Fama and MacBeth regressions: MAX(3) and idiosyncratic risks
| MAX | IV | Iskew | MAX | IV | Iskew | |
|---|---|---|---|---|---|---|
| Variables | (1) | (2) | (3) | (4) | (5) | (6) |
| Intercept | 2.233*** (3.45) | 0.795 (1.23) | 0.779 (1.23) | 3.237*** (2.94) | 1.586 (1.49) | 1.608 (1.51) |
| Max | −0.220*** (−5.91) | 0.312*** (3.75) | 0.285*** (3.55) | −0.244*** (−6.97) | 0.265*** (3.33) | 0.241*** (3.16) |
| MAX x IRISK | −6.322*** (−4.89) | −6.333*** (−4.92) | −6.320*** (−4.90) | −6.301*** (−4.93) | ||
| IRISK | −14.217 (−0.65) | −8.557 (−0.41) | −8.299 (−0.39) | −3.639 (−0.18) | ||
| Size | −0.046** (−2.30) | −0.051*** (−2.62) | −0.051*** (−2.60) | −0.024 (−1.44) | −0.028* (−1.67) | −0.028* (−1.71) |
| BEME | 0.628*** (3.01) | 0.724*** (3.58) | 0.715*** (3.53) | 0.730*** (3.65) | 0.826*** (4.23) | 0.818*** (4.18) |
| Pre1yr__ret | −0.000 (−0.20) | 0.001 (0.48) | 0.001 (0.39) | −0.001 (−0.69) | −0.000 (−0.15) | −0.000 (−0.23) |
| Trading Volume | −0.011 (−0.79) | −0.008 (−0.60) | −0.008 (−0.63) | −0.013 (−0.98) | −0.010 (−0.78) | −0.011 (−0.81) |
| ILLIQ | 0.003 (0.62) | 0.011* (1.89) | 0.010* (1.83) | 0.004 (0.81) | 0.011** (2.12) | 0.011** (2.05) |
| Firm age | 0.002 (0.29) | 0.003 (0.41) | 0.003 (0.41) | −0.003 (−0.39) | −0.002 (−0.26) | −0.002 (−0.26) |
| ROA | 1.353*** (3.10) | 1.035** (2.52) | 1.059** (2.57) | 1.443*** (3.35) | 1.136*** (2.81) | 1.156*** (2.85) |
| Industry-fixed effects | No | No | No | Yes | Yes | Yes |
| Adjusted R-Sq | 0.037 | 0.046 | 0.045 | 0.068 | 0.076 | 0.076 |
| N | 271,620 | 271,620 | 271,620 | 271,620 | 271,620 | 271,620 |
| MAX | IV | Iskew | MAX | IV | Iskew | |
|---|---|---|---|---|---|---|
| Variables | (1) | (2) | (3) | (4) | (5) | (6) |
| Intercept | 2.233 | 0.795 (1.23) | 0.779 (1.23) | 3.237 | 1.586 (1.49) | 1.608 (1.51) |
| Max | −0.220 | 0.312 | 0.285 | −0.244 | 0.265 | 0.241 |
| MAX x IRISK | −6.322 | −6.333 | −6.320 | −6.301 | ||
| IRISK | −14.217 (−0.65) | −8.557 (−0.41) | −8.299 (−0.39) | −3.639 (−0.18) | ||
| Size | −0.046 | −0.051 | −0.051 | −0.024 (−1.44) | −0.028 | −0.028 |
| BEME | 0.628 | 0.724 | 0.715 | 0.730 | 0.826 | 0.818 |
| Pre1yr__ret | −0.000 (−0.20) | 0.001 (0.48) | 0.001 (0.39) | −0.001 (−0.69) | −0.000 (−0.15) | −0.000 (−0.23) |
| Trading Volume | −0.011 (−0.79) | −0.008 (−0.60) | −0.008 (−0.63) | −0.013 (−0.98) | −0.010 (−0.78) | −0.011 (−0.81) |
| ILLIQ | 0.003 (0.62) | 0.011 | 0.010 | 0.004 (0.81) | 0.011 | 0.011 |
| Firm age | 0.002 (0.29) | 0.003 (0.41) | 0.003 (0.41) | −0.003 (−0.39) | −0.002 (−0.26) | −0.002 (−0.26) |
| ROA | 1.353 | 1.035 | 1.059 | 1.443 | 1.136 | 1.156 |
| Industry-fixed effects | No | No | No | Yes | Yes | Yes |
| Adjusted | 0.037 | 0.046 | 0.045 | 0.068 | 0.076 | 0.076 |
| 271,620 | 271,620 | 271,620 | 271,620 | 271,620 | 271,620 |
Notes:
This table present results of monthly Fama-Macbeth regressions. The dependent variable is the stock return for the month t. Independent variables are lag variables (t−1). MAX (3) is the average of the three highest daily returns of the previous month. IV is the variance of the residuals in the regression analysis using equation (2). Iskew is obtained from the residuals of the regression analysis using equation (3). Size is the market capitalization of the stock (in million won). BEME is book to market ratio. Pre1yr_ret is the past one-year return excluding the previous month. Trading volume is the stock trading volume of the previous year. ILLIQ is the Amihud’s (2002) illiquidity index, which equals the ratio of a stock’s absolute returns to its value traded. Firm age is the age of the firm in a given year at the time of the incorporation. ROA is calculated by dividing the pre-tax income by total assets of the previous year. All regressions include the industry fixed effects using 2-digit KSIC. Newey-West(1987) adjusted standard errors with the lag of four months are used to compute t-statistic (in parentheses). Asterisks denote the statistical significance level: * for 0.1, ** for 0.5, *** for 0.01
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