Following Ferguson and Shockley’s (2003) methodology, we construct two factors asso-ciated with relative leverage (based on the ratio of debt-to-equity) and relative distress (based on Altman’s Z). In June of each year t, firms are assigned to one of three book debt-to-market equity (BD/ME) portfolios based on the 33% and 67% percentile cuts determined only from the NYSE firms in the sample. Independently and simultane-ously, firms are assigned to one of two Altman’s Z portfolios: Z ≤ 2.675 and Z > 2.675.
The Altman’s Z is defined as:
Z = 1.2× W C
T A + 1.4× RE
T A + 3.3× EBIT
T A + 0.6× M E
BD + 1.0× S T A,
where W C is net working capital, T A is total book assets, RE is retained earnings, BD is book debt, EBIT is earnings before interest and taxes, S is total sales revenue, and M E is market value of equity.
The intersection of the two sorts based on BD/ME and Z results in six portfolios as of June of each year. For July of t through June of t + 1, the return on each portfolio is calculated as the value-weighted average return of the stocks in the portfolio. As a result, we have six return series that cover the period from July 1964 to December 2008.
In each month t, RD/E is calculated as the simple average return of the two Z portfolios within the highly levered firms minus the simple average return of the two Z portfolios within the least levered firms. Similarly, RZ is the simple average return of the three D/E portfolios within high-Z firms minus the simple average return of the three D/E portfolios within the low-Z firms.
21
References
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Chou, P.-H. and K.-C. Ko (2008). Characteristics, covariances, and structural breaks.
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Fama, E. F. and K. R. French (1998). Value versus growth: The international evi-dence. Journal of Finance 53, 1975–2000.
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Ferguson, M. F. and R. L. Shockley (2003). Equilibrium “anomalies”. Journal of Finance 58, 2549–2580.
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974. Amsterdam: North Holland.
23
Table 1: Average monthly returns of leverage sorted portfolios
This table reports average monthly returns (in %) on five quintile portfolios (P 1 to P 5) sorted by book leverage and market leverage for all NYSE, AMEX and NASDAQ stocks over the period from July 1964 to December 2008.
Individual stocks are sorted into five quintile portfolios according to their corresponding book- or market-leverage.
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. Panel A reports monthly returns for portfolios formed by book-leverage, while Panel B reports monthly returns for portfolios formed by market-leverage. Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. * denotes significance at the 10% level, ** denotes significance at the 5% level, and *** denotes significance at the 1% level.
Portfolio P 1 P 2 P 3 P 4 P 5 P 5-P 1
Panel A: Portfolios sorted by book-leverage
1964-2008 1.255 *** 1.243 *** 1.227 *** 1.161 *** 1.083 *** -0.172
(3.96) (4.23) (4.24) (4.15) (3.19) (-1.56)
1964-1980 1.525 *** 1.467 *** 1.401 *** 1.295 ** 1.504 ** -0.021
(3.20) (3.02) (2.70) (2.57) (2.59) (-0.15)
1981-2008 1.096 *** 1.111 *** 1.124 *** 1.083 *** 0.835 ** -0.261 *
(2.63) (3.02) (3.30) (3.29) (2.03) (-1.73)
Panel B: Portfolios sorted by market-leverage
1964-2008 0.974 *** 1.213 *** 1.275 *** 1.284 *** 1.471 *** 0.497 ***
(2.90) (4.05) (4.46) (4.52) (4.43) (2.80)
1964-1980 1.321 *** 1.401 *** 1.313 *** 1.339 *** 1.764 *** 0.443 *
(2.63) (2.72) (2.62) (2.73) (3.08) (1.83)
1981-2008 0.769 * 1.101 *** 1.253 *** 1.252 *** 1.298 *** 0.529 **
(1.74) (3.02) (3.65) (3.64) (3.23) (2.20)
24
Table 2: Fama-MacBeth regressions
This table reports regression results for all NYSE, AMEX and Nasdaq common stocks with non-negative BM values over the period from July 1964 to December 2008. For returns from July of year t to June of t + 1, we match them with the natural logarithm of a firm’s market equity, Ln(Size), at the end of June of year t, the natural logarithm of its book equity to market equity, Ln(BM), at the end of December of year t− 1, the natural logarithm of its book leverage, Ln(BLev), and the natural logarithm of its book leverage, Ln(MLev), at the end of December of year t− 1. For each month, we regress a stock’s excess returns (in %) on its firm characteristics. Time-series averages of the coefficients associated with the characteristics are reported. Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. * denotes significance at the 10% level, ** denotes significance at the 5% level, and *** denotes significance at the 1% level.
