CHARACTERISTICS AND RETURNS 341Table 9.7
Time-Series Regressions—Predicted SMB Factor Loading-Sorted PortfoliosThe upper two panels present the intercepts and rSMBcoefficient estimates and t-
statistics from the following multivariate time-series regression:
The coefficient estimates for βHMLand βMktare not presented here.
The left hand side portfolios are formed based on size (SZ), book-to-market
(B/M) and preformation SMB factor loadings, with the exception that the factor
loadings used to form the portfolios are the SMB factor loadings (rather than the
HML factor loadings).
The lower left panel gives the mean monthly returns (in %) for the 45 portfolios,
and the lower right the t-statistics for the regressions of the characteristic-balanced
portfolios on the factors. The bottom row of the lower right panel gives the coefficients
and t-statistics (in parenthesis) for the regression of the combined characteristic-
balanced portfolio on the factors.
Char Port αˆ t(αˆ)
B/M SZ 1 2 3 4 51 2 345
11 −0.28 −0.01 −0.06 −0.10 −0.65 −1.94 −0.06 −0.44 −0.75 −3.58
12 0.07 0.20 0.13 0.01 0.01 0.57 1.79 1.10 0.08 0.03
13 0.25 0.06 0.01 −0.08 0.05 2.40 0.55 0.06 −0.67 0.38
21 0.16 0.07 0.06 −0.05 0.06 1.38 0.73 0.69 −0.48 0.37
22 0.11 −0.10 0.06 0.12 −0.05 0.84 −0.87 0.54 1.05 −0.38
23 0.08 0.01 −0.16 0.10 −0.03 0.50 0.08 −1.04 0.88 −0.27
31 0.02 0.11 −0.06 −0.13 −0.11 0.21 1.14 −0.63 −1.14 −0.75
32 0.19 0.23 −0.12 −0.01 0.15 1.20 1.79 −0.91 −0.07 0.75
33 0.23 −0.10 −0.16 −0.38 0.08 1.29 −0.67 −1.09 −2.58 0.45
Average 0.09 0.05 −0.03 −0.06 −0.05 0.72 0.50 −0.19 −0.41 −0.33
Char Port βˆSMB t(βˆSMB)
B/M SZ 1 2 3 4 51 2 345
11 1.01 1.06 1.18 1.20 1.45 19.14 24.93 26.04 25.18 21.96
12 0.49 0.54 0.59 0.71 0.84 11.33 13.21 13.38 15.00 15.40
13 −0.29 −0.11 −0.11 −0.03 0.15 −7.81 −2.58 −2.50 −0.69 2.89
21 0.84 0.85 0.91 1.17 1.57 20.58 26.15 26.53 29.86 28.18
22 0.25 0.45 0.47 0.67 0.86 5.29 10.74 12.01 16.38 18.15
23 −0.38 −0.26 −0.14 0.06 0.25 −6.38 −5.46 −2.54 1.44 5.44
31 0.89 0.93 1.06 1.23 1.49 21.34 26.51 30.70 28.70 27.07
32 0.12 0.34 0.57 0.65 0.91 2.05 7.43 11.53 12.56 12.96
33 −0.33 −0.11 0.05 0.00 0.20 −5.27 −2.04 0.87 0.01 3.21
Average 0.29 0.41 0.51 0.63 0.86 6.70 10.99 12.89 14.27 15.03
RR ̃ ̃ ̃ss bm fl,,−=+ ⋅ + ⋅ + ⋅ −f αβHML RHML βSMB RSMB βMkt (RR ̃Mkt f).