1. Top of page

This is the first study that uses Merton's (1974) option pricing model to compute default measures for individual firms and assess the effect of default risk on equity returns. The size effect is a default effect, and this is also largely true for the book-to-market (BM) effect. Both exist only in segments of the market with high default risk. Default risk is systematic risk. The Fama–French (FF) factors SMB and HML contain some default-related information, but this is not the main reason that the FF model can explain the cross section of equity returns.

  • 1
  • 2

    For instance, many studies have shown that the yield spread between BAA and AAA corporate bond spread can predict expected returns in stocks and bonds. Such studies include those of Fama and Schwert (1977), Keim and Stambaugh (1986), Campbell (1987), and Fama and French (1989), among others. In addition, Chen, Roll, and Ross (1986), Fama and French (1993), Jagannathan and Wang (1996), and Hahn and Lee (2001) consider variations of the default spread in asset-pricing tests.

  • 3
  • 4

    For instance, Kwan (1996) shows that lagged stock returns can predict current bond yield changes. However, Hotchkiss and Ronen (2001) find that although the correlation between bond and stock returns is positive and significant, there is no causal relation between the two markets.

  • 5

    There are two main differences between our approach and the one used by KMV. They use a more complicated method to assess the asset volatility than we do, which incorporates Bayesian adjustments for the country, industry, and size of the firm. They also allow for convertibles and preferred stocks in the capital structure of the firm, whereas we allow only equity, as well as short- and long-term debt.

  • 6

    Our procedure also differs from the one used in KMV with respect to the way we calculate the distance to default. Whereas we use the formula that follows from the Black-Scholes model, KMV uses the one below: DD = (Market value of Assets − Default Point)/(Market value of Assets × Asset Volatility).

  • 7

    To obtain an idea of how sensitive our results would be to our choice about the proportion of long-term debt included in our calculations of DLI, we performed the following test. We examined the variation of the ratio of long-term debt to total debt across size and BM quintiles. If there is no substantial variation, our results should not be influenced by the choice we make. We find that there is virtually no variation across BM portfolios. There is a small variation across size portfolios, with the small firms having a somewhat smaller ratio than the big firms. However, the small firms have also a larger standard deviation than the big firms. Overall, the difference in the ratios is not deemed large enough to alter the qualitative results of the paper.

  • 8

    The SEC requires firms to report 10K within three months after the end of the fiscal year, but a small percentage of firms report it with a longer delay.

  • 9

    We thank Ken French for making the data available. Details about the data, as well as the actual data series, can be obtained from

  • 10

    See, “Rating Methodology: Moody's Public Firm Risk Model: A Hybrid Approach to Modeling Short Term Default Risk,” Moody's Investors Service, March 2000. The AC ratio is somewhat related to the Kolmogorov-Smirnov test.

  • 11

    For recent references, see for instance Chan, Hamao, and Lakonishok (1991) and Fama and French (1992).

  • 12

    This interpretation assumes that default risk is systematic, and therefore, not diversifiable. In Section V we test whether default risk is priced in the cross section of equity returns. Our results show that default risk is indeed priced, and therefore, it constitutes a systematic source of risk.

  • 13
  • 14

    The results presented in Section IV based on sequential sorts hold also when independent sorts are performed. To conserve space, we do not report those results here. The main insight offered by the independent sorts is that most small stocks are also high-DLI stocks, whereas most big stocks are low-DLI stocks. Similarly, most value stocks are high default risk stocks, whereas most growth stocks have low risk of default.

  • 15

    Note that, in principle, we could examine all three effects simultaneously, that is the size, BM, and default effects. This, however, would increase the parameters to be estimated considerably, at the expense of efficiency. For that reason, we concentrate on two effects at a time.

  • 16
  • 17

    For an interpretation of the HJ-distance as the maximum annualized pricing error, see Campbell and Cochrane (2000).

  • 18

    See Cochrane (2001), Section 13.5.

  • 19

    Vassalou (2003) shows, for instance, that a model which includes the market factor along with news about future GDP growth absorbs most of the priced information in SMB and HML. In the presence of news about future GDP growth in the pricing kernel, SMB and HML lose virtually all their ability to explain the cross section. Furthermore, Li, Vassalou, and Xing (2000) show that the investment component of GDP growth can price equity returns very well, and can completely explain the priced information in the Fama–French factors.