Model (1) Model (2) Model (3) Model (4)
Intercept 1.398 *** 1.952 *** 1.395 *** 2.026 ***
(4.78) (4.21) (4.80) (4.35)
Ln(Size) -0.147 *** -0.165 ***
(-2.81) (-3.11)
Ln(BM) 0.371 *** 0.246 ***
(5.56) (3.27)
Ln(BLev) -0.476 *** -0.357 ***
(-7.80) (-5.02)
Ln(MLev) 0.430 *** 0.292 ***
(5.80) (3.46)
Ln(BLev)+Ln(MLev) -0.045 -0.065
(-0.99) (-1.50)
25
Table 3: Regressions for portfolios formed on book-leverage, firm characteristics, and RD/E loadings
We construct the characteristic-balanced portfolios based on book-leverage, alternative firm characteristics, and factor loadings on RD/E, using all NYSE, AMEX and NASDAQ stocks with nonnegative BE for year t− 1. We independently sort individual stocks into three book-leverage and three size (or Altman’s Z-score) groups based on their corresponding values on these firm characteristics for December of the preceding year. The breakpoints are the 33rd and 67th percentiles for the NYSE firms in the sample. Nine portfolios at the intersections of the three book-leverage and three size (or Z-score) groups are formed. We then subdivide each of the nine portfolios into five sub-portfolios using pre-formation slopes. Value-weighted returns on the portfolios are calculated from July of year t to June of year t + 1. We form the arbitrage portfolios, (Hh− Lh)i, defined as the difference between the average of returns on the two highest RD/E loading portfolios of a leverage-size (or Z-score) group minus the average of returns on the two lowest RD/Eloading portfolios of the leverage-size (or Z-score) for each of the nine portfolios. A combined portfolio is simply calculated as the average of the nine portfolios. We then perform the following regressions:
(Hh− Lh)i,t= ai+ biRM KT ,t+ diRD/E,t+ ziRZ,t+ εi,t,
for portfolios i. Panels A and B report the regression results for portfolios firstly formed on book-leverage/size, and book-leverage/Z-score, respectively. Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. * denotes significance at the 10% level, ** denotes significance at the 5% level, and *** denotes significance at the 1% level.
Portfolio Mean Returns and Regression Coefficients
Leverage size Ave. (%) a b d z
Panel B: Portfolio formed on book-leverage, size and RD/Eslopes
1 1 0.126 0.089 -0.141 *** 0.263 *** -0.337 ***
Combined 0.135 0.070 -0.126 *** 0.343 *** -0.449 ***
portfolio (1.31) (0.89) (-7.11) (11.89) (-9.64)
26
Table 3 Continued
Portfolio Mean Returns and Regression Coefficients
Leverage Z-score Ave. (%) a b d z
Panel B: Portfolio formed on book-leverage, Z-score and RD/E slopes
1 1 -0.268 -0.180 -0.290 *** 0.176 -0.405 *
(-0.75) (-0.47) (-3.36) (1.25) (-1.78)
1 2 0.085 0.109 -0.398 *** 0.232 ** -0.126
(0.31) (0.43) (-7.09) (2.54) (-0.85)
1 3 0.129 0.101 -0.148 *** 0.335 *** -0.555 ***
(0.61) (0.50) (-3.26) (4.54) (-4.66)
2 1 0.519 *** 0.435 ** -0.085 ** 0.413 *** -0.616 ***
(2.62) (2.25) (-1.97) (5.84) (-5.39)
2 2 0.601 *** 0.592 *** -0.128 *** 0.261 *** -0.466 ***
(3.89) (4.14) (-3.99) (4.99) (-5.52)
2 3 0.258 0.181 0.034 0.223 *** -0.315 ***
(1.35) (1.01) (0.86) (3.41) (-2.99)
3 1 0.171 0.096 -0.069 * 0.390 *** -0.620 ***
(0.93) (0.59) (-1.86) (6.49) (-6.38)
3 2 0.343 * 0.231 0.042 0.361 *** -0.549 ***
(1.85) (1.23) (0.99) (5.25) (-4.94)
3 3 0.018 -0.061 -0.258 *** 0.543 *** -0.728 ***
(0.05) (-0.17) (-3.29) (4.25) (-3.53)
Combined 0.206 0.167 -0.144 *** 0.326 *** -0.487 ***
portfolio (1.54) (1.39) (-5.36) (7.43) (-6.87)
27
Table 4: Regressions for portfolios formed on market-leverage, firm characteristics, and RD/E loadings
