Table 3 Descriptive statistics of...

Table 3

Descriptive statistics of portfolios sorted into idiosyncratic risk measures

Portfolio	Panel A: IE			Panel B: IS			Panel C: IV			Panel D: IK
Portfolio	Mean	IE	Carhart alpha	Mean	IS	Carhart alpha	Mean	IV	Carhart alpha	Mean	IK	Carhart alpha
1 (Low)	1.09	0.06	1.19 (3.73)^*	0.92	0.04	1.00 (3.40)^*	1.02	0.011	0.98 (3.22)^*	−1.20	0.82	−1.21 (−3.88)^*
2	0.90	0.11	0.98 (2.33)^*	−1.11	0.16	−1.02 (−2.80)^*	−1.01	0.015	−1.00 (−3.01)^*	−0.89	1.17	−1.17 (−3.35)^*
3	0.69	0.12	0.74 (1.98)^**	−1.14	0.18	−1.12 (−2.99)^*	−1.08	0.019	−1.06 (−3.05)^*	−0.92	1.47	−1.20 (−3.47)^*
4	−1.08	0.17	−1.14 (−3.21)^*	−1.19	0.26	−1.14 (−3.14)^*	−1.14	0.021	−1.17 (−3.59)^*	−1.00	2.00	−1.26 (−3.55)^*
5 (High)	−1.33	0.31	−1.28 (−3.69)^*	−1.20	0.40	−1.23 (−3.25)^*	−1.20	0.039	−1.22 (−3.49)^*	0.97	4.03	1.00 (2.37)^*
5–1	−2.42 (−4.49)^*		−2.47 (−4.46)^*	−2.12 (−4.00)^*		−2.23 (−4.06)^*	−2.22 (−4.11)^*		−2.10 (−4.10)^*	2.17 (3.33)^*		2.21 (3.44)^*

Portfolio	Panel A: IE			Panel B: IS			Panel C: IV			Panel D: IK
Portfolio	Mean	IE	Carhart alpha	Mean	IS	Carhart alpha	Mean	IV	Carhart alpha	Mean	IK	Carhart alpha
1 (Low)	1.09	0.06	1.19 (3.73)^*	0.92	0.04	1.00 (3.40)^*	1.02	0.011	0.98 (3.22)^*	−1.20	0.82	−1.21 (−3.88)^*
2	0.90	0.11	0.98 (2.33)^*	−1.11	0.16	−1.02 (−2.80)^*	−1.01	0.015	−1.00 (−3.01)^*	−0.89	1.17	−1.17 (−3.35)^*
3	0.69	0.12	0.74 (1.98)^**	−1.14	0.18	−1.12 (−2.99)^*	−1.08	0.019	−1.06 (−3.05)^*	−0.92	1.47	−1.20 (−3.47)^*
4	−1.08	0.17	−1.14 (−3.21)^*	−1.19	0.26	−1.14 (−3.14)^*	−1.14	0.021	−1.17 (−3.59)^*	−1.00	2.00	−1.26 (−3.55)^*
5 (High)	−1.33	0.31	−1.28 (−3.69)^*	−1.20	0.40	−1.23 (−3.25)^*	−1.20	0.039	−1.22 (−3.49)^*	0.97	4.03	1.00 (2.37)^*
5–1	−2.42 (−4.49)^*		−2.47 (−4.46)^*	−2.12 (−4.00)^*		−2.23 (−4.06)^*	−2.22 (−4.11)^*		−2.10 (−4.10)^*	2.17 (3.33)^*		2.21 (3.44)^*

Note(s): We calculate the estimates ${I E}_{i, t + T}$ (shown in Panel A) at the end of each month from January 1988 to June 2019, as described in Equations (11) and (12), using a 60-day formation period. The risk factors applied in these cross-sectional regressions are the same as those in Model 6 of Table 2. Subsequently, stocks are categorized into portfolios at the end of each month based on $E_{t} [{I E}_{i, t + T}]$ ⁠, and we compute the value-weighted returns for each portfolio in the following month (t+1). Similar analyses are also performed for ${I S}_{i, t + T}$ (Panel B), ${I V}_{i, t + T}$ (Panel C), and ${I K}_{i, t + T}$ (Panel D). The panels in this table provide summary statistics for the five portfolios sorted by each risk factor. Portfolio 1 includes stocks with the lowest predicted risk, while Portfolio 5 comprises those with the highest. The first column in each panel shows the time-series average of the value-weighted portfolio returns, and the second column details their respective idiosyncratic risk. The third column in each panel presents the estimated alphas according to the Carhart (1997) four-factor model. Significance at 1% and 5% levels are indicated with * and **, respectively

Source(s): Created by the author

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