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ABSTRACT

  1. Top of page
  2. ABSTRACT
  3. REFERENCES

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.

Footnotes
  • 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 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/

  • 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.

REFERENCES

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