We construct the characteristic-balanced portfolios based on market-leverage, alternative firm characteristics, and factor loadings on RD/E, using all NYSE, AMEX and NASDAQ stocks with nonnegative BE for year t− 1. We independently sort individual stocks into three market-leverage and three size (or Z-score) groups based on their corresponding values on these firm characteristics for December of the preceding year. The breakpoints are the 33rd and 67th percentiles for the NYSE firms in the sample. Nine portfolios at the intersections of the three market-leverage and three size (or Z-score) groups are formed. We then subdivide each of the nine portfolios into five sub-portfolios using pre-formation slopes. Value-weighted returns on the portfolios are calculated from July of year t to June of year t + 1. We form the arbitrage portfolios, (Hh− Lh)i, defined as the difference between the average of returns on the two highest RD/E loading portfolios of a leverage-size (or Z-score) group minus the average of returns on the two lowest RD/E loading portfolios of the leverage-size (or Z-score) for each of the nine portfolios.
A combined portfolio is simply calculated as the average of the nine portfolios. We then perform the following regressions:
(Hh− Lh)i,t= ai+ biRM KT ,t+ diRD/E,t+ ziRZ,t+ εi,t,
for portfolios i. Panels A and B report the regression results for portfolios firstly formed on market-leverage/size, and market-leverage/Z-score, respectively. Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. * denotes significance at the 10% level, ** denotes significance at the 5% level, and *** denotes significance at the 1% level.
Portfolio Mean Returns and Regression Coefficients
Leverage size Ave. (%) a b d z
Panel A: Portfolio formed on market-leverage, size and RD/E slopes
1 1 0.109 0.108 -0.183 *** 0.201 *** -0.261 ***
Combined 0.111 0.078 -0.125 *** 0.244 *** -0.323 ***
portfolio (1.18) (1.02) (-7.33) (8.81) (-7.21)
28
Table 4 Continued
Portfolio Mean Returns and Regression Coefficients
Leverage Z-score Ave. (%) a b d z
Panel B: Portfolio formed on market-leverage, Z-score and RD/Eslopes
1 1 0.296 0.264 -0.085 * 0.343 *** -0.644 ***
(1.30) (1.17) (-1.69) (4.17) (-4.86)
1 2 0.150 0.261 -0.381 *** 0.133 -0.253 *
(0.58) (1.12) (-7.32) (1.56) (-1.85)
1 3 -0.094 -0.130 -0.109 * 0.220 ** -0.271 *
(-0.34) (-0.50) (-1.89) (2.34) (-1.79)
2 1 0.269 0.206 -0.070 * 0.350 *** -0.559 ***
(1.59) (1.27) (-1.93) (5.90) (-5.84)
2 2 0.487 *** 0.404 ** -0.123 *** 0.375 *** -0.465 ***
(2.61) (2.35) (-3.17) (5.95) (-4.57)
2 3 -0.020 0.021 -0.194 *** 0.108 * -0.172 *
(-0.13) (0.12) (-5.06) (1.72) (-1.71)
3 1 0.241 0.246 -0.137 *** 0.251 *** -0.482 ***
(1.14) (1.18) (-2.92) (3.30) (-3.93)
3 2 0.387 ** 0.385 ** 0.004 0.134 ** -0.352 ***
(2.12) (2.41) (0.11) (2.30) (-3.73)
3 3 0.421 ** 0.324 * 0.020 0.214 *** -0.191 *
(2.28) (1.81) (0.50) (3.27) (-1.81)
Combined 0.238 * 0.220 * -0.119 *** 0.236 *** -0.377 ***
portfolio (1.74) (1.83) (-4.44) (5.39) (-5.32)
29
Table 5: Regressions for portfolios formed on book or market-leverage, firm character-istics, and RD/E loadings in subperiods
We construct the combined portfolio based on the nine characteristic-balanced portfolios, and perform the following regression:
(Hh− Lh)p,t= ap+ bpRM KT ,t+ dpRD/E,t+ zpRZ,t+ εp,t,
in two subperiods, 1964-1980 and 1981-2008. Panels A and B report the regression results for portfolios firstly formed on book-leverage and size/Z-score, respectively. Panels C and D report the regression results for portfolios firstly formed on market-leverage and size/Z-score, respectively. Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. * denotes significance at the 10% level, ** denotes significance at the 5% level, and *** denotes significance at the 1% level.
