Single-sorted portfolio return
| Portfolio | 1 (Low) | 2 | 3 | 4 | 5 (High) | High-Low |
|---|---|---|---|---|---|---|
| Panel A: VaR1 | ||||||
| Excess return | 0.52 | 0.80* | 1.03** | 0.57 | −0.33 | −0.85 |
| (1.35) | (1.66) | (2.09) | (0.94) | (−0.54) | (−1.59) | |
| CAPM-alpha | 0.04 | 0.22 | 0.33* | −0.18 | −1.04** | −1.08** |
| (0.23) | (1.06) | (1.66) | (−0.56) | (−2.47) | (−2.19) | |
| FF3-alpha | 0.05 | 0.23 | 0.31 | −0.31 | −1.33** | −1.38** |
| (0.27) | (1.10) | (1.48) | (−0.76) | (−2.46) | (−2.12) | |
| Panel B: VaR5 | ||||||
| Excess return | 0.61 | 0.77 | 1.05** | 0.61 | −0.47 | −1.08* |
| (1.54) | (1.62) | (2.04) | (1.04) | (−0.73) | (−1.83) | |
| CAPM-alpha | 0.15 | 0.17 | 0.39*** | −0.13 | −1.24*** | −1.39*** |
| (0.74) | (0.87) | (2.81) | (−0.44) | (−2.88) | (−2.72) | |
| FF3-alpha | 0.17 | 0.25 | 0.27 | −0.28 | −1.45*** | −1.62** |
| (0.70) | (1.05) | (1.56) | (−0.73) | (−2.74) | (−2.41) | |
| Panel C: ES1 | ||||||
| Excess return | 0.52 | 0.85* | 0.90* | 0.51 | −0.14 | −0.66 |
| (1.30) | (1.68) | (1.74) | (0.88) | (−0.26) | (−1.35) | |
| CAPM-alpha | 0.03 | 0.22 | 0.23 | −0.24 | −0.83** | −0.86* |
| (0.17) | (1.03) | (1.44) | (−0.82) | (−2.09) | (−1.88) | |
| FF3-alpha | 0.06 | 0.31 | 0.14 | −0.37 | −1.16** | −1.22* |
| (0.30) | (1.29) | (0.82) | (−0.97) | (−2.26) | (−1.93) | |
| Panel D: ES5 | ||||||
| Excess return | 0.57 | 0.97* | 0.79 | 0.69 | −0.53 | −1.09* |
| (1.42) | (1.94) | (1.39) | (1.31) | (−0.80) | (−1.82) | |
| CAPM-alpha | 0.09 | 0.37 | 0.11 | −0.07 | −1.28*** | −1.37** |
| (0.49) | (1.48) | (0.47) | (−0.29) | (−2.63) | (−2.51) | |
| FF3-alpha | 0.12 | 0.45 | −0.04 | −0.19 | −1.49** | −1.61** |
| (0.59) | (1.52) | (−0.14) | (−0.62) | (−2.45) | (−2.25) | |
| Panel E: SEMI-V | ||||||
| Excess return | 0.59 | 0.68 | 1.18** | 0.48 | −0.56 | −1.15* |
| (1.43) | (1.39) | (2.32) | (0.83) | (−0.84) | (−1.78) | |
| CAPM-alpha | 0.12 | 0.07 | 0.48** | −0.25 | −1.30*** | −1.42** |
| (0.59) | (0.37) | (2.49) | (−0.83) | (−2.67) | (−2.42) | |
| FF3-alpha | 0.16 | 0.16 | 0.30 | −0.37 | −1.55** | −1.71** |
| (0.65) | (0.68) | (1.39) | (−0.93) | (−2.54) | (−2.22) | |
| Panel F: PC1 | ||||||
| Excess return | 0.59 | 0.97** | 0.83 | 0.65 | −0.60 | −1.19* |
| (1.44) | (1.99) | (1.55) | (1.10) | (−0.91) | (−1.92) | |
| CAPM-alpha | 0.10 | 0.38 | 0.14 | −0.11 | −1.35*** | −1.46** |
| (0.59) | (1.37) | (0.66) | (−0.43) | (−2.61) | (−2.54) | |
| FF3-alpha | 0.15 | 0.45 | 0.01 | −0.33 | −1.53** | −1.67** |
| (0.73) | (1.34) | (0.04) | (−0.92) | (−2.39) | (−2.25) | |
| Portfolio | 1 (Low) | 2 | 3 | 4 | 5 (High) | High-Low |
|---|---|---|---|---|---|---|
