OR Spectrum

, Volume 37, Issue 4, pp 843–867 | Cite as

Factor neutral portfolios

  • C. A. Valle
  • N. Meade
  • J. E. BeasleyEmail author
Regular Article


In this paper, we consider the problem of constructing a factor neutral portfolio (FNP). This is a portfolio of financial assets that exhibits performance independent from a number of underlying factors. We formulate this problem as a mixed-integer linear program, minimising the time-averaged absolute value factor contribution to portfolio return. In this paper, we investigate both ordinary (least-squares, mean) regression and quantile regression, specifically median regression, to estimate factor coefficients. Computational results are given for constructing FNPs using stocks drawn from the Standard and Poor’s 500 index.


Factor neutral portfolio Fama and French three-factor model Portfolio construction Quantile regression 



The authors would like to acknowledge the comments made upon an earlier version of this paper by the referees.


  1. Agrawal M, Mohapatra D, Pollak I (2012) Empirical evidence against CAPM: relating alphas and returns to betas. IEEE J Sel Top Signal Process 6(4):298–310CrossRefGoogle Scholar
  2. Avellaneda M, Lee J-H (2010) Statistical arbitrage in the US equities market. Quant Financ 10(7):761–782CrossRefGoogle Scholar
  3. Carhart MM (1997) On persistence in mutual fund performance. J Financ 52(1):57–82CrossRefGoogle Scholar
  4. Faff R (2004) A simple test of the Fama and French model using daily data: Australian evidence. Appl Financ Econ 14(2):83–92CrossRefGoogle Scholar
  5. Fama EF, French KR (1993) Common risk factors in the returns on stocks and bonds. J Financ Econ 33(1):3–56CrossRefGoogle Scholar
  6. Fama EF, French KR (1996) Multifactor explanations of asset pricing anomalies. J Financ 51(1):55–84CrossRefGoogle Scholar
  7. Fama EF, French KR (2004) The Capital Asset Pricing Model: theory and evidence. J Econ Perspect 18(3):25–46CrossRefGoogle Scholar
  8. Fama EF, French KR (2012) Size, value, and momentum in international stock returns. J Financ Econ 105(3):457–472CrossRefGoogle Scholar
  9. Fang Y, Lai KK, Wang S-Y (2006) Portfolio rebalancing model with transaction costs based on fuzzy decision theory. Eur J Oper Res 175(2):879–893CrossRefGoogle Scholar
  10. French KR (2014) Fama/French factors (weekly). Accessed 17 Jan 2014
  11. Galagedera DUA (2007) A review of capital asset pricing models. Manag Financ 33(10):821–832Google Scholar
  12. Ganesan G (2011) A subspace approach to portfolio analysis: a focus on equity investments. IEEE Signal Process Mag 28(5):49–60CrossRefGoogle Scholar
  13. Gharghori P, Chan H, Faff R (2007) Are the Fama–French factors proxying default risk? Aust J Manag 32(2):223–249CrossRefGoogle Scholar
  14. Gregory A, Tharyan R, Christidis A (2013) Constructing and testing alternative versions of the Fama–French and Carhart models in the UK. J Bus Financ Account 40(1–2):172–214Google Scholar
  15. Griffin JM (2002) Are the Fama and French factors global or country specific? Rev Financ Stud 15(3):783–803CrossRefGoogle Scholar
  16. Gupta P, Mehlawat MK, Saxena A (2010) A hybrid approach to asset allocation with simultaneous consideration of suitability and optimality. Inf Sci 180(11):2264–2285CrossRefGoogle Scholar
  17. Hao J, Naiman DQ (2007) Quantile regression. Sage Publications, LondonGoogle Scholar
  18. IBM, ILOG CPLEX (2012). Accessed 17 Jan 2014
  19. Kellerer H, Mansini R, Speranza MG (2000) Selecting portfolios with fixed costs and minimum transaction lots. Ann Oper Res 99:287–304CrossRefGoogle Scholar