Period Ave. (%) a b d z
Panel A: Portfolio formed on book-leverage, size and RD/E slopes
1964-1980 0.182 0.127 -0.080 *** 0.371 *** -0.454 ***
(1.22) (1.13) (-3.32) (7.36) (-6.10)
1981-2008 0.113 0.053 -0.152 *** 0.328 *** -0.431 ***
(0.85) (0.51) (-6.27) (9.08) (-7.29)
Panel B: Portfolio formed on book-leverage, Z-score and RD/E slopes
1964-1980 0.382 * 0.304 0.008 0.389 *** -0.502 ***
(1.97) (1.65) (0.19) (4.67) (-4.08)
1981-2008 0.122 0.136 -0.232 *** 0.280 *** -0.426 ***
(0.71) (0.90) (-6.61) (5.34) (-4.97)
Panel C: Portfolio formed on market-leverage, size and RD/E slopes
1964-1980 0.178 0.154 -0.066 *** 0.203 *** -0.206 ***
(1.37) (1.37) (-2.71) (4.02) (-2.76)
1981-2008 0.079 0.055 -0.154 *** 0.252 *** -0.345 ***
(0.64) (0.55) (-6.73) (7.38) (-6.18)
Panel D: Portfolio formed on market-leverage, Z-score and RD/Eslopes
1964-1980 0.448 ** 0.379 ** 0.018 0.335 *** -0.450 ***
(2.34) (2.27) (0.50) (4.45) (-4.05)
1981-2008 0.136 0.175 -0.200 *** 0.182 *** -0.300 ***
(0.77) (1.12) (-5.51) (3.35) (-3.38)
30
Table6:Regressionsforportfoliosformedonbookormarket-leverage,firmcharacteristics,andRD/Eloadingsafter consideringtheJanuaryseasonality Weconstructthecombinedportfoliobasedontheninecharacteristic-balancedportfolios,andperformthefollowingregression: (Hh−Lh)p,t=ap0+ap1DJan+bpRMKT,t+dpRD/E,t+zpRZ,t+εp,t, whereDJanequals1forthemonthofJanuary,and0otherwise.Regressionareconductedforfourportfoliosformedonbook-leverageandsize,book-leverageand Z-score,market-leverageandsize,andmarket-leverageandZ-score,respectively.Exceptforthecolumnundera0+a1,numbersintheparenthesesarethet-statistics calculatedusingtheNewey-West(1987)robuststandarderrors.Numbersintheparenthesesundera0+a1aretheF-statisticsunderthenullhypothesisofa0+a1=0. *denotessignificanceatthe10%level,**denotessignificanceatthe5%level,and***denotessignificanceatthe1%level. PortfoliossortedbyJan.Non-Jan. Ave.(%)Ave.(%)a0a1bdza0+a1 book-leverage/size0.0300.1450.145*-0.957***-0.122***0.370***-0.510***-0.812*** (0.07)(1.22)(1.77)(-3.12)(-6.91)(12.38)(-10.17)(7.68) book-leverage/Z-Score0.0480.2200.262**-1.211***-0.139***0.360***-0.564***-0.949** (0.09)(1.47)(2.10)(-2.59)(-5.18)(7.90)(-7.37)(4.51) market-leverage/size-0.1200.1320.145*-0.863***-0.121***0.269***-0.378***-0.717** (-0.35)(1.24)(1.84)(-2.92)(-7.13)(9.34)(-7.83)(6.46) market-leverage/Z-Score-0.0620.264*0.314**-1.204**-0.114***0.270***-0.453***-0.890** (-0.11)(1.76)(2.52)(-2.58)(-4.25)(5.93)(-5.93)(3.97)
31
Table 7: Regressions for portfolios formed on size, BM, and RD/E loadings