  1. Top of page
  • Aharony, Joseph, Charles P. Jones, and Itzhak Swary, 1980, An analysis of risk and return characteristics of bankruptcy using capital market data, Journal of Finance 35, 10011016.
  • Altman, Edward I, 1968, Financial ratios, discriminant analysis and the prediction of corporate bankruptcy, Journal of Finance 23, 589609.
  • Asquith, Paul, Robert Gertner, and David Sharfstein, 1994, Anatomy of financial distress: An examination of junk-bond issuers, Quarterly Journal of Economics 109, 625658.
  • Black, Fischer, and Myron Scholes, 1973, The pricing of options and corporate liabilities, Journal of Political Economy 81, 637659.
  • Campbell, John Y., 1987, Stock returns and the Term Structure, Journal of Financial Economics 18, 373399.
  • Campbell, John Y., and John H. Cochrane, 2000, Explaining the poor performance of consumption-based asset pricing models, The Journal of Finance 55, 28632879.
  • Campbell, John Y., and Martin Lettau, Burton G. Malkiel, and Yexiao Xu, 2001, Have individual stocks become more volatile? An empirical exploration of idiosyncratic risk, Journal of Finance 143.
  • Campbell, John Y., and Glen B. Taksler, 2003, Equity volatility and bond yields, Journal of Finance 58, 23212350.
  • Chan, Louis K.C., Yasushi Hamao, and Josef Lakonishok, 1991, Fundamentals and stock returns in Japan, The Journal of Finance 46, 17391764.
  • Chen, Nai-Fu, Richard Roll, and Stephen A. Ross, 1986, Economic forces and the stock market, Journal of Business 59, 383404.
  • Cochrane, John H., 2001, Asset Pricing (Princeton University Press, Princeton ).
  • Crosbie, Peter J., 1999, Modeling Default Risk (KMV LLC). Available at
  • Daniel, Kent, and Sheridan Titman, 1997, Evidence on the characteristics of cross-sectional variation in stock returns, Journal of Finance 52, 133.
  • Denis, David J., and Diane Denis, 1995, Causes of financial distress following leveraged re-capitalization, Journal of Financial Economics 27, 411418.
  • Dichev, Ilia D., 1998, Is the risk of bankruptcy a systematic risk? Journal of Finance 53, 11311148.
  • Dichev, Ilia D., and Joseph D. Piotroski, 2001, The long-run stock returns following bond ratings changes, Journal of Finance 56, 173204.
  • Duffee, Gregory, 1999, Estimating the price of default risk, Review of Financial Studies 12, 197226.
  • Duffie, Darrell, and Kenneth J. Singleton, 1995, Modeling term structures of defaultable bonds, Working paper, Stanford Graduate School of Business .
  • Duffie, Darrell, and Kenneth J. Singleton, 1997, An econometric model of the term structure of interest-rate swap yields, Journal of Finance 52, 12871321.
  • Elton, Edwin J., Martin J. Gruber, Deepak Agrawal, and Christopher Mann, 2001, Explaining the rate spread on corporate bonds, Journal of Finance 247277.
  • Fama, Eugene, and G. William. Schwert, 1977, Asset returns and inflation, Journal of Financial Economics 5, 115146.
  • Fama, Eugene F., and Kenneth R. French, 1989, Business conditions and expected returns on stocks and bonds, Journal of Financial Economics 25, 2349.
  • Fama, Eugene F., and Kenneth R. French, 1992, The cross-section of expected stock returns, Journal of Finance 47, 427465.
  • Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on bonds and stocks, Journal of Financial Economics 33, 356.
  • Fama, Eugene F., and Kenneth R. French, 1996, Multifactor explanations of asset pricing anomalies, Journal of Finance 5584.
  • Fama, Eugene F., and J. MacBeth, 1973, Risk, return, and equilibrium: Empirical tests, Journal of Political Economy 81, 607636.
  • Griffin, John M., and Michael L. Lemmon, 2002, Book-to-market equity, distress risk, and stock returns, Journal of Finance 57, 23172336.
  • Hahn, Jaehoon, and Hangyong Lee, 2001, An empirical investigation of risk and return under capital market imperfection, Working paper, Columbia Business School .
