Advanced Search
MyIDEAS: Login

A two-Factor Asset Pricing Model and the Fat Tail Distribution of Firm Sizes

Contents:

Author Info

  • Y. Malevergne
  • D. Sornette

Abstract

In the standard equilibrium and/or arbitrage pricing framework, the value of any asset is uniquely specified from the belief that only the systematic risks need to be remunerated by the market. Here, we show that, even for arbitrary large economies when the distribution of the capitalization of firms is sufficiently heavy-tailed as is the case of real economies, there may exist a new source of significant systematic risk, which has been totally neglected up to now but must be priced by the market. This new source of risk can readily explain several asset pricing anomalies on the sole basis of the internal-consistency of the market model. For this, we derive a theoretical two-factor model for asset pricing which has empirically a similar explanatory power as the Fama-French three-factor model. In addition to the usual market risk, our model accounts for a diversification risk, proxied by the equally-weighted portfolio, and which results from an ``internal consistency factor'' appearing for arbitrary large economies, as a consequence of the concentration of the market portfolio when the distribution of the capitalization of firms is sufficiently heavy-tailed as in real economies. Our model rationalizes the superior performance of the Fama and French three-factor model in explaining the cross section of stock returns: the size factor constitutes an alternative proxy of the diversification factor while the book-to-market effect is related to the increasing sensitivity of value stocks to this factor.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://arxiv.org/pdf/physics/0702027
File Function: Latest version
Download Restriction: no

Bibliographic Info

Paper provided by arXiv.org in its series Papers with number physics/0702027.

as in new window
Length:
Date of creation: Feb 2007
Date of revision:
Handle: RePEc:arx:papers:physics/0702027

