Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Advertisement

Springer Nature Link
Log in

A hybrid combinatorial approach to a two-stage stochastic portfolio optimization model with uncertain asset prices

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Portfolio optimization is one of the most important problems in the finance field. The traditional Markowitz mean-variance model is often unrealistic since it relies on the perfect market information. In this work, we propose a two-stage stochastic portfolio optimization model with a comprehensive set of real-world trading constraints to address this issue. Our model incorporates the market uncertainty in terms of future asset price scenarios based on asset return distributions stemming from the real market data. Compared with existing models, our model is more reliable since it encompasses real-world trading constraints and it adopts CVaR as the risk measure. Furthermore, our model is more practical because it could help investors to design their future investment strategies based on their future asset price expectations. In order to solve the proposed stochastic model, we develop a hybrid combinatorial approach, which integrates a hybrid algorithm and a linear programming (LP) solver for the problem with a large number of scenarios. The comparison of the computational results obtained with three different metaheuristic algorithms and with our hybrid approach shows the effectiveness of the latter. The superiority of our model is mainly embedded in solution quality. The results demonstrate that our model is capable of solving complex portfolio optimization problems with tremendous scenarios while maintaining high solution quality in a reasonable amount of time and it has outstanding practical investment implications, such as effective portfolio constructions.

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Ahmadi-Javid A, Fallah-Tafti M (2019) Portfolio optimization with entropic value-at-risk. Eur J Oper Res 279(1):225–241

    MathSciNet  MATH  Google Scholar 

  • Alexander GJ, Baptista AM (2004) A comparison of var and cvar constraints on portfolio selection with the mean-variance model. Manag Sci 50(9):1261–1273

    Google Scholar 

  • Alexander S, Coleman TF, Li Y (2006) Minimizing cvar and var for a portfolio of derivatives. J Bank Finance 30(2):583–605

    Google Scholar 

  • Andersson F, Uryasev S, Uryasev S (2001) Credit risk optimization with conditional value-at-risk criterion. Math Program 89(2):273–291

    MathSciNet  MATH  Google Scholar 

  • Artzner P, Delbaen F, Eber J-M, Heath D (1999) Coherent measures of risk. Math Finance 9(3):203–228

    MathSciNet  MATH  Google Scholar 

  • Badescu A, Elliott RJ, Ortega J-P (2015) Non-Gaussian GARCH option pricing models and their diffusion limits. Eur J Oper Res 247(3):820–830

    MathSciNet  MATH  Google Scholar 

  • Balanda KP, Macgillivray HL (1988) Kurtosis: a critical review. Am Stat 42(2):111–119

    Google Scholar 

  • Baldacci R, Boschetti MA, Christofides N, Christofides S (2009) Exact methods for large-scale multi-period financial planning problems. CMS 6(3):281–306

    MathSciNet  MATH  Google Scholar 

  • Baluja S, Caruana R (1995) Removing the genetics from the standard genetic algorithm. Technical report, Pittsburgh, PA, USA

    Google Scholar 

  • Baluja S (1994) Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning. Technical report, Pittsburgh, PA, USA

  • Ban G-Y, Karoui NE, Lim AEB (2016) Machine learning and portfolio optimization. Manag Sci 64(3):1136–1154

    Google Scholar 

  • Barro D, Canestrelli E (2005) Dynamic portfolio optimization: time decomposition using the maximum principle with a scenario approach. Eur J Oper Res 163(1):217–229 (Financial Modelling and Risk Management)

    MathSciNet  MATH  Google Scholar 

  • Beasley JE (1990) OR-Library: distributing test problems by electronic mail. J Oper Res Soc 41(11):1069–1072

    Google Scholar 

  • Beltratti A, Consiglio A, Zenios SA (1999) Scenario modeling for the management of international bond portfolios. Ann Oper Res 85(0):227–247

    MathSciNet  MATH  Google Scholar 

  • Best MJ, Grauer RR (1991) On the sensitivity of mean-variance-efficient portfolios to changes in asset means: some analytical and computational results. Rev Financ Stud 4(2):315

    Google Scholar 

  • Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer series in operations research and financial engineering. United States Government Publishing Office, Washington, D.C

    Google Scholar 

  • Black F, Litterman R (1992) Global portfolio optimization. Financ Anal J 48(5):28–43

