Review of Quantitative Finance and Accounting

, Volume 45, Issue 2, pp 337–362

Testing index-based models in U.K. stock returns

  • J. Richard Davies
  • Jonathan Fletcher
  • Andrew Marshall
Original Research


We examine whether index-based models similar to Cremers et al. (Crit Financ Rev 2:1–48, 2012) are more effective in explaining cross-sectional U.K. stock returns than the more traditional Fama and French (J Financ Econ 33:3–56, 1993) and Carhart (J Financ 52:57–82, 1997) factor models using the two-pass cross-sectional regression approach. We find that the seven-index model has the highest cross-sectional R2 across all models. However the superior performance of the seven-index model relative to the Fama and French (1993) and Carhart (1997) models is not robust in the multiple model comparison tests of Kan et al. (Rev Financ Stud 22:3449–3490, 2013). For these models and a conditional version of the Fama and French (1993) model, we cannot reject the null hypothesis that these models perform as least as well as the other competing models. In contrast, the four-index model of Cremers et al. (2012) performs poorly relative to the competing models. Our results suggest there is little benefit in using the seven-index model as an alternative to the Carhart (1997) model in practical applications that require the estimation of expected returns.


Index-based models Cross-sectional R2 Model misspecification 

JEL Classification

G11 G12 


  1. Al-Horani A, Pope PF, Stark AW (2003) Research and development activity and expected returns in the United Kingdom. Eur Financ Rev 7:27–46CrossRefGoogle Scholar
  2. Ang A, Liu J, Schwarz K (2010) Using stocks or portfolios in tests of factor models. Working Paper, Columbia UniversityGoogle Scholar
  3. Antoniou A, Garrett I, Priestley R (1998) Macroeconomic variables as common pervasive risk factors and the empirical content of the arbitrage pricing theory. J Empir Financ 5:221–240CrossRefGoogle Scholar
  4. Bekaert G, Hodrick RJ, Zhang X (2009) International stock return comovements. J Financ 64:2591–2626CrossRefGoogle Scholar
  5. Black F, Jensen MC, Scholes M (1972) The capital asset pricing model: some empirical findings. In: Jensen MC (ed) Studies in the theory of capital markets. Praeger, New YorkGoogle Scholar
  6. Campbell JY (1996) Understanding risk and return. J Political Econ 104:298–345CrossRefGoogle Scholar
  7. Carhart MM (1997) Persistence in mutual fund performance. J Financ 52:57–82CrossRefGoogle Scholar
  8. Chan LKC, Dimmock SG, Lakonishok J (2009) Benchmarking money manager performance: issues and evidence. Rev Financ Stud 22:4553–4599CrossRefGoogle Scholar
  9. Chen X, Ludvigson S (2009) Land of addicts? An empirical investigation of habit-based asset pricing models. J Appl Econom 24:1057–1093CrossRefGoogle Scholar
  10. Chordia T, Goyal A, Shanken J (2012) Cross-sectional asset pricing with individual stocks. Working Paper, Emory UniversityGoogle Scholar
  11. Chou PH, Ho PH, Ko KC (2012) Do industries matter in explaining stock returns and asset-pricing anomalies? J Bank Financ 36:355–370CrossRefGoogle Scholar
  12. Cochrane JH (1996) A cross-sectional test of an investment based asset pricing model. J Political Econ 104:572–621CrossRefGoogle Scholar
  13. Cochrane JH (2005) Asset pricing: revised edition. Princeton University Press, Princeton NJGoogle Scholar
  14. Connor G, Korajczyk RA (1986) Performance measurement with the arbitrage pricing theory: a new framework for analysis. J Financ Econ 15:373–394CrossRefGoogle Scholar
  15. Connor G, Korajczyk RA (1987) Estimating pervasive economic factors with missing observations. Working Paper, Northwestern UniversityGoogle Scholar
  16. Connor G, Korajczyk RA (1991) The attributes, behavior, and performance of U.S. mutual funds. Rev Quant Financ Account 1:5–26CrossRefGoogle Scholar
  17. Cremers M, Petajisto A, Zitzewitz E (2012) Should benchmark indices have alpha? Revisiting performance evaluation. Crit Financ Rev 2:1–48CrossRefGoogle Scholar
  18. Dimson E, Marsh PR (2001) U.K. financial market returns 1955–2000. J Bus 74:1–31CrossRefGoogle Scholar
