Results in Fama and French (1992) and Chen and Zhang (1998), as well as those con-veyed in Table 2 of this paper, indicate that BM may contain information of both book-leverage and market-leverage effects. Since empirical evidence in Section 3 sug-gests that book-leverage and market-leverage, as separate effects, are both explained by Ferguson and Shockley’s (2003) three-factor model, it is of interest to examine whether Ferguson and Shockley’s (2003) three-factor model can also explain the size-BM-related characteristic model. Such an investigation is important because Daniel and Titman (1997) find that size and BM, as proxies for leverage and distress, support the character-istic model against Fama and French’s (1993) three-factor model. We hypothesize that Daniel and Titman’s (1997) result may be due to mis-measured factor risk using Fama and French’s (1993) model. In other words, if relative leverage and distress can really
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capture mis-measured market risk, as argued by Ferguson and Shockley (2003), we ex-pect Daniel and Titman’s (1997) characteristic model would be rejected by Ferguson and Shockley’s (2003) model.
To explore this possibility, we replicate the testing procedure described in Section 3.1 but with size and BM as the alternative characteristic model. That is, we form 45 portfolios by sorting firms according to size, BM, and RD/E slopes (di). Likewise, we construct characteristic-balanced portfolios by investing a one-dollar long position in the high (fourth and fifth) di portfolios, and a one-dollar short position in the low (first and second) di portfolios within each of the nine size-BM-sorted groupings, and perform time-series regression of Equation (4) for the combined portfolio , (Hh− Lh)p. The estimation results are given in Table 7. Average returns of the combined portfolio are all positive, although insignificant, for the full period and two subperiods. The estimated intercepts for Equation (4) are 0.081 (t-statistic = 1.05), 0.066 (t-statistic = 0.69), and 0.107 (t-statistic = 1.04) for 1964-2008, 1964-1980, and 1981-2008. Thus, tests of intercepts confirm our conjecture that the size-BM-based characteristic model is rejected by Ferguson and Shockley’s (2003) model.
[Insert Table 7 about here]
To further examine whether Daniel and Titman’s (1997) results are due to the prob-lem of using Fama and French’s three-factor model that may mis-measure leverage/distress-related factor risk, we provide a parallel test based on their settings. For that purpose, we briefly describe Daniel and Titman’s testing procedure as follows. First, test port-folios are formed on size, BM, and loadings on Fama and French’s (1993) three factors.
Then, the combined characteristic-balanced portfolio, (Hh−Lh)DTp , is formed based on similar size and BM controlling for loadings on Fama-French factors. Daniel and Tit-man (1997) show that the estimated intercept for the following regression is significantly
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negative,5
(Hh− Lh)DTp,t = ap+ bpRM KT,t+ spRSM B,t+ hpRHM L,t+ εp,t. (6)
Daniel and Titman (1997) argue that the negative intercept indicates that aver-age return of the combined portfolio is too low relative to the prediction of Fama and French’s (1993) three-factor model. If Ferguson and Shockley’s (2003) model is really priced, we expect that it can also correctly predict average return of the (Hh− Lh)DTp
portfolio. In that case, the intercept from the following regression should not be signif-icantly different from zero:
(Hh− Lh)DTp,t = ap+ bpRM KT,t+ dpRD/E,t+ zpRZ,t+ εp,t. (7)
Estimation results of Table 8 confirm our conjecture. We provide results for port-folios formed on MKT, SMB, and HML loadings in Panels A, B, and C for different sample periods, including the full, pre-1980, post-1980 periods, and the 1973-1993 pe-riod used by Daniel and Titman (1997). The estimated intercepts for Equation (6) are significantly negative for most cases, especially for Daniel and Titman’s (1997) period.
However, the estimated intercepts for Equation (7) are all insignificantly different from zero, even for the 1973-1993 period examined in Daniel and Titman, for which the esti-mated intercepts are -0.136 (t-statistic = -1.04), -0.159 (t-statistic = -1.58), and -0.184 (t-statistic = -1.64) for combined portfolios formed by MKT, SMB, and HML loadings, respectively.