We construct the characteristic-balanced portfolios based on size, BM, and factor loadings on RD/E, using all NYSE, AMEX and NASDAQ stocks with nonnegative BE for year t− 1. We independently sort individual stocks into three size and three BM groups based on their corresponding values on these firm characteristics for December of the preceding year. The breakpoints are the 33rd and 67th percentiles for the NYSE firms in the sample. Nine portfolios at the intersections of the three size and three BM groups are formed. We then subdivide each of the nine portfolios into five sub-portfolios using pre-formation slopes. Value-weighted returns on the portfolios are calculated from July of year t to June of year t + 1. We form the arbitrage portfolios, (Hh− Lh)i, defined as the difference between the average of returns on the two highest loading portfolios of a size-BM group minus the average of returns on the two lowest loading portfolios of the size-BM for each of the nine portfolios. We then construct the combined portfolio based on the nine characteristic-balanced portfolios, and perform the following regression:
(Hh− Lh)p,t= ap+ bpRM KT ,t+ dpRD/E,t+ zpRZ,t+ εp,t.
Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. * denotes significance at the 10% level, ** denotes significance at the 5% level, and *** denotes significance at the 1% level.
Period Ave. (%) a b d z
1964-2008 0.124 0.081 -0.124 *** 0.263 *** -0.335 ***
(1.28) (1.05) (-7.17) (9.36) (-7.38)
1964-1980 0.090 0.066 -0.043 ** 0.177 *** -0.178 ***
(0.86) (0.69) (-2.08) (4.07) (-2.77)
1981-2008 0.140 0.107 -0.166 *** 0.275 *** -0.364 ***
(1.06) (1.04) (-6.97) (7.72) (-6.24)
32
Table 8: Regressions for portfolios formed on size, BM, and loadings on Fama-French factors
We construct the characteristic-balanced portfolios based on size, BM, and factor loadings on Fama-French factors, using all NYSE, AMEX and NASDAQ stocks with nonnegative BE for year t− 1. We independently sort individual stocks into three size and three BM groups based on their corresponding values on these firm characteristics for December of the preceding year. The breakpoints are the 33rd and 67th percentiles for the NYSE firms in the sample.
Nine portfolios at the intersections of the three size and three BM groups are formed. We then subdivide each of the nine portfolios into five sub-portfolios using pre-formation slopes. Value-weighted returns on the portfolios are calculated from July of year t to June of year t + 1. We form the arbitrage portfolios, (Hh− Lh)DTi , defined as the difference between the average of returns on the two highest loading portfolios of a size-BM group minus the average of returns on the two lowest loading portfolios of the size-BM group for each of the nine portfolios. We then construct the combined portfolio based on the nine characteristic-balanced portfolios, and perform the following regressions:
(Hh− Lh)DTp,t = ap+ bpRM KT ,t+ spRSM B,t+ hpRHM L,t+ εp,t, and
(Hh− Lh)DTp,t = ap+ bpRM KT ,t+ dpRD/E,t+ zpRZ,t+ εp,t.
Panels A, B, and C report the regression results for portfolios formed on loadings on RM KT, RSM B, and RHM L, respectively. Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. * denotes significance at the 10% level, ** denotes significance at the 5% level, and *** denotes significance at the 1% level.