    Google Scholar 

  • Broadie M (1993) Computing efficient frontiers using estimated parameters. Ann Oper Res 45(1):21–58

    MATH  Google Scholar 

  • Carhart MM (1997) On persistence in mutual fund performance. J Finance 52(1):57–82

    Google Scholar 

  • Chang TJ, Meade N, Beasley JE, Sharaiha YM (2000) Heuristics for cardinality constrained portfolio optimisation. Comput Oper Res 27(13):1271–1302

    MATH  Google Scholar 

  • Chen N, Kou S, Wang C (2017) A partitioning algorithm for Markov decision processes with applications to market microstructure. Manag Sci 64(2):784–803

    Google Scholar 

  • Chen Y, Wang X (2015) A hybrid stock trading system using genetic network programming and mean conditional value-at-risk. Eur J Oper Res 240(3):861–871

    MathSciNet  MATH  Google Scholar 

  • Chopra VK, Ziemba WT (1993) The effect of errors in means, variances, and covariances on optimal portfolio choice. J Portf Manag 19(2):6–11

    Google Scholar 

  • Conrad J, Kaul G (1998) An anatomy of trading strategies. Rev Financ Stud 11(3):489–519

    Google Scholar 

  • Cooper MJ, Gutierrez RC, Hameed A (2004) Market states and momentum. J Finance 59(3):1345–1365

    Google Scholar 

  • Crama Y, Schyns M (2003) Simulated annealing for complex portfolio selection problems. Eur J Oper Res 150(3):546–571

    MATH  Google Scholar 

  • Cui T, Bai R, Parkes AJ, He F, Qu R, Li J (2015) A hybrid genetic algorithm for a two-stage stochastic portfolio optimization with uncertain asset prices. In Proceedings of the 2015 IEEE congress on evolutionary computation (CEC), pp 2519–2525, May 2015

  • Cui T, Cheng S, Bai R (July 2014) A combinatorial algorithm for the cardinality constrained portfolio optimization problem. In Proceedings of the 2014 IEEE congress on evolutionary computation (CEC), pp 491–498

  • Dantzig GB (1963) Linear programming and extensions. Rand corporation research study. Princeton University Press, Princeton

    Google Scholar 

  • Dantzig GB (2004) Linear programming under uncertainty. Manag Sci 50(12 Supplement):1764–1769

    Google Scholar 

  • Di Gaspero L, Di Tollo G, Roli A, Schaerf A (2011) Hybrid metaheuristics for constrained portfolio selection problem. Quant Finance 11(10):1473–1488

    MathSciNet  MATH  Google Scholar 

  • Embrechts P, Resnick SI, Samorodnitsky G (1999) Extreme value theory as a risk management tool. N Am Actuar J 3(2):30–41

    MathSciNet  MATH  Google Scholar 

  • Escudero LF, Garín A, Merino M, Pérez G (2007) A two-stage stochastic integer programming approach as a mixture of branch-and-fix coordination and benders decomposition schemes. Ann Oper Res 152(1):395–420

    MathSciNet  MATH  Google Scholar 

  • Fama EF (1965) The behavior of stock-market prices. J Bus 38(1):34–105

    Google Scholar 

  • Fama EF, French KR (1993) Common risk factors in the returns on stocks and bonds. J Financ Econ 33(1):3–56

    MATH  Google Scholar 

  • Fama EF, French KR (2012) Size, value, and momentum in international stock returns. J Financ Econ 105(3):457–472

    Google Scholar 

  • Fleten S-E, Høyland K, Wallace SW (2002) The performance of stochastic dynamic and fixed mix portfolio models. Eur J Oper Res 140(1):37–49

    MathSciNet  MATH  Google Scholar 

  • Gaivoronski AA, Krylov S, van der Wijst N (2005) Optimal portfolio selection and dynamic benchmark tracking. Eur J Oper Res 163(1):115–131 (Financial Modelling and Risk Management)

    MathSciNet  MATH  Google Scholar 

  • Gao J, Li D (2013) Optimal cardinality constrained portfolio selection. Oper Res 61(3):745–761

    MathSciNet  MATH  Google Scholar 

  • Glasserman P, Xu X (2013) Robust portfolio control with stochastic factor dynamics. Oper Res 61(4):874–893

