Optimization and Engineering

, Volume 18, Issue 2, pp 443–466 | Cite as

Factor-based robust index tracking

  • Roy H. Kwon
  • Dexiang Wu


We consider a robust optimization approach for the problem of tracking a benchmark portfolio. A strict subset of assets are selected from the benchmark such that the expected return is maximized subject to both risk and tracking error limits. A robust version of the Fama-French 3 factor model is developed whereby uncertatiny sets for the expected return and factor loading matrix are generated. The resulting model is a mixed integer second-order conic problem. Computational results in tracking the S&P 100 out of sample show that the robust model can generate tracking portfolios that have better tracking error and Sharpe ratio than those generated by the nominal model.


Index tracking Uncertainty Robust optimization Factor model 


  1. Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Op Res 23(4):769–805MathSciNetCrossRefMATHGoogle Scholar
  2. Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88(3):411–424MathSciNetCrossRefMATHGoogle Scholar
  3. Ben-Tal A, Margalit T, Nemirovski A (2000) Robust modeling of multi-stage portfolio problems. In: Frenk H, Roos K, Terlaky T, Zhang S (eds) High performance optimization, applied optimization, vol 33. Springer, US, pp 303–328CrossRefGoogle Scholar
  4. Bertsimas D, Pachamanova D (2008) Robust multiperiod portfolio management in the presence of transaction costs. Comput Oper Res 35(1):3–17MathSciNetCrossRefMATHGoogle Scholar
  5. Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev 53(3):464–501. doi: 10.1137/080734510 MathSciNetCrossRefMATHGoogle Scholar
  6. Birge JR, Louveaux F (2011) Introduction to stochastic programming. SpringerGoogle Scholar
  7. Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, New YorkCrossRefMATHGoogle Scholar
  8. Burmeister E, Roll R, Ross SA (2003) Using macroeconomic factors to control portfolio risk. Tech RepGoogle Scholar
  9. Canakgoz N, Beasley J (2009) Mixed-integer programming approaches for index tracking and enhanced indexation. Eur J Op Res 196(1):384–399MathSciNetCrossRefMATHGoogle Scholar
  10. Chang T, Meade N, Beasley J, Sharaiha Y (2000) Heuristics for cardinality constrained portfolio optimisation. Comput Op Res 27:1271–1302CrossRefMATHGoogle Scholar
  11. Chen C, Kwon RH (2012) Robust portfolio selection for index tracking. Comput Op Res 39(4):829–837MathSciNetCrossRefMATHGoogle Scholar
  12. Chen C, Li X, Tolman C, Wang S, Ye Y (2013) Sparse portfolio selection via quasi-norm regularization, working paperGoogle Scholar
  13. Chopra VK, Ziemba WT (1993) The effect of errors in means, variances, and covariances on optimal portfolio choice. J Portf Manag 19(2):6–11CrossRefGoogle Scholar
  14. Corielli F, Marcellino M (2006) Factor based index tracking. J Bank Financ 30(8):2215–2233Google Scholar
  15. Cornuejols G, Tutuncu R (2006) Optimization methods in finance. Finance and risk, Cambridge University Press, MathematicsGoogle Scholar
  16. D’ecclesia RL, Zenios SA (1994) Risk factor analysis and portfolio immunization in the italian bond market. J Fixed Income 4(2):51–58MathSciNetCrossRefGoogle Scholar
  17. Erdogan E, Goldfarb D, Iyengar G (2004) Robust portfolio management. Tech Report CORC TR-2004-11, IEOR, Columbia University, New YorkGoogle Scholar
  18. Fama E, French K (1993) Common risk factors in the returns on stocks and bonds. J Financ Econ 33(1):3–56CrossRefMATHGoogle Scholar
  19. Gulpinar N, Katata K, Pachamanova DA (2011) Robust portfolio allocation under discrete choice constraints. J Asset Manag 12:67–83CrossRefGoogle Scholar
  20. Goldfarb D, Iyengar G (2003) Robust portfolio selection problems. Math Op Res 28(1):1–38. doi: 10.1287/moor. MathSciNetCrossRefMATHGoogle Scholar
  21. Gurobi Optimization I (2015) Gurobi optimizer reference manualGoogle Scholar
  22. Jorion P (2003) Portfolio optimization with tracking error constraints. Financ Anal J 59(5):70–82CrossRefGoogle Scholar
  23. Karlow D, Rossbach P (2011) A method for robust index tracking. In: Hu B, Morasch K, Pickl S, Siegle M (eds) Operations research proceedings 2010. Operations research proceedings. Springer, Berlin Heidelberg, pp 9–14Google Scholar
  24. Kolbert F, Wormald L (2010) Robust portfolio optimization using second-order cone programmingGoogle Scholar
  25. Lejeune MA, Samatlı-Paç G (2013) Construction of risk-averse enhanced index funds. INFORMS J Comput 25(4):701–719MathSciNetCrossRefGoogle Scholar
  26. Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Op Res 43(2):264–281. doi: 10.1287/opre.43.2.264 MathSciNetCrossRefMATHGoogle Scholar
  27. Sadjadi SJ, Gharakhani M, Safari E (2012) Robust optimization framework for cardinality constrained portfolio problem. Appl Soft Comput 12(1):91–99CrossRefGoogle Scholar
  28. Tutuncu R, Koenig M (2004) Robust asset allocation. Annals Op Res 132(1–4):157–187MathSciNetCrossRefMATHGoogle Scholar
  29. Zenios SA (2006) Practical financial optimization: decision making for financial engineers. Blackwell, IncorporatedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringUniversity of TorontoOntarioCanada

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