CHARACTERISTICS AND RETURNS 343Table 9.8
Time-Series Regressions—Predicted Mkt Factor Loading-Sorted PortfoliosThe upper two panels present the intercepts, rMktcoefficient estimates, and t-
statistics from the following multivariate time-series regression:
The coefficient estimates for βHMLand βSMBare not presented here.
The left-hand-side portfolios are formed based on size (SZ), book-to-market
(BM) and preformation Mkt factor loadings, with the exception that the factor
loading used to sort the portfolios is the Mkt factor loading (rather than the HML
factor loading).
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 coeffi-
cients 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 −0.22 −0.11 −0.07 −0.16 −0.39 −1.30 −0.89 −0.54 −1.22 −2.46
12 0.31 0.26 0.08 −0.10 −0.17 2.76 2.42 0.64 −0.72 −1.17
13 0.31 0.07 0.05 0.00 −0.30 2.40 0.66 0.42 0.03 −2.16
21 −0.02 0.16 0.25 −0.06 −0.08 −0.19 1.64 2.30 −0.69 −0.60
22 0.16 0.09 −0.02 −0.01 −0.01 1.22 0.82 −0.14 −0.10 −0.10
23 0.04 −0.03 −0.01 0.01 −0.21 0.24 −0.18 −0.07 0.04 −1.23
31 0.25 0.07 0.09 −0.05 −0.36 1.77 0.69 1.05 −0.50 −3.63
32 0.21 0.39 −0.06 0.19 −0.31 1.18 2.65 −0.43 1.36 −1.57
33 0.08 −0.11 0.05 −0.06 −0.25 0.38 −0.66 0.32 −0.39 −1.45
Average 0.12 0.09 0.04 −0.03 −0.23 0.94 0.79 0.39 −0.24 −1.60
Char Port βˆMkt t(βˆMkt)
B/M SZ 1 2 3 4 51 2 345
11 1.00 0.96 1.07 1.11 1.20 25.90 32.58 38.44 36.26 32.20
12 0.95 0.98 1.07 1.16 1.20 36.16 39.08 35.77 34.41 35.14
13 0.90 0.95 1.00 1.07 1.16 30.51 38.71 36.38 40.47 35.94
21 0.79 0.87 0.94 1.04 1.19 27.77 37.87 37.78 47.48 39.26
22 0.81 0.91 0.99 1.07 1.23 26.48 34.61 40.70 42.46 34.61
23 0.82 0.91 1.05 1.15 1.21 21.27 25.42 27.76 35.02 30.03
31 0.84 0.85 0.97 1.08 1.26 25.44 34.55 46.30 45.87 54.38
32 0.84 0.94 1.04 1.13 1.30 20.44 27.72 32.63 35.62 28.09
33 0.84 0.94 1.09 1.19 1.20 18.06 25.15 28.39 33.62 30.59
Average 0.87 0.92 1.02 1.11 1.22 25.78 32.85 36.02 39.02 35.58
RR ̃ ̃ ̃ss bm fl,,−=+ ⋅ + ⋅ + ⋅ −f αβHMLRHMLβSMB RSMB βMkt (RR ̃Mkt f).