Double-sort portfolio return
| Excess return | CAPM-alpha | FF3-alpha | |||||||
|---|---|---|---|---|---|---|---|---|---|
| 1 (Low) | 5 (High) | High-Low | 1 (Low) | 5 (High) | High-Low | 1 (Low) | 5 (High) | High-Low | |
| BM | 0.78* | 0.10 | −0.68 | 0.31* | −0.64* | −0.95** | 0.00 | −1.04*** | −1.04** |
| (1.83) | (0.18) | (−1.64) | (1.72) | (−1.87) | (−2.47) | (0.03) | (−2.64) | (−2.39) | |
| BETA | 0.64* | −0.64 | −1.29*** | 0.20 | −1.22*** | −1.42*** | −0.02 | −1.60*** | −1.58*** |
| (1.71) | (−1.24) | (−3.41) | (1.15) | (−3.17) | (−3.62) | (−0.14) | (−3.38) | (−3.75) | |
| Betadown | 0.83* | −0.32 | −1.15** | 0.32** | −0.93** | −1.24** | 0.16 | −1.28** | −1.43** |
| (1.96) | (−0.54) | (−2.34) | (2.54) | (−2.09) | (−2.57) | (1.60) | (−2.41) | (−2.55) | |
| Coskew | 0.70* | −0.16 | −0.86* | 0.26 | −0.85** | −1.11** | −0.04 | −1.19** | −1.15** |
| (1.74) | (−0.26) | (−1.91) | (1.38) | (−2.00) | (−2.47) | (−0.29) | (−2.26) | (−2.27) | |
| GKMHI | 0.60 | −0.94 | −1.54*** | 0.12 | −1.63*** | −1.75*** | 0.07 | −1.86*** | −1.94*** |
| (1.27) | (−1.47) | (−2.73) | (0.57) | (−3.45) | (−3.35) | (0.29) | (−3.29) | (−2.76) | |
| GKMLO | 0.56* | −0.46 | −1.02* | 0.09 | −1.19*** | −1.28*** | 0.01 | −1.52** | −1.53** |
| (1.68) | (−0.72) | (−1.88) | (0.45) | (−2.60) | (−2.66) | (0.03) | (−2.51) | (−2.43) | |
| ILLIQ | 0.85** | −0.06 | −0.91** | 0.46* | −0.65 | −1.10** | 0.02 | −1.14** | −1.16** |
| (2.09) | (−0.11) | (−1.97) | (1.95) | (−1.59) | (−2.39) | (0.12) | (−2.44) | (−2.43) | |
| IVOL | 0.63 | 0.02 | −0.61 | 0.17 | −0.70* | −0.87** | −0.06 | −0.97** | −0.91** |
| (1.52) | (0.03) | (−1.56) | (0.96) | (−1.92) | (−2.30) | (−0.36) | (−2.08) | (−2.00) | |
| MAX | 0.72* | −0.13 | −0.86* | 0.23* | −0.81** | −1.03** | 0.10 | −1.15** | −1.25** |
| (1.82) | (−0.24) | (−1.92) | (1.88) | (−2.08) | (−2.55) | (0.78) | (−2.23) | (−2.12) | |
| MOM | 0.75* | −0.53 | −1.29*** | 0.28* | −1.22*** | −1.50*** | 0.01 | −1.54*** | −1.55*** |
| (1.88) | (−0.95) | (−3.10) | (1.71) | (−3.15) | (−3.55) | (0.11) | (−3.26) | (−3.23) | |
| SIZE | 1.11*** | 0.23 | −0.87*** | 0.70*** | −0.38 | −1.08*** | 0.17 | −0.86** | −1.03*** |
| (2.92) | (0.46) | (−2.67) | (3.07) | (−1.26) | (−3.58) | (1.34) | (−2.38) | (−2.85) | |
| STR | 0.72** | −0.28 | −1.00** | 0.25* | −0.98** | −1.23*** | 0.13 | −1.32*** | −1.45** |
| (1.97) | (−0.48) | (−2.05) | (1.72) | (−2.40) | (−2.69) | (0.87) | (−2.75) | (−2.53) | |
| VOLDU | 0.65* | 0.12 | −0.52 | 0.22 | −0.52 | −0.74* | −0.08 | −0.95** | −0.88** |
| (1.70) | (0.22) | (−1.29) | (1.16) | (−1.33) | (−1.90) | (−0.61) | (−2.19) | (−2.01) | |
| Excess return | CAPM-alpha | FF3-alpha | |||||||
|---|---|---|---|---|---|---|---|---|---|
| 1 (Low) | 5 (High) | High-Low | 1 (Low) | 5 (High) | High-Low | 1 (Low) | 5 (High) | High-Low | |
| BM | 0.78* | 0.10 | −0.68 | 0.31* | −0.64* | −0.95** | 0.00 | −1.04*** | −1.04** |