  19. Dimson P, Nagel S, Quigley G (2003) Capturing the value premium in the U.K. 1955–2001. Financ Anal J 5559:35–45CrossRefGoogle Scholar
  20. Dittmar RF (2002) Nonlinear pricing kernels, kurtosis preference and cross-section of equity returns. J Financ 57:369–403CrossRefGoogle Scholar
  21. Fama EF, French KR (1993) Common risk factors in the returns on stocks and bonds. J Financ Econ 33:3–56CrossRefGoogle Scholar
  22. Fama EF, French KR (2010) Luck versus skill in the cross section of mutual fund returns. J Financ 65:1915–1947CrossRefGoogle Scholar
  23. Fama EF, French KR (2012) Size, value, and momentum in international stock returns. J Financ Econ 105:457–472CrossRefGoogle Scholar
  24. Fama EF, MacBeth JD (1973) Risk, return, and equilibrium: empirical tests. J Political Econ 71:607–636CrossRefGoogle Scholar
  25. Fletcher J (2001) An examination of alternative factor models in UK stock returns. Rev Quant Financ Account 16:117–130CrossRefGoogle Scholar
  26. Fletcher J (2007) Can asset pricing models price idiosyncratic risk in U.K. stock returns? Financ Rev 42:507–535CrossRefGoogle Scholar
  27. Fletcher J (2010) Arbitrage and the evaluation of linear factor models in U.K. stock returns. Financ Rev 45:449–468CrossRefGoogle Scholar
  28. Fletcher J (2013) Benchmark models of expected returns in U.K. portfolio performance: an empirical investigation. International Review of Economics and Finance, forthcomingGoogle Scholar
  29. Fletcher J, Kihanda J (2005) An examination of alternative CAPM Based models in U.K. stock returns. J Bank Financ 29:2995–3014CrossRefGoogle Scholar
  30. Florackis C, Gregorious A, Kostakis A (2011) Trading frequency and asset pricing on the London stock exchange: evidence from a new price impact ratio. J Bank Financ 35:3335–3350CrossRefGoogle Scholar
  31. Gao P, Huang KXD (2008) Aggregate consumption-wealth ratio and the cross-section of stock returns: some international evidence. Ann Econ Financ 9:1–37Google Scholar
  32. Gospodinov N, Robotti C (2013) Asset pricing theories, models, and tests. In: Baker HK, Filbeck MG (eds) Portfolio theory and management, chapter 3. Oxford University Press, OxfordGoogle Scholar
  33. Gospodinov N, Kan R, Robotti C (2012) On the Hansen-Jagannathan distance with a no-arbitrage constraint. Working Paper, University of TorontoGoogle Scholar
  34. Gospodinov N, Kan R, Robotti C (2013) Chi squared tests for evaluation and comparison of asset pricing models. J Econom 173:108–125CrossRefGoogle Scholar
  35. Gregory A, Michou M (2009) Industry costs of equity: UK evidence. J Bus Financ Account 36:679–704CrossRefGoogle Scholar
  36. 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 40:172–214Google Scholar
  37. Griffin JM (2002) Are the Fama and French factors global or country-specific? Rev Financ Stud 15:783–803CrossRefGoogle Scholar
  38. Hansen LP, Jagannathan R (1997) Assessing specification errors in stochastic discount factor models. J Financ 52:591–607Google Scholar
  39. Hou K, Karolyi GA, Kho BC (2011) What factors drive global stock returns? Rev Financ Stud 24:2527–2574CrossRefGoogle Scholar
  40. Hwang T, Gao S, Owen H (2012) A two-pass study of the CAPM: evidence from the UK stock market. Stud Econ Financ 29:89–104CrossRefGoogle Scholar
  41. Hyde S, Sherif M (2005) Consumption asset pricing models: evidence from the U.K. Manch Sch 73:343–363CrossRefGoogle Scholar
  42. Jagannathan R, Wang Z (1998) An asymptotic theory for estimating beta-pricing models using cross-sectional regression. J Financ 53:1285–1309CrossRefGoogle Scholar
  43. Jagannathan R, Skoulakis G, Wang Z (2010) The analysis of the cross section of security returns. In: Ait-Sahalia Y, Hansesn L (eds), Handbook of financial econometrics 2:73–134Google Scholar
  44. Jagannathan R, Marakani S, Takehara H, Wang Y (2012) Calendar cycles, infrequent decisions and the cross-section of stock returns. Manag Sci 58:507–522CrossRefGoogle Scholar
  45. Jones CS (2001) Extracting factors from heteroskedastic asset returns. J Financ Econ 62:293–325CrossRefGoogle Scholar