  20. Koenker R (2013) Package ‘quantreg’. Accessed 17 Jan 2014
  21. Koenker R, Bassett G (1978) Regression quantiles. Econometrica 46(1):33–50CrossRefGoogle Scholar
  22. Koenker R, Hallock KF (2001) Quantile regression. J Econ Perspect 15(4):143–156CrossRefGoogle Scholar
  23. Konno H, Koshizuka T (2005) Mean-absolute deviation model. IIE Trans 37(10):893–900CrossRefGoogle Scholar
  24. Konno H, Wijayanayake A (2001) Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Math Program Ser B 89(2):233–250CrossRefGoogle Scholar
  25. Konno H, Yamazaki H (1991) Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Manag Sci 37(5):519–531CrossRefGoogle Scholar
  26. Kwan CCY (1999) A note on market-neutral portfolio selection. J Bank Financ 23(5):773–799CrossRefGoogle Scholar
  27. Lintner J (1965) The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev Econ Stat 47(1):13–37CrossRefGoogle Scholar
  28. Ma Y, MacLean L, Xu K, Zhao Y (2011) A portfolio optimization model with regime-switching risk factors for sector exchange traded funds. Pac J Optim 7(2):281–296Google Scholar
  29. Mansini R, Ogryczak W, Speranza MG (2003) On LP solvable models for portfolio selection. Informatica 14(1):37–62Google Scholar
  30. Mansini R, Ogryczak W, Speranza MG (2014) Twenty years of linear programming based portfolio optimization. Eur J Oper Res 234(2):518–535CrossRefGoogle Scholar
  31. Markowitz H (1952) Portfolio selection. J Financ 7(1):77–91Google Scholar
  32. Meade N, Beasley JE (2011) Detection of momentum effects using an index out-performance strategy. Quant Financ 11(2):313–326CrossRefGoogle Scholar
  33. Mezali H, Beasley JE (2013) Quantile regression for index tracking and enhanced indexation. J Oper Res Soc 64(11):1676–1692CrossRefGoogle Scholar
  34. Pai GAV, Michel T (2012) Differential evolution based optimization of risk budgeted equity market neutral portfolios. In: Proceedings of WCCI’12, IEEE world congress on computational intelligence (IEEE-WCCI). IEEE, New YorkGoogle Scholar
  35. Patton AJ (2009) Are “market neutral” hedge funds really market neutral? Rev Financ Stud 22(7):2495–2530CrossRefGoogle Scholar
  36. Rudolf M, Wolter H-J, Zimmermann H (1999) A linear model for tracking error minimization. J Bank Financ 23(1):85–103CrossRefGoogle Scholar
  37. Sharpe WF (1964) Capital asset prices: a theory of market equilibrium under conditions of risk. J Financ 19(3):425–442Google Scholar
  38. Sharpe WF (1966) Mutual fund performance. J Bus 39(1):119–138CrossRefGoogle Scholar
  39. Sharpe WF (1975) Adjusting for risk in portfolio performance measurement. J Portf Manag 1(2):29–34Google Scholar
  40. Sharpe WF (1994) The Sharpe ratio. J Portf Manag 21(1):49–58Google Scholar
  41. Speranza MG (1996) A heuristic algorithm for a portfolio optimization model applied to the Milan stock market. Comput Oper Res 23(5):433–441CrossRefGoogle Scholar
  42. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimisation over continuous spaces. J Glob Optim 11(4):341–359CrossRefGoogle Scholar
  43. Treynor J (1961) Towards a theory of market value of risky assets. (Unpublished manuscript). doi: 10.2139/ssrn.628187. Accessed 17 Jan 2014
  44. Yu K, Lu Z, Stander J (2003) Quantile regression: applications and current research areas. Statistician 52(3):331–350Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematical SciencesBrunel UniversityUxbridgeUK
  2. 2.Business SchoolImperial CollegeLondonUK
  3. 3.JB ConsultantsMordenUK

Personalised recommendations