Regression on Fama-French factors Regression on Ferguson-Shockley factors
Period Ave. (%) a b s h a b d z
Panel A: Portfolio formed on size, BM, and RM KT slopes
1964-2008 -0.036 -0.177 * 0.305 *** 0.293 *** -0.052 -0.109 0.355 *** -0.069 * -0.035
(-0.26) (-1.92) (13.91) (9.90) (-1.57) (-1.11) (16.08) (-1.93) (-0.61)
1964-1980 -0.027 -0.161 0.231 *** 0.192 *** 0.042 -0.107 0.291 *** 0.108 ** -0.151 *
(-0.16) (-1.43) (8.37) (4.98) (1.00) (-0.90) (11.33) (2.02) (-1.92)
1981-2008 -0.041 -0.219 * 0.369 *** 0.361 *** -0.033 -0.123 0.397 *** -0.093 ** -0.017
(-0.21) (-1.80) (12.41) (9.03) (-0.72) (-0.93) (12.88) (-2.01) (-0.22)
1973-1993 0.008 -0.243 ** 0.246 *** 0.368 *** 0.009 -0.136 0.304 *** 0.059 -0.200 **
(0.04) (-2.09) (8.96) (8.57) (0.21) (-1.04) (10.40) (1.02) (-2.56)
Panel B: Portfolio formed on size, BM, and RSM Bslopes
1964-2008 -0.083 -0.160 ** 0.175 *** 0.347 *** -0.118 *** -0.085 0.239 *** -0.110 *** -0.053
(-0.71) (-2.05) (9.40) (13.85) (-4.15) (-0.97) (12.15) (-3.41) (-1.03)
1964-1980 -0.024 -0.188 ** 0.102 *** 0.392 *** -0.009 -0.118 0.235 *** 0.226 *** -0.369 ***
(-0.14) (-2.09) (4.59) (12.66) (-0.26) (-0.99) (9.13) (4.24) (-4.68)
1981-2008 -0.112 -0.158 0.206 *** 0.326 *** -0.161 *** -0.067 0.241 *** -0.195 *** 0.060
(-0.72) (-1.50) (7.97) (9.38) (-4.04) (-0.60) (9.16) (-4.97) (0.94)
1973-1993 -0.060 -0.270 *** 0.125 *** 0.368 *** 0.044 -0.159 0.180 *** 0.132 *** -0.349 ***
(-0.45) (-3.14) (6.19) (11.59) (1.30) (-1.58) (7.99) (2.98) (-5.79)
Panel C: Portfolio formed on size, BM, and RHM Lslopes
1964-2008 0.109 -0.065 -0.024 0.014 0.416 *** 0.010 -0.070 *** 0.344 *** -0.392 ***
(1.08) (-0.89) (-1.38) (0.61) (15.63) (0.13) (-4.02) (12.15) (-8.59)
1964-1980 -0.081 -0.184 * -0.037 -0.113 *** 0.408 *** -0.110 -0.121 *** 0.280 *** -0.315 ***
(-0.52) (-1.78) (-1.45) (-3.19) (10.61) (-0.88) (-4.45) (4.97) (-3.78)
1981-2008 0.201 -0.031 0.011 0.098 *** 0.472 *** 0.057 -0.039 * 0.373 *** -0.439 ***
(1.58) (-0.33) (0.47) (3.16) (13.27) (0.59) (-1.72) (11.06) (-7.96)
1973-1993 -0.059 -0.298 *** 0.012 0.054 0.417 *** -0.184 -0.022 0.348 *** -0.369 ***
(-0.44) (-2.94) (0.49) (1.44) (10.58) (-1.64) (-0.87) (7.05) (-5.51)
33
Table9:Fama-MacBethregressionsforotherG7countries ThistablereportstheregressionresultsforeachofthesixG7countries.ForreturnsfromJulyofyearttoJuneoft+1,wematchthemwiththenaturallogarithm ofafirm’smarketequity,Ln(Size),attheendofJuneofyeart,thenaturallogarithmofitsbookequitytomarketequity,Ln(BM),attheendofDecemberofyear t−1,thenaturallogarithmofitsbookleverage,Ln(BLev),andthenaturallogarithmofitsbookleverage,Ln(MLev),attheendofDecemberofyeart−1.Foreach month,weregressastock’sexcessreturn(in%)onitsfirmcharacteristics.Time-seriesaveragesofthecoefficientsassociatedwiththecharacteristicsarereported. Numbersintheparenthesesarethet-statisticscalculatedusingtheNewey-West(1987)robuststandarderrors.