Table 10 Robustness checks: FM...

Table 10

Robustness checks: FM regressions on alternative entropy measures

Regressors	Panel A: Renyi’s entropy	Panel B: Tsallis’s entropy	Panel C: Kullback and Leibler’s entropy
Constant	0.13 (0.59)	0.15 (0.57)	0.07 (0.27)
$E_{t} [{I E}_{p, t + T}]$	−0.35 (−3.08)^*	−0.41 (−3.66)^*	−0.16 (−2.74)^*
${I S}_{p, t}$	−0.76 (−5.77)^*	−0.83 (−5.98)^*	−0.58 (−3.87)^*
${I V}_{p, t}$	−0.12 (−2.72)^*	−0.27 (−2.93)	−0.08 (−1.77)^***
${I K}_{p, t}$	3.11 (12.74)^*	3.35 (12.66)^*	1.80 (5.00)^*
${M K T}_{p, t}$	−0.18 (−2.44)^**	−0.35 (−3.98)^*	−0.048 (−1.91)^***
${S M B}_{p, t}$	0.031 (1.54)	0.046 (1.55)	0.006 (0.94)
${H M L}_{p, t}$	−0.12 (−2.22)^**	−0.27 (−3.82)^*	−0.06 (−1.32)
${M O M}_{p, t}$	−0.011 (−0.78)	−0.017 (−0.77)	−0.002 (−0.62)
${C o s k e w}_{p, t}$	−0.12 (−3.66)^*	−0.23 (−3.93)^*	−0.06 (−2.23)^*
${L I Q}_{p, t}$	−0.80 (−4.53)^*	−0.97 (−5.43)^*	−0.39 (−2.77)^*
${MAX}_{p, t}$	−0.077 (−3.55)^*	−0.082 (−3.63)^*	−0.065 (−2.97)^*
${MIN}_{p, t}$	−0.010 (−1.08)	−0.011 (−1.15)	−0.008 (−0.85)
$χ^{2}$	990.22 [0.00]	997.21 [0.00]	600.10 [0.00]
Pricing error	0.0036	0.0033	0.0083
Adj $R^{2}$	0.37	0.39	0.17

Regressors	Panel A: Renyi’s entropy	Panel B: Tsallis’s entropy	Panel C: Kullback and Leibler’s entropy
Constant	0.13 (0.59)	0.15 (0.57)	0.07 (0.27)
$E_{t} [{I E}_{p, t + T}]$	−0.35 (−3.08)^*	−0.41 (−3.66)^*	−0.16 (−2.74)^*
${I S}_{p, t}$	−0.76 (−5.77)^*	−0.83 (−5.98)^*	−0.58 (−3.87)^*
${I V}_{p, t}$	−0.12 (−2.72)^*	−0.27 (−2.93)	−0.08 (−1.77)^***
${I K}_{p, t}$	3.11 (12.74)^*	3.35 (12.66)^*	1.80 (5.00)^*
${M K T}_{p, t}$	−0.18 (−2.44)^**	−0.35 (−3.98)^*	−0.048 (−1.91)^***
${S M B}_{p, t}$	0.031 (1.54)	0.046 (1.55)	0.006 (0.94)
${H M L}_{p, t}$	−0.12 (−2.22)^**	−0.27 (−3.82)^*	−0.06 (−1.32)
${M O M}_{p, t}$	−0.011 (−0.78)	−0.017 (−0.77)	−0.002 (−0.62)
${C o s k e w}_{p, t}$	−0.12 (−3.66)^*	−0.23 (−3.93)^*	−0.06 (−2.23)^*
${L I Q}_{p, t}$	−0.80 (−4.53)^*	−0.97 (−5.43)^*	−0.39 (−2.77)^*
${MAX}_{p, t}$	−0.077 (−3.55)^*	−0.082 (−3.63)^*	−0.065 (−2.97)^*
${MIN}_{p, t}$	−0.010 (−1.08)	−0.011 (−1.15)	−0.008 (−0.85)
$χ^{2}$	990.22 [0.00]	997.21 [0.00]	600.10 [0.00]
Pricing error	0.0036	0.0033	0.0083
Adj $R^{2}$	0.37	0.39	0.17

Note(s): The methodology used here mirrors that of Table 4, with the only difference being the substitution of Shannon entropy (calculated using Equation (5) with Renyi’s collision entropy (Equation (14), Tsallis’s entropy (Equation (15), and Kullback and Leibler’s entropy (Equation (16)). We then replicate the same pricing analyses as those shown in Table 4. The symbols *, **, and *** represent statistical significance at the 1%, 5%, and 10% levels, respectively. The Fama-MacBeth (FM) t-statistics and the $χ^{2}$ test results are noted in parentheses and brackets, respectively

Source(s): Created by the author

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