  46. Kan R, Robotti C (2009) Model comparison using the Hansen-Jagannathan distance. Rev Financ Stud 22:3449–3490CrossRefGoogle Scholar
  47. Kan R, Robotti C (2011) On the estimation of asset pricing models using univariate betas. Econ Lett 110:117–121CrossRefGoogle Scholar
  48. Kan R, Robotti C (2012) Evaluation of asset pricing models using two-pass cross-sectional regressions. In: Duan JC (eds), Handbook of computational finance 223–251Google Scholar
  49. Kan R, Zhou G (2004) Hansen-Jagannathan distance: geometry and exact distribution. Working Paper, University of TorontoGoogle Scholar
  50. Kan R, Robotti C, Shanken J (2013) Pricing model performance and the two-pass cross-sectional regression methodology. J Financ 68:2617–2649CrossRefGoogle Scholar
  51. Kandel S, Stambaugh RF (1995) Portfolio inefficiency and the cross-section of expected returns. J Financ 50:157–184CrossRefGoogle Scholar
  52. Kassimatis K (2011) Risk aversion with local risk seeking and stock returns: evidence from the UK market. J Bus Financ Acc 38:713–739CrossRefGoogle Scholar
  53. Lettau M, Ludvigson S (2001) Resurrecting the (C)CAPM: a cross-sectional test when risk premia are time-varying. J Political Econ 109:1238–1287CrossRefGoogle Scholar
  54. Lettau M, Ludvigson S (2010) Measuring and modelling variation in the risk-return tradeoff. In: Ait-Sahalia Y, Hansen L (eds) Handbook of financial econometrics 1:617–690Google Scholar
  55. Lewellen S, Nagel S (2006) The conditional CAPM does not explain asset-pricing anomalies. J Financ Econ 82:289–314CrossRefGoogle Scholar
  56. Lewellen J, Nagel S, Shanken J (2010) A skeptical appraisal of asset-pricing tests. J Financ Econ 96:175–194CrossRefGoogle Scholar
  57. Lewis KK (2011) Global asset pricing. Ann Rev Financ Econ 3:435–466CrossRefGoogle Scholar
  58. Li H, Xu Y, Zhang X (2010) Evaluating asset pricing models using the second Hansen-Jagannathan distance. J Financ Econ 97:279–301CrossRefGoogle Scholar
  59. Liu W, Strong N (2008) Biases in decomposing holding period portfolio returns. Rev Financ Stud 21:2243–2274CrossRefGoogle Scholar
  60. Ludvigson S (2013) Advances in consumption-based asset pricing: empirical tests. In: Constantinides G, Harris M, Stulz R (eds), Handbook of the economics of finance 2: 799–906Google Scholar
  61. Merton RC (1973) An intertemporal capital asset pricing model. Econometrica 41:867–888CrossRefGoogle Scholar
  62. Mouselli S, Michou M, Stark AW (2008) On the information content of the Fama and French factors in the UK. Working Paper, Manchester Business SchoolGoogle Scholar
  63. Nguyen D, Puri TN (2009) Higher-order systematic comoments and asset pricing: new evidence. Financ Rev 44:311–459Google Scholar
  64. Petkova R (2006) Do the Fama-French factors proxy for innovations in predictive variables. J Financ 61:581–612CrossRefGoogle Scholar
  65. Ross SA (1976) The arbitrage theory of capital asset pricing. J Econ Theory 13:341–360CrossRefGoogle Scholar
  66. Shanken J (1992) On the estimation of beta-pricing models. Rev Financ Stud 5:1–33CrossRefGoogle Scholar
  67. Shumway T (1997) The delisting bias in CRSP data. J Financ 52:327–340CrossRefGoogle Scholar
  68. Wang Z, Zhang X (2012) Empirical evaluation of asset pricing models: arbitrage and pricing errors in contingent claims. J Empir Financ 19:65–78CrossRefGoogle Scholar
  69. White H (1980) A heteroskedasticity consistent covariance matrix estimator and a direct test of heteroskedasticity. Econometrica 48:817–838CrossRefGoogle Scholar
  70. Wolak FA (1987) An exact test for multiple inequality and equality constraints in the linear regression model. J Am Stat Assoc 82:782–793CrossRefGoogle Scholar
  71. Wolak FA (1989) Testing inequality constraints in linear econometric models. J Econom 31:205–235CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • J. Richard Davies
    • 1
  • Jonathan Fletcher
    • 1
  • Andrew Marshall
    • 1
    • 2
  1. 1.Department of Accounting and FinanceUniversity of StrathclydeGlasgowUK
  2. 2.Department of Finance and Decision SciencesHong Kong Baptist UniversityKowloonChina

Personalised recommendations