    MathSciNet  MATH  Google Scholar 

  • Glover F, Laguna M (1997) Tabu search. Kluwer Academic Publishers, Norwell

    MATH  Google Scholar 

  • Golub B, Holmer M, McKendall R, Pohlman L, Zenios SA (1995) A stochastic programming model for money management. Eur J Oper Res 85(2):282–296

    MATH  Google Scholar 

  • Greco S, Matarazzo B, Słowiński R (2013) Beyond Markowitz with multiple criteria decision aiding. J Bus Econ 83(1):29–60

    Google Scholar 

  • Grundy BD, Martin JSM (2001) Understanding the nature of the risks and the source of the rewards to momentum investing. Rev Financ Stud 14(1):29–78

    Google Scholar 

  • Gupta P, Inuiguchi M, Mehlawat MK, Mittal G (2013) Multiobjective credibilistic portfolio selection model with fuzzy chance-constraints. Inf Sci 229:1–17

    MathSciNet  MATH  Google Scholar 

  • Gupta P, Mehlawat MK, Saxena A (2010) A hybrid approach to asset allocation with simultaneous consideration of suitability and optimality. Inf Sci 180(11):2264–2285

    Google Scholar 

  • He F, Rong Q (2014) A two-stage stochastic mixed-integer program modelling and hybrid solution approach to portfolio selection problems. Inf Sci 289:190–205

    Google Scholar 

  • Higle JL, Wallace SW (2003) Sensitivity analysis and uncertainty in linear programming. Interfaces 33(4):53–60

    Google Scholar 

  • Høyland K, Kaut M, Wallace SW (2003) A heuristic for moment-matching scenario generation. Comput Optim Appl 24(2–3):169–185

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Huang C-F, Litzenberger RH (1988) Foundations for financial economics. North-Holland, New York

    MATH  Google Scholar 

  • IBM ILOG CPLEX V12.1 User’s Manual for CPLEX, (2009)

  • Jegadeesh N, Titman S (1993) Returns to buying winners and selling losers: implications for stock market efficiency. J Finance 48(1):65–91

    Google Scholar 

  • Jorion P (2006) Value at risk: the new benchmark for managing financial risk, 3rd edn. McGraw-Hill Education, New York

    Google Scholar 

  • Junior LS, Franca IDP (2012) Correlation of financial markets in times of crisis. Physica A 391(1–2):187–208

    Google Scholar 

  • Kall P, Wallace SW (1994) Stochastic programming. Wiley-interscience series in systems and optimization. Wiley, New York

    Google Scholar 

  • Kaut M, Wallace SW (2007) Evaluation of scenario-generation methods for stochastic programming. Pac J Optim 3(2):257–271

    MathSciNet  MATH  Google Scholar 

  • Kaut M, Wallace SW (2011) Shape-based scenario generation using copulas. CMS 8(1–2):181–199

    MathSciNet  Google Scholar 

  • Kaut M, Wallace SW, Vladimirou H, Zenios S (2007) Stability analysis of portfolio management with conditional value-at-risk. Quant Finance 7(4):397–409

    MathSciNet  MATH  Google Scholar 

  • Kearns P, Pagan A (1997) Estimating the density tail index for financial time series. Rev Econ Stat 79(2):171–175

    Google Scholar 

  • Kellerer H, Mansini R, Speranza MG (2000) Selecting portfolios with fixed costs and minimum transaction lots. Ann Oper Res 99(1):287–304

    MathSciNet  MATH  Google Scholar 

  • Wallace SW (2012) Modeling with stochastic programming. Springer series in operations research and financial engineering. Springer, New York

    Google Scholar 

  • King MA, Wadhwani S (1990) Transmission of volatility between stock markets. Rev Financ Stud 3(1):5–33

    Google Scholar 

  • Koedijk KG, Kool CJM (1992) Tail estimates of east european exchange rates. J Bus Econ Stat 10(1):83–96

    Google Scholar 

  • Konno H, Wijayanayake A (2001) Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Math Program 89(2):233–250

    MathSciNet  MATH  Google Scholar 

  • Krokhmal P, Palmquist J, Uryasev S (2002) Portfolio optimization with conditional value-at-risk objective and constraints. J Risk 4:11–27

    Google Scholar 

  • Lanne M, Meitz M, Saikkonen P (2017) Identification and estimation of non-Gaussian structural vector autoregressions. J Econom 196(2):288–304