| (1.83) | (0.18) | (−1.64) | (1.72) | (−1.87) | (−2.47) | (0.03) | (−2.64) | (−2.39) | |
| BETA | 0.64* | −0.64 | −1.29*** | 0.20 | −1.22*** | −1.42*** | −0.02 | −1.60*** | −1.58*** |
| (1.71) | (−1.24) | (−3.41) | (1.15) | (−3.17) | (−3.62) | (−0.14) | (−3.38) | (−3.75) | |
| Betadown | 0.83* | −0.32 | −1.15** | 0.32** | −0.93** | −1.24** | 0.16 | −1.28** | −1.43** |
| (1.96) | (−0.54) | (−2.34) | (2.54) | (−2.09) | (−2.57) | (1.60) | (−2.41) | (−2.55) | |
| Coskew | 0.70* | −0.16 | −0.86* | 0.26 | −0.85** | −1.11** | −0.04 | −1.19** | −1.15** |
| (1.74) | (−0.26) | (−1.91) | (1.38) | (−2.00) | (−2.47) | (−0.29) | (−2.26) | (−2.27) | |
| GKMHI | 0.60 | −0.94 | −1.54*** | 0.12 | −1.63*** | −1.75*** | 0.07 | −1.86*** | −1.94*** |
| (1.27) | (−1.47) | (−2.73) | (0.57) | (−3.45) | (−3.35) | (0.29) | (−3.29) | (−2.76) | |
| GKMLO | 0.56* | −0.46 | −1.02* | 0.09 | −1.19*** | −1.28*** | 0.01 | −1.52** | −1.53** |
| (1.68) | (−0.72) | (−1.88) | (0.45) | (−2.60) | (−2.66) | (0.03) | (−2.51) | (−2.43) | |
| ILLIQ | 0.85** | −0.06 | −0.91** | 0.46* | −0.65 | −1.10** | 0.02 | −1.14** | −1.16** |
| (2.09) | (−0.11) | (−1.97) | (1.95) | (−1.59) | (−2.39) | (0.12) | (−2.44) | (−2.43) | |
| IVOL | 0.63 | 0.02 | −0.61 | 0.17 | −0.70* | −0.87** | −0.06 | −0.97** | −0.91** |
| (1.52) | (0.03) | (−1.56) | (0.96) | (−1.92) | (−2.30) | (−0.36) | (−2.08) | (−2.00) | |
| MAX | 0.72* | −0.13 | −0.86* | 0.23* | −0.81** | −1.03** | 0.10 | −1.15** | −1.25** |
| (1.82) | (−0.24) | (−1.92) | (1.88) | (−2.08) | (−2.55) | (0.78) | (−2.23) | (−2.12) | |
| MOM | 0.75* | −0.53 | −1.29*** | 0.28* | −1.22*** | −1.50*** | 0.01 | −1.54*** | −1.55*** |
| (1.88) | (−0.95) | (−3.10) | (1.71) | (−3.15) | (−3.55) | (0.11) | (−3.26) | (−3.23) | |
| SIZE | 1.11*** | 0.23 | −0.87*** | 0.70*** | −0.38 | −1.08*** | 0.17 | −0.86** | −1.03*** |
| (2.92) | (0.46) | (−2.67) | (3.07) | (−1.26) | (−3.58) | (1.34) | (−2.38) | (−2.85) | |
| STR | 0.72** | −0.28 | −1.00** | 0.25* | −0.98** | −1.23*** | 0.13 | −1.32*** | −1.45** |
| (1.97) | (−0.48) | (−2.05) | (1.72) | (−2.40) | (−2.69) | (0.87) | (−2.75) | (−2.53) | |
| VOLDU | 0.65* | 0.12 | −0.52 | 0.22 | −0.52 | −0.74* | −0.08 | −0.95** | −0.88** |
| (1.70) | (0.22) | (−1.29) | (1.16) | (−1.33) | (−1.90) | (−0.61) | (−2.19) | (−2.01) | |
Note(s): The stocks were first sorted by control variable and subsequently sorted by PC1 within each control group. For each quintile by PC1, value-weighted returns are averaged across the control groups. To save space, excess returns, CAPM alphas and FF3 alphas are computed only for low-, high-, and high-minus-low portfolios. The Newey–West adjusted t-statistics with a lag of 12 are reported in parentheses. ***, ** and * indicate the 1%, 5% and 10% statistical significance, respectively
Source(s): Created by authors
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