Abstract
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.
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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):298–310
Avellaneda M, Lee J-H (2010) Statistical arbitrage in the US equities market. Quant Financ 10(7):761–782
Carhart MM (1997) On persistence in mutual fund performance. J Financ 52(1):57–82
Faff R (2004) A simple test of the Fama and French model using daily data: Australian evidence. Appl Financ Econ 14(2):83–92
Fama EF, French KR (1993) Common risk factors in the returns on stocks and bonds. J Financ Econ 33(1):3–56
Fama EF, French KR (1996) Multifactor explanations of asset pricing anomalies. J Financ 51(1):55–84
Fama EF, French KR (2004) The Capital Asset Pricing Model: theory and evidence. J Econ Perspect 18(3):25–46
Fama EF, French KR (2012) Size, value, and momentum in international stock returns. J Financ Econ 105(3):457–472
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):879–893
French KR (2014) Fama/French factors (weekly). http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_factors.html Accessed 17 Jan 2014
Galagedera DUA (2007) A review of capital asset pricing models. Manag Financ 33(10):821–832
Ganesan G (2011) A subspace approach to portfolio analysis: a focus on equity investments. IEEE Signal Process Mag 28(5):49–60
Gharghori P, Chan H, Faff R (2007) Are the Fama–French factors proxying default risk? Aust J Manag 32(2):223–249
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):172–214
Griffin JM (2002) Are the Fama and French factors global or country specific? Rev Financ Stud 15(3):783–803
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
Hao J, Naiman DQ (2007) Quantile regression. Sage Publications, London
IBM, ILOG CPLEX (2012). http://cran.r-project.org/web/packages/quantreg/quantreg.pdf. Accessed 17 Jan 2014
Kellerer H, Mansini R, Speranza MG (2000) Selecting portfolios with fixed costs and minimum transaction lots. Ann Oper Res 99:287–304
Koenker R (2013) Package ‘quantreg’. http://cran.r-project.org/web/packages/quantreg/quantreg.pdf. Accessed 17 Jan 2014
Koenker R, Bassett G (1978) Regression quantiles. Econometrica 46(1):33–50
Koenker R, Hallock KF (2001) Quantile regression. J Econ Perspect 15(4):143–156
Konno H, Koshizuka T (2005) Mean-absolute deviation model. IIE Trans 37(10):893–900
Konno H, Wijayanayake A (2001) Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Math Program Ser B 89(2):233–250
Konno H, Yamazaki H (1991) Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Manag Sci 37(5):519–531
Kwan CCY (1999) A note on market-neutral portfolio selection. J Bank Financ 23(5):773–799
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):13–37
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):281–296
Mansini R, Ogryczak W, Speranza MG (2003) On LP solvable models for portfolio selection. Informatica 14(1):37–62
Mansini R, Ogryczak W, Speranza MG (2014) Twenty years of linear programming based portfolio optimization. Eur J Oper Res 234(2):518–535
Markowitz H (1952) Portfolio selection. J Financ 7(1):77–91
Meade N, Beasley JE (2011) Detection of momentum effects using an index out-performance strategy. Quant Financ 11(2):313–326
Mezali H, Beasley JE (2013) Quantile regression for index tracking and enhanced indexation. J Oper Res Soc 64(11):1676–1692
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 York
Patton AJ (2009) Are “market neutral” hedge funds really market neutral? Rev Financ Stud 22(7):2495–2530
Rudolf M, Wolter H-J, Zimmermann H (1999) A linear model for tracking error minimization. J Bank Financ 23(1):85–103
Sharpe WF (1964) Capital asset prices: a theory of market equilibrium under conditions of risk. J Financ 19(3):425–442
Sharpe WF (1966) Mutual fund performance. J Bus 39(1):119–138
Sharpe WF (1975) Adjusting for risk in portfolio performance measurement. J Portf Manag 1(2):29–34
Sharpe WF (1994) The Sharpe ratio. J Portf Manag 21(1):49–58
Speranza MG (1996) A heuristic algorithm for a portfolio optimization model applied to the Milan stock market. Comput Oper Res 23(5):433–441
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimisation over continuous spaces. J Glob Optim 11(4):341–359
Treynor J (1961) Towards a theory of market value of risky assets. (Unpublished manuscript). doi:10.2139/ssrn.628187. Accessed 17 Jan 2014
Yu K, Lu Z, Stander J (2003) Quantile regression: applications and current research areas. Statistician 52(3):331–350
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The authors would like to acknowledge the comments made upon an earlier version of this paper by the referees.
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Valle, C.A., Meade, N. & Beasley, J.E. Factor neutral portfolios. OR Spectrum 37, 843–867 (2015). https://doi.org/10.1007/s00291-015-0392-0
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DOI: https://doi.org/10.1007/s00291-015-0392-0