5Here the superscript of DT means Daniel and Titman’s (1997) setting to avoid confusion with the notations used in this paper. In addition, it should be noted that the intercept is positive in Daniel and Titman’s (1997) original paper because their characteristic-balanced portfolios are formed by a long position in the low factor loading portfolios and a short position in the high factor loading portfolios.
Here the portfolios are the reverse of the portfolios in Daniel and Titman (1997), thus the intercept takes the inverse signs. Our setting is consistent with Davis, Fama, and French (2000) and Daniel, Titman, and Wei (2001).
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[Insert Table 8 about here]
To further understand why we observe insignificant intercepts for regressions with Ferguson and Shockley’s (2003) model, we take a closer look at the regression coefficients obtained from Equation (7). The combined balanced portfolio which has positive ex-ante MKT loadings, has significantly positive ex-post loadings on both MKT and SMB factors for regressions with Fama and French’s (1993) model, as reported in Panel A. Since the realized risk premia for the two factors (MKT and SMB) are positive, the intercept is negative to offset the positive return premia implied by the product of the positive MKT and SMB loadings and the positive expected MKT and SMB returns, which leads to Daniel and Titman’s (1997) contention that Fama and French’s (1993) model is rejected. However, for the regressions with Ferguson and Shockley’s (2003) model, the MKT and RD/E coefficients for the combined balanced portfolio with positive ex-ante MKT loadings are positive and negative, respectively. The negative ex-post RD/E loading suggests a negative relation between MKT and RD/E factors.
Indeed, Ferguson and Shockley (2003) has demonstrated that the market portfolio is negatively related to the leverage factor, as presented in their Table II on page 2565. As a result, our insignificant intercept from estimating Equation (7) is due to the negative ex-post loadings on the RD/E factor, given that Ferguson and Shockley’s (2003) model is a more appropriate model in describing stock returns.
The story also applies for the HML-sorted portfolios, as reported in Panel C. Since the HML factor is positively (negatively) related to the RD/E (RZ) factor, we observe positively (negatively) ex-post RD/E (RZ) loadings for regressions with Ferguson and Shockley’s (2003) model. As a result, the negative RZ return premia implied by the product of the negative RZ loadings and the positive expected RZ returns offsets the positive RD/E return premia implied by the product of the positive RD/E loadings and the positive expected RZ returns, leading to an insignificant intercept.
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The result for the SMB-sorted portfolios reported in Panel B, on the other hand, is not so consistent as those for the HML-sorted portfolios, and deserves some further discussion. Subsample analyses from Panel B suggest that individual stocks’ ex-ante SMB loadings have different signs on ex-post RD/E and RZfactors for pre- and post-1980 samples, suggesting possible structural change on individual stock’s SMB loadings. This is not surprising because Horowitz, Loughran, and Savin (2000) and Schwert (2002) both find that the size anomaly is not as robust as the BM effect in the U.S. stock market, and is disappearing after 1980. For the pre-1980 period, we find that the SMB-sorted (Hh− Lh)DT portfolio loads positively on the RD/E factor, and negatively on the RZ factor. The negative RZ loading thus offsets the positive return premium implied by the positive return premia on RD/E and MKT, leading to the insignificant intercept. It is also the case for Daniel and Titman’s (1997) 1973-1993 sample.
Overall, our results suggest that the BM effect, as a combination of book- and market-leverage effects, along with the size effect, is still rejected by Ferguson and Shockley’s (2003) model. Furthermore, we argue that Daniel and Titman’s (1997) result is due to the use of an asset-pricing model with possible mis-measured factor risk. By using Ferguson and Shockley’s (2003) model, which captures firms’ relative leverage and relative distress, as the alternative factor model, we show that Daniel and Titman’s (1997) characteristic model is rejected.