Financial Markets and Portfolio Management

, Volume 30, Issue 1, pp 19–61 | Cite as

Which stocks drive the size, value, and momentum anomalies and for how long? Evidence from a statistical leverage analysis

  • Kevin AretzEmail author
  • Marc Aretz


A large number of neoclassical, behavioral, and bias-based theories try to explain the tendency of small, value, and winner stocks to outperform big, growth, and loser stocks, three well-known characteristic anomalies. Because the theories often predict similar relationships between a stock’s propensity to contribute to the anomalies and a set of correlated firm characteristics, existing studies focusing on single theories do not tell us which theory is most successful in explaining the anomalies. To fill this gap, we use a new non-parametric methodology to run a horse race between the theories. In the first step, we use statistical leverage analysis to find out which stocks are ultimately responsible for the anomalies. In the second, we use the firm characteristics suggested by the theories to forecast the identity of the anomaly drivers, with the purpose of determining which theory is most supported by the data. We find that behavioral theories are most convincing in explaining the size and book-to-market anomalies, while no theory is convincing in explaining the momentum anomaly.


Characteristic anomalies Statistical leverage analysis Efficient markets 

JEL Classification

G11 G12 G15 



We are greatly indebted to Markus Schmid (the editor) and an anonymous referee for helping us to improve our work. We are also indebted to Behzet Cengiz, Massimo Guidolin, Peter Pope, Rüdiger von Nitzsch, as well as seminar participants at the ACATIS Value Conference in Frankfurt for their valuable and constructive comments and advice.


