2.1 Data Description
Our sample consists of all NYSE/AMEX/NASDAQ ordinary common stocks from July 1964 to December 2008. We obtain monthly data on returns and market equity from the Center for Research in Security Prices (CRSP) database. Book equity and debt data are retrieved from the Compustat. Following Fama and French (1992), for the period from July of year t to June of t + 1, we use a firm’s market equity at the end of June of year t as its size, and together with the book equity at the end of December of year t− 1 to construct the book-to-market ratio. Book-leverage is calculated as the ratio of book value of debt to total assets, while market-leverage is calculated as the ratio of book value of debt to the sum of market equity and book value of debt at the end of December of year t− 1. To be included in our sample, we require a firm to have at least 24 monthly returns between January of year t− 5 and December of year t− 1 to calculate the ex ante factor loadings for individual stocks. As in Fama and French (1992), we exclude financial firms and stocks with negative book equity from our sample.
To calculate Ferguson and Shockley’s (2003) D/E and Z factors (denoted as RD/E and RZ), we retrieve the required accounting variables from the Compustat. The two factors are constructed over the period from July 1964 to December 2008. The detail of the portfolio formation process is presented in the Appendix.
2.2 Do Leverage Premia Exist?
Based on the data constructed in Section 2.1, we examine whether stock returns are related to firm leverage. More specifically, we examine whether there exist significant
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premia for book-leverage and market-leverage, respectively. To do so, we construct characteristic-sorted portfolios by following a procedure similar to the one used by Fama and French (1992). From July of year t to June of year t+1, individual stocks are sorted into five quintile portfolios according to their corresponding market-leverage (or book-leverage) at the end of December of year t− 1. The breakpoints are determined using all NYSE firms in the sample. From July of year t to June of year t + 1, we calculate the equally-weighted monthly returns on these portfolios. The portfolios are rebalanced once a year in June.
[Insert Table 1 about here]
Panel A of Table 1 presents average monthly returns for book-leverage sorted portfo-lios, and return spreads between the most-levered quintile portfolio and the least-levered quintile portfolio (P 5-P 1) for the full period, and two subperiods before and after 1980.
The cutoff point is chosen because George and Hwang (2010) find that the book-leverage premium is is only significantly different from zero in the post-1980 period. Consistent with George and Hwang (2010), our reported premia for high minus low book-leverage are 0.172% (with a tstatistic of 1.56), 0.021% (with a tstatistic of 0.15), and -0.261% (with a t-statistic of -1.73) for 1964-2008, 1964-1980, and 1981-2008 periods, respectively. Panel B of Table 1 reports results for market-leverage-sorted portfolios Unlike book-leverage premia, market-leverage premia for the full sample and two sub-periods are all significant. The P 5-P 1 spreads are 0.497 (with a t-statistic of 2.80), 0.443 (with a t-statistic of 1.83), and 0.529 (with a t-statistic of 2.20), respectively.
Thus, we confirm the existence of both book-leverage premia and market-leverage premia in our sample. Among which, the negative relationship between book-leverage and stock returns holds only for the post-1980 period.
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2.3 Are Leverage Effects Independent of the Book-to-Market Effect?
Although there exist both book-leverage and market-leverage premia in our sample, Fama and French (1992) argue that the BM captures both book-leverage and market-leverage anomalies in the Fama-MacBeth cross-sectional regression. They observe sim-ilar slopes in absolute values but with opposite signs for book-leverage and market-leverage variables. Furthermore, they show that the BM slope is close in absolute value to both slopes for the two leverage variables, and conclude that the combination of book-leverage effect and market-leverage effect is an equivalent way to interpret the BM effect in stock returns.
To further clarify the relation between leverage effects and the BM effect, we examine whether Fama and French’s (1992) argument holds true in our sample. Similar to Fama and French (1992), we take logarithm form for all explanatory variables. Slightly different from Fama and French (1992), we use the debt-to-equity ratios, instead of the asset-to-equity ratios, as the leverage variables.2
[Insert Table 2 about here]
As reported in Model (1) of Table 2, the coefficients on the natural logarithm of the leverage variables, Ln(BLev) and Ln(MLev), are -0.476 (t-statistic = -7.80) and 0.430 (t-statistic = 5.80), respectively. An additional test on Ln(BLev)+Ln(MLev) is also provided in the bottom row of Table 2. Conceptually, if BM captures the informational content of both book-leverage and market-leverage, the sum of the coefficients on the two leverage variables should not be significantly different from zero. The insignificant value of -0.045 (t-statistic = -0.99) confirms such a conjecture. As presented in Model
2We obtain similar results by using asset-to-equity ratios as proxies for leverage, as employed by Fama and French (1992).
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(2), the results are largely the same when firm size, Ln(Size), is included in the regres-sion, where the test statistic on Ln(BLev)+Ln(MLev) is -0.065 (t-statistic = -1.50).
Moreover, coefficients on BM reported in Models (3) and (4) are both significant, and are quantitatively similar to the absolute values of the coefficients on the two leverage variables.
Overall, we have documented two stylized facts. First, we find that stock returns are related to both book-leverage and market-leverage in our data. Second, the two leverage effects in combination is not independent of the BM effect, suggesting that they are not new anomalies beyond the BM effect. However, an intriguing question remains as to what driving forces are behind the leverage effects, risk-based or behavioral-based?
And, if there is a common force that drives both leverage effects, does it also explain the BM anomaly? We offer more detailed discussions of these questions in Section 3 and Section 4.