Contact details of provider:
Web page: http://arxiv.org/

Related research

Keywords:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Xavier Gabaix, 2011. "The Granular Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(3), pages 733-772, 05.
  2. Ramsden, J.J. & Kiss-Haypál, Gy., 2000. "Company size distribution in different countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(1), pages 220-227.
  3. Chan, K C, 1988. "On the Contrarian Investment Strategy," The Journal of Business, University of Chicago Press, vol. 61(2), pages 147-63, April.
  4. Orietta Marsili, 2005. "Technology and the Size Distribution of Firms: Evidence from Dutch Manufacturing," Review of Industrial Organization, Springer, vol. 27(4), pages 303-328, December.
  5. Jones, Charles M & Kaul, Gautam, 1996. " Oil and the Stock Markets," Journal of Finance, American Finance Association, vol. 51(2), pages 463-91, June.
  6. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06.
  7. John Y. Campbell & Tuomo Vuolteenaho, 2003. "Bad Beta, Good Beta," NBER Working Papers 9509, National Bureau of Economic Research, Inc.
  8. Douglas K. Pearce & V. Vance Roley, 1985. "Stock Prices and Economic News," NBER Working Papers 1296, National Bureau of Economic Research, Inc.
  9. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, 09.
  10. Alexander, Gordon J. & Baptista, Alexandre M., 2002. "Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1159-1193, July.
  11. Sharpe, William F, 1991. " Capital Asset Prices with and without Negative Holdings," Journal of Finance, American Finance Association, vol. 46(2), pages 489-509, June.
  12. Lakonishok, Josef & Shleifer, Andrei & Vishny, Robert W, 1994. " Contrarian Investment, Extrapolation, and Risk," Journal of Finance, American Finance Association, vol. 49(5), pages 1541-78, December.
  13. Grinblatt, Mark & Titman, Sheridan, 1983. "Factor pricing in a finite economy," Journal of Financial Economics, Elsevier, vol. 12(4), pages 497-507, December.
  14. Anthony J. Richards, 1997. "Winner-Loser Reversals in National Stock Market Indices," IMF Working Papers 97/182, International Monetary Fund.
  15. Geske, Robert & Roll, Richard, 1983. " The Fiscal and Monetary Linkage between Stock Returns and Inflation," Journal of Finance, American Finance Association, vol. 38(1), pages 1-33, March.
  16. Blume, Marshall E, 1980. "Stock Returns and Dividend Yields: Some More Evidence," The Review of Economics and Statistics, MIT Press, vol. 62(4), pages 567-77, November.
  17. Huberman, Gur, 1982. "A simple approach to arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 28(1), pages 183-191, October.
  18. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
  19. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2005. "Institutional Investors and Stock Market Volatility," NBER Working Papers 11722, National Bureau of Economic Research, Inc.
  20. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
  21. Mark J. Flannery & Aris A. Protopapadakis, 2002. "Macroeconomic Factors Do Influence Aggregate Stock Returns," Review of Financial Studies, Society for Financial Studies, vol. 15(3), pages 751-782.
  22. John Y. Campbell & Christopher Polk & Tuomo Vuolteenaho, 2010. "Growth or Glamour? Fundamentals and Systematic Risk in Stock Returns," Review of Financial Studies, Society for Financial Studies, vol. 23(1), pages 305-344, January.
  23. Burmeister, Edwin & Wall, Kent D, 1986. "The Arbitrage Pricing Theo;ry and Macroeconomic Factor Measures," The Financial Review, Eastern Finance Association, vol. 21(1), pages 1-20, February.
  24. Ingersoll, Jonathan E, Jr, 1984. " Some Results in the Theory of Arbitrage Pricing," Journal of Finance, American Finance Association, vol. 39(4), pages 1021-39, September.
  25. Ferson, Wayne E & Harvey, Campbell R, 1993. "The Risk and Predictability of International Equity Returns," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 527-66.
  26. Ravi Jagannathan & Yong Wang, 2007. "Lazy Investors, Discretionary Consumption, and the Cross-Section of Stock Returns," Journal of Finance, American Finance Association, vol. 62(4), pages 1623-1661, 08.
  27. Bodie, Zvi, 1976. "Common Stocks as a Hedge against Inflation," Journal of Finance, American Finance Association, vol. 31(2), pages 459-70, May.
  28. Ravi Jagannathan & Zhenyu Wang, 1996. "The conditional CAPM and the cross-section of expected returns," Staff Report 208, Federal Reserve Bank of Minneapolis.
  29. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. " Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
  30. Narasimhan Jegadeesh, 2001. "Profitability of Momentum Strategies: An Evaluation of Alternative Explanations," Journal of Finance, American Finance Association, vol. 56(2), pages 699-720, 04.
  31. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
  32. Rubinstein, Mark E., 1973. "The Fundamental Theorem of Parameter-Preference Security Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(01), pages 61-69, January.
  33. Chopra, Navin & Lakonishok, Josef & Ritter, Jay R., 1992. "Measuring abnormal performance : Do stocks overreact?," Journal of Financial Economics, Elsevier, vol. 31(2), pages 235-268, April.
  34. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-52, September.
  35. Pearce, Douglas K & Roley, V Vance, 1983. " The Reaction of Stock Prices to Unanticipated Changes in Money: A Note," Journal of Finance, American Finance Association, vol. 38(4), pages 1323-33, September.
  36. Fama, Eugene F & French, Kenneth R, 1996. " Multifactor Explanations of Asset Pricing Anomalies," Journal of Finance, American Finance Association, vol. 51(1), pages 55-84, March.
  37. Chan, Louis K C & Jegadeesh, Narasimhan & Lakonishok, Josef, 1996. " Momentum Strategies," Journal of Finance, American Finance Association, vol. 51(5), pages 1681-1713, December.
  38. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  39. Harvey, Campbell R, 1991. " The World Price of Covariance Risk," Journal of Finance, American Finance Association, vol. 46(1), pages 111-57, March.
  40. Fama, Eugene F & French, Kenneth R, 1992. " The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-65, June.
  41. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Zoltan Kuscsik & Denis Horvath, 2007. "Statistical properties of agent-based market area model," Papers 0710.0459, arXiv.org.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:arx:papers:physics/0702027. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.