  1. Admati, A., Pfleiderer, P.: A theory of intraday patterns: volume and price variability. Rev. Financ. Stud. 1, 3–40 (1988)CrossRefGoogle Scholar
  2. Amihud, Y.: Illiquidity and stock returns: cross-section and time-series effects. J. Financ. Mark. 5, 31–56 (2002)CrossRefGoogle Scholar
  3. Aretz, K., Bartram, S.M., Pope, P.F.: Macroeconomic risks and characteristic-based factor models. J. Bank. Financ. 34, 1383–1399 (2010)CrossRefGoogle Scholar
  4. Avramov, D., Chordia, T., Jostova, G., Philipov, A.: Credit ratings and the cross-section of stock returns. J. Financ. Mark. 12, 469–499 (2009)CrossRefGoogle Scholar
  5. Avramov, D., Chordia, T., Jostova, G., Philipov, A.: Anomalies and financial distress. Emory Business School Working Paper Series (2011)Google Scholar
  6. Ball, R., Kothari, S.P., Shanken, J.: Problems in measuring portfolio performance: an application to contrarian investment strategies. J. Financ. Econ. 38, 79–107 (1995)CrossRefGoogle Scholar
  7. Banz, R.W.: The relationship between return and market value of common stocks. J. Financ. Econ. 9, 3–18 (1981)CrossRefGoogle Scholar
  8. Barberis, N., Shleifer, A., Vishny, R.: A model of investor sentiment. J. Financ. Econ. 49, 307–343 (1998)CrossRefGoogle Scholar
  9. Belsley, D.A., Kuh, E., Welsch, R.E.: Regression Analysis: Identifying Influential Data and Sources of Collinearity. Wiley, New York (1980)Google Scholar
  10. Berk, J.B., Green, R.C., Naik, V.: Optimal investment, growth options, and security returns. J. Financ. 54, 1153–1607 (1999)CrossRefGoogle Scholar
  11. Black, F.: Return and the beta. J. Portf. Manag. 20, 8–18 (1993)CrossRefGoogle Scholar
  12. Blume, M.E., Stambaugh, R.F.: Biases in computed returns: an application to the size effect. J. Financ. Econ. 12, 387–404 (1983)CrossRefGoogle Scholar
  13. Boguth, O., Carlson, M., Fisher, A., Simutin, M.: On horizon effects and microstructure bias in average returns and alphas. University of Toronto Working Paper Series (2011)Google Scholar
  14. Brennan, M.J., Subrahmanyam, A.: Market microstructure and asset pricing: on the compensation for illiquidity in stock returns. J. Financ. Econ. 41, 441–464 (1996)CrossRefGoogle Scholar
  15. Campbell, J., Hilscher, J., Szilagyi, J.: In search of distress risk. J. Financ. 63, 2899–2939 (2008)CrossRefGoogle Scholar
  16. Carhart, M.M.: On persistence in mutual fund performance. J. Financ. 52, 57–82 (1997)CrossRefGoogle Scholar
  17. Chan, K.C., Chen, N.F.: Structural and return characteristics of small and large firms. J. Financ. 46, 1467–1484 (1991)CrossRefGoogle Scholar
  18. Chan, K.C., Chen, N.F., Hsieh, D.A.: An explanatory investigation of the firm size effect. J. Financ. Econ. 14, 451–471 (1985)CrossRefGoogle Scholar
  19. Chan, L.K.C., Jegadeesh, N., Lakonishok, J.: Momentum strategies. J. Financ. 51, 1681–1713 (1996)CrossRefGoogle Scholar
  20. Chan, L.K.C., Karceski, J., Lakonishok, J.: The level and persistence of growth rates. J. Financ. 58, 643–684 (2003)CrossRefGoogle Scholar
  21. Chen, N.F., Roll, R., Ross, S.A.: Economic forces and the stock market. J. Bus. 59, 383–403 (1986)CrossRefGoogle Scholar
  22. Chordia, T., Shivakumar, L.: Momentum, business cycle, and time-varying expected returns. J. Financ. 57, 985–1019 (2002)CrossRefGoogle Scholar
  23. Cochrane, J.H.: Asset Pricing. Princeton University Press, New Jersey (2001)Google Scholar
  24. Cooper, M.J., Gutierrez, R.C., Hameed, A.: Market states and momentum. J. Financ. 59, 1345–1365 (2004)CrossRefGoogle Scholar
  25. Daniel, K., Titman, S.: Evidence on the characteristics of cross sectional variation in stock returns. J. Financ. 52, 1–33 (1997)CrossRefGoogle Scholar
  26. Daniel, K., Grinblatt, M., Titman, S., Wermers, R.: Measuring mutual fund performance with characteristic-based benchmarks. J. Financ. 52, 1035–1058 (1997)CrossRefGoogle Scholar
  27. Daniel, K., Hirshleifer, D., Subrahmanyam, A.: Investor psychology and security market under and over-reactions. J. Financ. 53, 1839–1885 (1998)CrossRefGoogle Scholar
  28. Davidson, R., MacKinnon, J.: Econometric Theory and Methods. Oxford University Press, New York (2004)Google Scholar
  29. Dichev, I.D.: Is the risk of bankruptcy a systematic risk? J. Financ. 53, 1131–1147 (1998)CrossRefGoogle Scholar
  30. Fama, E.F.: Foundations of Finance. Basic Books, New York (1976)Google Scholar
  31. Fama, E.F., French, K.R.: The cross-section of expected stock returns. J. Financ. 47, 427–465 (1992)CrossRefGoogle Scholar
  32. Fama, E.F., French, K.R.: Common risk factors in the returns on stocks and bonds. J. Financ. Econ. 33, 3–56 (1993)CrossRefGoogle Scholar
  33. Fama, E.F., French, K.R.: Size and book-to-market factors in earnings and returns. J. Financ. 50, 131–155 (1995)CrossRefGoogle Scholar
  34. Fama, E.F., MacBeth, J.D.: Risk, return, and equilibrium: empirical tests. J. Polit. Econ. 71, 607–636 (1973)CrossRefGoogle Scholar