  • Hand, John R.M., Robert W. Holthausen, and Richard W. Leftwich, 1992, The effect of bond rating agency announcements on bond and stock prices, Journal of Finance 47, 733752.
  • Hansen, Lars P., 1982, Large sample properties of generalized method of moments estimators, Econometrica 50, 10291054.
  • Hansen, Lars P., and Ravi Jagannathan, 1997, Assessing specification errors in stochastic discount factor models, Journal of Finance 52, 557590.
  • Heston, Steve, and K. Geert Rouwenhorst, 1994, Does industrial structure explain the benefits of international diversification? Journal of Financial Economics 36, 327.
  • Holthausen, Robert W., and Richard W. Leftwich, 1986, The effect of bond rating changes on common stock prices, Journal of Financial Economics 17, 5789.
  • Hotchkiss, Edith S., 1995, Post-bankruptcy performance and management turnover, The Journal of Finance 50, 321.
  • Hotchkiss, Edith S., and Tavy Ronen, 2001, The informational efficiency of the corporate bond market: An intraday analysis, Review of Financial Studies 15, 13251354.
  • Jagannathan, Ravi, and Zhenyu Wang, 1996, The conditional CAPM and the cross-section of expected returns, Journal of Finance 51, 353.
  • Jarrow, Robert A., and Stuart M. Turnbull, 1995, Pricing derivatives on financial securities subject to credit risk, Journal of Finance 50, 5386.
  • Kealhofer, Stephen, Sherry Kwok, and Wenlong Weng, 1998, Uses and abuses of bond default rates, KMV Corporation . Available at http//
  • Keim, Donald B., and Robert F. Stambaugh, 1986, Predicting returns in the stock and bond markets, Journal of Financial Economics 17, 357390.
  • Kwan, Simon, 1996, Firm specific information and the correlation between individual stocks and bonds, Journal of Financial Economics 40, 6380.
  • Lando, David, 1998, On cox processes and credit risky securities, Review of Derivatives Research 2, 99120.
  • Li, Qing, Maria Vassalou, and Yuhang Xing, 2000, An investment-growth asset pricing model, Working paper, Columbia University .
  • Longstaff, Francis A., and Eduardo S. Schwartz, 1995, A simple approach to valuing risky fixed and floating rate debt, Journal of Finance 50, 789820.
  • Madan, Dilip B., and Haluk Unal, 1994, Pricing the risks of default, Working paper 94-16, Wharton School, University of Pennsylvania .
  • Merton, Robert C., 1974, On the pricing of corporate debt: The risk structure of interest rates, Journal of Finance 29, 449470.
  • Moulton, Wilbur N., and Howard Thomas, 1993, Bankruptcy as a deliberate strategy: Theoretical considerations and empirical evidence, Strategic Management Journal 14, 125135.
  • Newey, Whitney, and Kenneth West, 1987, A simple positive-definitive heteroskedasticity and autocorrelation consistent covariance matrix, Econometrica 55, 703708.
  • Nijman, Theo, Laurens Swinkels, and Marno Verbeek, 2002, Do countries or industries explain momentum in Europe? Working paper, Erasmus University of Rotterdam .
  • Ohlson, James, 1980, Financial ratios and the probabilistic prediction of bankruptcy, Journal of Accounting Research 18, 109131.
  • Opler, Tim, and Sheridan Titman, 1994, Financial distress and corporate performance, Journal of Finance 49, 10151040.
  • Roll, Richard, 1992, Industrial structure and the comparative behavior of international stock market indices, Journal of Finance 47, 342.
  • Sobehart, Jorge R., Roger M. Stein, Victoriya Mikityanskaya, and Li Li, 2000, Moody's public firm risk model: A hybrid approach to modeling short term default risk, Moody Investors Services .
  • Vassalou, Maria, 2003, News related to future GDP growth as a risk factor in equity returns, Journal of Financial Economics 68, 4773.
  • White, Halbert, 1980, A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity, Econometrica 48, 817838.
  • Zhou, Chunsheng, 1997, A jump-diffusion approach to modeling credit risk and valuing defaultable securities, Working paper 1997-15, Federal Reserve Board .