FM regressions
| Regressors | Models | ||||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
| Constant | 0.12 (1.00) | 0.11 (1.79)*** | 0.12 (0.88) | 0.13 (1.19) | 0.13 (0.77) | 0.20 (0.73) | 0.21 (0.70) |
| −0.66 (−4.25)* | −0.66 (−4.05)* | −0.43 (−3.40)* | −0.33 (−3.01)* | ||||
| −1.03 (−8.24)* | −0.98 (−7.79)* | −0.90 (−6.94)* | |||||
| −0.22 (−3.02)* | −0.15 (−2.96)* | −0.11 (−2.72)* | |||||
| 5.22 (15.17)* | 5.22 (15.16)* | 3.44 (12.34)* | |||||
| −0.13 (−3.93)* | −0.10 (−2.45)* | ||||||
| 0.061 (3.01)* | 0.041 (1.92)*** | ||||||
| −0.11 (−3.66)* | −0.09 (−3.33)* | ||||||
| −0.0022 (−0.44) | −0.002 (−0.40) | ||||||
| −0.16 (−4.22)* | −0.14 (−3.96)* | ||||||
| −0.93 (−6.18)* | −0.89 (−6.12)* | ||||||
| −0.069 (−3.22)* | −0.064 (−3.09)* | ||||||
| −0.009 (−1.11) | −0.008 (−1.00) | ||||||
| 74.25 [0.00] | 133.12 [0.00] | 63.12 [0.00] | 188.16 [0.00] | 592.14 [0.00] | 844.22 [0.00] | 992.28 [0.00] | |
| Pricing error | 0.035 | 0.029 | 0.04 | 0.018 | 0.0086 | 0.0052 | 0.0033 |
| Adj | 0.029 | 0.041 | 0.027 | 0.089 | 0.17 | 0.30 | 0.39 |
| Regressors | Models | ||||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
| Constant | 0.12 (1.00) | 0.11 (1.79)*** | 0.12 (0.88) | 0.13 (1.19) | 0.13 (0.77) | 0.20 (0.73) | 0.21 (0.70) |
| −0.66 (−4.25)* | −0.66 (−4.05)* | −0.43 (−3.40)* | −0.33 (−3.01)* | ||||
| −1.03 (−8.24)* | −0.98 (−7.79)* | −0.90 (−6.94)* | |||||
| −0.22 (−3.02)* | −0.15 (−2.96)* | −0.11 (−2.72)* | |||||
| 5.22 (15.17)* | 5.22 (15.16)* | 3.44 (12.34)* | |||||
| −0.13 (−3.93)* | −0.10 (−2.45)* | ||||||
| 0.061 (3.01)* | 0.041 (1.92)*** | ||||||
| −0.11 (−3.66)* | −0.09 (−3.33)* | ||||||
| −0.0022 (−0.44) | −0.002 (−0.40) | ||||||
| −0.16 (−4.22)* | −0.14 (−3.96)* | ||||||
| −0.93 (−6.18)* | −0.89 (−6.12)* | ||||||
| −0.069 (−3.22)* | −0.064 (−3.09)* | ||||||
| −0.009 (−1.11) | −0.008 (−1.00) | ||||||
| 74.25 [0.00] | 133.12 [0.00] | 63.12 [0.00] | 188.16 [0.00] | 592.14 [0.00] | 844.22 [0.00] | 992.28 [0.00] | |
| Pricing error | 0.035 | 0.029 | 0.04 | 0.018 | 0.0086 | 0.0052 | 0.0033 |
| Adj | 0.029 | 0.041 | 0.027 | 0.089 | 0.17 | 0.30 | 0.39 |
Note(s): This table outlines the results from the Fama and MacBeth (1973) regressions, along with their average coefficients, as per Equation (13). We analyze 100 portfolios that are sorted each month according to . These regressions are calculated at the end of each month, from January 1988 to June 2019. For portfolio p, expected entropy and other risk factors are determined by the value-weighted average of firm-level measures across all stocks in the portfolio. The measures are computed as described in Equations (11) and (12) using a 60-day formation period. To estimate , the cross-sectional regressions utilize the risk factors from Model 6 in Table 2. Using the same formation period, we also calculate , , and for portfolio p via Equations (8), (9), and (10), respectively. represents the excess market return at month-end t, and are the excess returns of small-cap stocks over large-cap stocks and high book-to-market stocks over low book-to-market stocks, respectively, in month t. is the difference in returns between two high prior return portfolios and two low prior return portfolios for that month. and correspond to Harvey and Siddique’s (2000) co-skewness and Pastor and Stambaugh’s (2003) liquidity measures, respectively, for month t. and are Bali, Cakici, and Whitelaw’s (2011) maximum and minimum factors, representing the average of the highest and the inverse of the lowest daily returns over the past two months. The table includes average coefficients and Newey and West (1987) t-statistics (shown in parentheses), along with average adjusted-R-squared values. Significance at 1% and 10% levels are indicated with * and ***, respectively. The Fama-MacBeth t-statistics and the test results are presented in parentheses and brackets, respectively
Source(s): Created by the author
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