loss distributions. J. Banking Financ. 26, 1443–1471 (2002)

    Article  Google Scholar 

  • Sarr, A., Lybek, T. (2002), Measuring Liquidity in Financial Markets. IMF Working Paper, WP/02/232

  • Seyhun H.N.: Insiders’ profits, costs of trading and market efficiency. J. Financ. Econ. 16(2), 189–212 (1986)

    Article  Google Scholar 

  • Skolpadungket, P., Dahal, K., Harnpornchai, N. (2007) Portfolio optimization using multi-objective genetic algorithms. IEEE Congr. Evol. Comput., 516–523

  • 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)

    Article  Google Scholar 

  • Steuer R.E., Qi Y., Hirschberger M.: Portfolio optimization: new capabilities and future methods. Zeitschrift für Betriebswirtschaft 76(2), 199–219 (2006)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 

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Correspondence to Ceren Tuncer Şakar.

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Tuncer Şakar, C., Köksalan, M. A stochastic programming approach to multicriteria portfolio optimization. J Glob Optim 57, 299–314 (2013). https://doi.org/10.1007/s10898-012-0005-2

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