    MathSciNet  MATH  Google Scholar 

  • Leland H (2000) Optimal portfolio implementation with transactions costs and capital gains taxes. Haas School of Business Technical Report

  • Li J, Xu J (2013) Multi-objective portfolio selection model with fuzzy random returns and a compromise approach-based genetic algorithm. Inf Sci 220:507–521 (Online Fuzzy Machine Learning and Data Mining)

    MathSciNet  MATH  Google Scholar 

  • Litterman B et al (2003) Modern investment management: an equilibrium approach, vol 246. Wiley, New York

    Google Scholar 

  • Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10

    Google Scholar 

  • Liu H (2004) Optimal consumption and investment with transaction costs and multiple risky assets. J Finance 59(1):289–338

    Google Scholar 

  • Lobo MS, Fazel M, Boyd S (2007) Portfolio optimization with linear and fixed transaction costs. Ann Oper Res 152(1):341–365

    MathSciNet  MATH  Google Scholar 

  • Longin FM (2000) From value at risk to stress testing: the extreme value approach. J Bank Finance 24(7):1097–1130

    Google Scholar 

  • Lwin K, Qu R (2013) A hybrid algorithm for constrained portfolio selection problems. Appl Intell 39(2):251–266

    Google Scholar 

  • Lwin KT, Qu R, MacCarthy BL (2017) Mean-var portfolio optimization: a nonparametric approach. Eur J Oper Res 260(2):751–766

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Markowitz HM (1991) Portfolio selection: efficient diversification of investments, 2nd edn. Wiley, New York

    Google Scholar 

  • Mausser H, Rosen D (1999) Beyond var: from measuring risk to managing risk. In: Proceedings of the IEEE/IAFE 1999 conference on computational intelligence for financial engineering (CIFEr 1999), pp 163–178

  • Metaxiotis K, Liagkouras K (2012) Multiobjective evolutionary algorithms for portfolio management: a comprehensive literature review. Expert Syst Appl 39(14):11685–11698

    Google Scholar 

  • Moral-Escudero R, Ruiz-Torrubiano R, Suárez A (2006) Selection of optimal investment portfolios with cardinality constraints. In Proceedings of the 2006 congress on evolutionary computation (CEC2006), pp 2382–2388

  • Moskowitz TJ, Grinblatt M (1999) Do industries explain momentum? J Finance 54(4):1249–1290

    Google Scholar 

  • Moskowitz TJ, Ooi YH, Pedersen LH (2012) Time series momentum. J Financ Econ 104(2):228–250 (Special Issue on Investor Sentiment)

    Google Scholar 

  • Mulvey JM, Rosenbaum DP, Shetty B (1999) Parameter estimation in stochastic scenario generation systems. Eur J Oper Res 118(3):563–577

    MATH  Google Scholar 

  • Mulvey JM, Vladimirou H (1992) Stochastic network programming for financial planning problems. Manag Sci 38(11):1642–1664

    MATH  Google Scholar 

  • Mulvey JM, Ziemba WT (1995) Handbooks in operations research and management science, volume Volume 9, chapter Chapter 15 Asset and liability allocation in a global environment. Elsevier, pp 435–463

  • Pflug GC (2000) Some remarks on the value-at-risk and the conditional value-at-risk. Probabilistic constrained optimization, vol 49. Springer, Berlin, pp 272–281

    MATH  Google Scholar 

  • Pritsker M (1997) Evaluating value at risk methodologies: accuracy versus computational time. J Financ Serv Res 12(2):201–242

    Google Scholar 

  • Quaranta AG, Zaffaroni A (2008) Robust optimization of conditional value at risk and portfolio selection. J Bank Finance 32(10):2046–2056

    Google Scholar 

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

    Google Scholar 

  • Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J Bank finance 26(7):1443–1471

    Google Scholar 

  • Rysz M, Vinel A, Krokhmal P, Eduardo P (2015) A scenario decomposition algorithm for stochastic programming problems with a class of downside risk measures. INFORMS J Comput 27(2):416–430

    MathSciNet  MATH  Google Scholar 

  • Shapiro JL (2002) The sensitivity of PBIL to its learning rate, and how detailed balance can remove it. In: Proceedings of the 7th workshop on foundations of genetic algorithms, Torremolinos, Spain, September 2-4, 2002, pp 115–132