*denotessignificanceatthe10%level,**denotes significanceatthe5%level,and***denotessignificanceatthe1%level. CountryCanadaFranceGermanyItalyJapanU.K. Model(1)Model(2)Model(1)Model(2)Model(1)Model(2)Model(1)Model(2)Model(1)Model(2)Model(1)Model(2) Intercept1.788**1.387**2.037**1.739**0.186-0.0810.314-0.1382.850**2.693*0.9180.965 (2.50)(2.08)(2.21)(2.05)(0.36)(-0.17)(0.35)(-0.17)(2.04)(1.96)(1.26)(1.54) Ln(Size)-0.048-0.035-0.058-0.0270.0350.0510.0330.071-0.109-0.1040.0100.004 (-1.13)(-0.82)(-0.89)(-0.42)(0.91)(1.32)(0.46)(1.09)(-1.62)(-1.58)(0.22)(0.10) Ln(BM)0.266**0.500***0.306***0.296*0.412***0.364*** (2.18)(3.51)(3.13)(1.70)(4.13)(4.41) Ln(BLev)-0.453**-0.607**-0.418***-0.845***-0.588***-0.336*** (-2.44)(-2.21)(-2.79)(-2.89)(-3.72)(-3.59) Ln(MLev)0.518***0.567**0.433***0.667***0.604***0.346*** (3.09)(2.52)(3.04)(2.75)(3.53)(3.61) Ln(BLev)+Ln(MLev)0.065-0.0400.014-0.1790.0150.011 (1.05)(-0.25)(0.40)(-1.63)(0.33)(0.36)
34
Table 10: Regressions for portfolios formed on book/market-leverage, size, and RD/E loadings for other G7 countries
We construct the combined portfolio based on the nine characteristic-balanced portfolios, and perform the following regression:
(Hh− Lh)p,t= ap+ bpRM KT ,t+ dpRD/E,t+ zpRZ,t+ εp,t,
for each of the six G7 countries. Panels A and B report the regression results for portfolios firstly formed on book-leverage and market-leverage, respectively. Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. * denotes significance at the 10% level, ** denotes significance at the 5% level, and *** denotes significance at the 1% level.
Mean Returns and Regression Coefficients
Country Period Ave. (%) a b d z
Panel A: Portfolio formed on book-leverage, BM and RD/E slopes
Canada 1989-2009 -0.042 -0.452 0.258 *** 0.011 -0.208 **
(-0.08) (-0.86) (3.99) (0.17) (-2.25)
France 1992-2009 0.208 0.235 -0.068 * 0.013 -0.062
(1.01) (1.14) (-1.82) (0.31) (-0.89)
Germany 1992-2009 -0.167 -0.212 -0.086 *** 0.135 *** -0.120 **
(-0.85) (-1.35) (-2.85) (4.07) (-2.49)
Italy 1998-2009 0.183 0.274 0.064 0.251 *** -0.021
(0.60) (1.04) (1.39) (5.69) (-0.29)
Japan 1989-2009 0.198 0.175 0.233 *** 0.150 *** 0.003
(0.91) (0.97) (6.92) (3.87) (0.03)
U.K. 1989-2009 0.047 0.052 -0.064 ** 0.050 -0.068
(0.32) (0.36) (-2.04) (1.42) (-1.25)
Panel B: Portfolio formed on market-leverage, BM and RD/E slopes
Canada 1989-2009 -0.335 -0.504 0.134 0.148 * -0.133
(-0.58) (-0.92) (1.59) (1.97) (-1.09)
France 1992-2009 0.232 0.286 -0.239 *** 0.022 0.003
(0.83) (1.10) (-5.05) (0.43) (0.03)
Germany 1992-2009 0.237 0.317 * -0.303 *** 0.001 -0.240 ***
(1.00) (1.67) (-8.30) (0.01) (-4.11)
Italy 1998-2009 -0.070 0.015 0.064 0.120 ** 0.034
(-0.19) (0.05) (1.09) (2.16) (0.38)
Japan 1989-2009 0.259 * 0.232 * 0.073 *** 0.101 *** 0.007
(1.77) (1.78) (3.00) (3.58) (0.12)
U.K. 1989-2009 0.226 0.250 -0.096 ** 0.083 * -0.064
(1.13) (1.35) (-2.35) (1.91) (-0.91)
35