  35. Garlappi, L., Shu, T., Yan, H.: Default risk, shareholder advantage and stock returns. Rev. Financ. Stud. 21, 2743–2778 (2008)CrossRefGoogle Scholar
  36. George, T.J., Hwang, C.-Y.: A resolution of the distress risk and leverage puzzles in the cross section of stock returns. J. Financ. Econ. 96, 56–79 (2010)CrossRefGoogle Scholar
  37. Griffin, J.M., Ji, S., Martin, J.S.: Momentum investing and business cycle risk: evidence from pole to pole. J. Financ. 58, 2515–2547 (2003)CrossRefGoogle Scholar
  38. Hahn, J., Lee, H.: Yield spreads as alternative risk factors for size and book-to-market. J. Financ. Quant. Stud. 41, 247–269 (2006)Google Scholar
  39. Hong, H., Stein, J.C.: A unified theory of underreaction, momentum trading, and overreaction in asset markets. J. Financ. 54(6), 2143–2184 (1999)CrossRefGoogle Scholar
  40. Jagannathan, R., Wang, Z.: The conditional CAPM and the cross-section of expected returns. J. Financ. 51, 3–53 (1996)CrossRefGoogle Scholar
  41. Jegadeesh, N., Titman, S.: Returns to buying winners and selling losers: implications for stock market efficiency. J. Financ. 48, 65–91 (1993)CrossRefGoogle Scholar
  42. Johnson, T.: Forecast dispersion and the cross section of expected returns. J. Financ. 59, 1957–1978 (2004)CrossRefGoogle Scholar
  43. Kaul, G., Nimalendran, M.: Price reversals: bid-ask errors or market overreaction. J. Financ. Econ. 28, 67–93 (1989)CrossRefGoogle Scholar
  44. Knez, P., Ready, M.: On the robustness of size and book-to-market in cross-sectional regressions. J. Financ. 52, 1355–1382 (1997)CrossRefGoogle Scholar
  45. Kothari, S., Shanken, J., Sloan, R.: Another look at the cross-section of expected returns. J. Financ. 50, 185–224 (1995)CrossRefGoogle Scholar
  46. Kyle, A.: Continuous auctions and insider trading. Econometrica 53, 1315–1335 (1985)CrossRefGoogle Scholar
  47. Lakonishok, J., Shleifer, A., Vishny, R.W.: Contrarian investment, extrapolation and risk. J. Financ. 49, 1541–1578 (1994)CrossRefGoogle Scholar
  48. Lambert, R., Leuz, C., Verrecchia, R.: Accounting information, disclosure, and the cost of capital. J. Account. Res. 45, 385–420 (2007)CrossRefGoogle Scholar
  49. La Porta, R.: Expectations and the cross-section of stock returns. J. Financ. 51, 1715–1742 (1996)CrossRefGoogle Scholar
  50. Lesmond, D., Ogden, J., Trzcinka, C.: A new estimate of transaction costs. Rev. Financ. Stud. 12, 1113–1141 (1999)CrossRefGoogle Scholar
  51. Lesmond, D.A., Schill, M.J., Zhou, C.: The illusory nature of momentum profits. J. Financ. Econ. 71, 349–380 (2004)CrossRefGoogle Scholar
  52. Lewellen, J., Nagel, S.: The conditional CAPM does not explain asset pricing anomalies. J. Financ. Econ. 82, 289–314 (2006)CrossRefGoogle Scholar
  53. Li, X., Brooks, C., Miffre, J.: The value premium and time-varying volatility. J. Bus. Financ. Account. 36, 1252–1272 (2009)CrossRefGoogle Scholar
  54. Malkiel, B.G., Xu, Y.: Idiosyncratic risk and security returns. University of Texas Working Paper Series (2006)Google Scholar
  55. Merton, R.C.: On the pricing of corporate debt: the risk structure of interest rates. J. Financ. 29, 449–470 (1974)Google Scholar
  56. Merton, R.C.: A simple model of capital market equilibrium with incomplete information. J. Financ. 42, 483–510 (1987)CrossRefGoogle Scholar
  57. Petersen, M.A.: Estimating standard errors in finance panel data sets: comparing approaches. Rev. Financ. Stud. 22, 435–480 (2009)CrossRefGoogle Scholar
  58. Petkova, R.: Do the Fama-and-French factors proxy for innovations in state variables? J. Financ. 61, 581–612 (2006)CrossRefGoogle Scholar
  59. Queen, M., Roll, R.: Firm mortality: using market indicators to predict survival. Financ. Anal. J. 43, 9–26 (1987)CrossRefGoogle Scholar
  60. Rosenberg, B., Reid, K., Lanstein, R.: Persuasive evidence of market inefficiency. J. Portf. Manag. 11, 9–17 (1985)CrossRefGoogle Scholar
  61. Rousseeuw, P.: Least median of squares regression. J. Am. Stat. Assoc. 79, 871–880 (1984)CrossRefGoogle Scholar
  62. Rousseeuw, P., Van Driessen, K.: Computing LTS regression for large data sets. Data Min. Knowl. Discov. 12, 29–45 (2006)CrossRefGoogle Scholar
  63. Shleifer, A., Vishny, R.W.: The limits of arbitrage. J. Financ. 52, 35–55 (1997)CrossRefGoogle Scholar
  64. Vassalou, M., Xing, Y.: Default risk in equity returns. J. Financ. 59, 831–868 (2004)CrossRefGoogle Scholar
  65. Wurgler, J., Zhuravskaya, E.: Does arbitrage flatten demand curves for stocks? J. Bus. 75, 583–608 (2002)CrossRefGoogle Scholar
  66. Xue, Y., Zhang, M.H.: Fundamental analysis, institutional investment, and limits to arbitrage. J. Bus. Financ. Account. 38, 1156–1183 (2011)CrossRefGoogle Scholar
  67. Zhang, X.F.: Information uncertainty and stock returns. J. Financ. 61, 105–136 (2006)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Accounting and Finance Division, Manchester Business SchoolThe University of ManchesterManchesterUK
  2. 2.Department of Economics and FinanceRWTH Aachen UniversityAachenGermany

Personalised recommendations