  • Stoyan SJ, Kwon RH (2010) A two-stage stochastic mixed-integer programming approach to the index tracking problem. Optim Eng 11(2):247–275

    MathSciNet  MATH  Google Scholar 

  • Stoyan SJ, Kwon RH (2011) A stochastic-goal mixed-integer programming approach for integrated stock and bond portfolio optimization. Comput Ind Eng 61(4):1285–1295

    Google Scholar 

  • Szego G (2002) Measures of risk. J Bank Finance 26(7):1253–1272

    Google Scholar 

  • Topaloglou N, Vladimirou H, Zenios SA (2002) CVaR models with selective hedging for international asset allocation. J Bank Finance 26(7):1535–1561

    Google Scholar 

  • Topaloglou N, Vladimirou H, Zenios SA (2008) A dynamic stochastic programming model for international portfolio management. Eur J Oper Res 185(3):1501–1524

    MathSciNet  MATH  Google Scholar 

  • Uryasev S (2000) Introduction to the theory of probabilistic functions and percentiles (value-at-risk). In: Uryasev SP (ed) Probabilistic constrained optimization. Nonconvex optimization and its applications, vol 49. Springer, Berlin, pp 1–25

    MATH  Google Scholar 

  • Vassiadou-Zeniou C, Zenios SA (1996) Robust optimization models for managing callable bond portfolios. Eur J Oper Res 91(2):264–273

    MATH  Google Scholar 

  • Wagner WH, Arnott RD (1990) The measurement and control of trading costs. Financ Anal J 46(6):73–80

    Google Scholar 

  • Woodside-Oriakhi M, Lucas C, Beasley JE (2011) Heuristic algorithms for the cardinality constrained efficient frontier. Eur J Oper Res 213(3):538–550

    MathSciNet  MATH  Google Scholar 

  • Woodside-Oriakhi M, Lucas C, Beasley JE (2013) Portfolio rebalancing with an investment horizon and transaction costs. Omega 41(2):406–420 (Management science and environmental issues)

    Google Scholar 

  • Xidonas P, Mavrotas G, Hassapis C, Zopounidis C (2017) Robust multiobjective portfolio optimization: a minimax regret approach. Eur J Oper Res 262(1):299–305

    MathSciNet  MATH  Google Scholar 

  • Yamai Y, Yoshiba T et al (2002) Comparative analyses of expected shortfall and value-at-risk: their estimation error, decomposition, and optimization. Monet Econ Stud 20(1):87–121

    MATH  Google Scholar 

  • Yano H (2014) Fuzzy decision making for fuzzy random multiobjective linear programming problems with variance covariance matrices. Inf Sci 272:111–125

    MathSciNet  MATH  Google Scholar 

  • Yu L-Y, Ji X-D, Wang S-Y (2003) Stochastic programming models in financial optimization: a survey. Adv Model Optim 5(1)

  • Yu L, Wang S, Wu Y, Lai KK (2004) A dynamic stochastic programming model for bond portfolio management. In: Marian B, GeertDick van Albada PMAS, Jack D (eds) Computational science-ICCS 2004, volume 3039 of lecture notes in computer science. Springer, Berlin Heidelberg, pp 876–883

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science, The University of Nottingham Ningbo China, Ningbo, China

    Tianxiang Cui & Ruibin Bai

  2. School of Business and Research Academy of Belt & Road, Ningbo University, Ningbo, China

    Shusheng Ding

  3. School of Computer Science, The University of Nottingham, Nottingham, UK

    Andrew J. Parkes & Rong Qu

  4. Department of Computer Science, Faculty of Science and Technology, University of Westminster, London, UK

    Fang He

  5. Division of Computing Science and Mathematics, University of Stirling, Stirling, UK

    Jingpeng Li

Authors
  1. Tianxiang Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ruibin Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shusheng Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andrew J. Parkes
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Rong Qu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Fang He
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Jingpeng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tianxiang Cui.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Communicated by Y. Ni.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cui, T., Bai, R., Ding, S. et al. A hybrid combinatorial approach to a two-stage stochastic portfolio optimization model with uncertain asset prices. Soft Comput 24, 2809–2831 (2020). https://doi.org/10.1007/s00500-019-04517-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-019-04517-y

Keywords

Search

Navigation