| Excess return | 0.52 | 0.80* | 1.03** | 0.57 | −0.33 | −0.85 |
| (1.35) | (1.66) | (2.09) | (0.94) | (−0.54) | (−1.59) | |
| CAPM-alpha | 0.04 | 0.22 | 0.33* | −0.18 | −1.04** | −1.08** |
| (0.23) | (1.06) | (1.66) | (−0.56) | (−2.47) | (−2.19) | |
| FF3-alpha | 0.05 | 0.23 | 0.31 | −0.31 | −1.33** | −1.38** |
| (0.27) | (1.10) | (1.48) | (−0.76) | (−2.46) | (−2.12) | |
| Excess return | 0.61 | 0.77 | 1.05** | 0.61 | −0.47 | −1.08* |
| (1.54) | (1.62) | (2.04) | (1.04) | (−0.73) | (−1.83) | |
| CAPM-alpha | 0.15 | 0.17 | 0.39*** | −0.13 | −1.24*** | −1.39*** |
| (0.74) | (0.87) | (2.81) | (−0.44) | (−2.88) | (−2.72) | |
| FF3-alpha | 0.17 | 0.25 | 0.27 | −0.28 | −1.45*** | −1.62** |
| (0.70) | (1.05) | (1.56) | (−0.73) | (−2.74) | (−2.41) | |
| Excess return | 0.52 | 0.85* | 0.90* | 0.51 | −0.14 | −0.66 |
| (1.30) | (1.68) | (1.74) | (0.88) | (−0.26) | (−1.35) | |
| CAPM-alpha | 0.03 | 0.22 | 0.23 | −0.24 | −0.83** | −0.86* |
| (0.17) | (1.03) | (1.44) | (−0.82) | (−2.09) | (−1.88) | |
| FF3-alpha | 0.06 | 0.31 | 0.14 | −0.37 | −1.16** | −1.22* |
| (0.30) | (1.29) | (0.82) | (−0.97) | (−2.26) | (−1.93) | |
| Excess return | 0.57 | 0.97* | 0.79 | 0.69 | −0.53 | −1.09* |
| (1.42) | (1.94) | (1.39) | (1.31) | (−0.80) | (−1.82) | |
| CAPM-alpha | 0.09 | 0.37 | 0.11 | −0.07 | −1.28*** | −1.37** |
| (0.49) | (1.48) | (0.47) | (−0.29) | (−2.63) | (−2.51) | |
| FF3-alpha | 0.12 | 0.45 | −0.04 | −0.19 | −1.49** | −1.61** |
| (0.59) | (1.52) | (−0.14) | (−0.62) | (−2.45) | (−2.25) | |
| Excess return | 0.59 | 0.68 | 1.18** | 0.48 | −0.56 | −1.15* |
| (1.43) | (1.39) | (2.32) | (0.83) | (−0.84) | (−1.78) | |
| CAPM-alpha | 0.12 | 0.07 | 0.48** | −0.25 | −1.30*** | −1.42** |
| (0.59) | (0.37) | (2.49) | (−0.83) | (−2.67) | (−2.42) | |
| FF3-alpha | 0.16 | 0.16 | 0.30 | −0.37 | −1.55** | −1.71** |
| (0.65) | (0.68) | (1.39) | (−0.93) | (−2.54) | (−2.22) | |
| Excess return | 0.59 | 0.97** | 0.83 | 0.65 | −0.60 | −1.19* |
| (1.44) | (1.99) | (1.55) | (1.10) | (−0.91) | (−1.92) | |
| CAPM-alpha | 0.10 | 0.38 | 0.14 | −0.11 | −1.35*** | −1.46** |
| (0.59) | (1.37) | (0.66) | (−0.43) | (−2.61) | (−2.54) | |
| FF3-alpha | 0.15 | 0.45 | 0.01 | −0.33 | −1.53** | −1.67** |
| (0.73) | (1.34) | (0.04) | (−0.92) | (−2.39) | (−2.25) | |
Note(s): Stocks are sorted by the left-tail risk measure for each month, and the value-weighted portfolio returns for the following month are computed. High-Low in the last column represents the zero-cost long-short portfolio that buys Portfolio 5 and sells Portfolio 1. 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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