Table 2 Descriptive statistics of...

Table 2

Descriptive statistics of monthly excess stock market returns, conditional variances and implied variance

Variable	Mean(%)	Median(%)	Max(%)	Min(%)	Std. Dev.(%)	Skewness	Kurtosis
Panel A: Whole sample period (191 monthly observations)
R_t+1	0.5364	0.8728	10.7706	−16.9984	3.8743	−0.7829	5.2820
$σ_{R W, t + 1}^{2}$	0.2801	0.1231	5.4539	0.0138	0.5796	6.0531	46.6412
$σ_{M, t + 1}^{2}$	0.3457	0.1430	8.7049	0.0391	0.7787	7.8393	76.4870
$σ_{G, t + 1}^{2}$	0.2981	0.1419	5.2800	0.0397	0.5856	6.0737	45.1464
$σ_{G J R, t + 1}^{2}$	0.2792	0.1654	3.3902	0.0422	0.4441	5.4099	35.8330
$σ_{I V, t + 1}^{2}$	4.1351	2.6569	35.8681	0.9044	4.6218	3.8514	21.5677

Variable	Mean(%)	Median(%)	Max(%)	Min(%)	Std. Dev.(%)	Skewness	Kurtosis
Panel A: Whole sample period (191 monthly observations)
R_t+1	0.5364	0.8728	10.7706	−16.9984	3.8743	−0.7829	5.2820
$σ_{R W, t + 1}^{2}$	0.2801	0.1231	5.4539	0.0138	0.5796	6.0531	46.6412
$σ_{M, t + 1}^{2}$	0.3457	0.1430	8.7049	0.0391	0.7787	7.8393	76.4870
$σ_{G, t + 1}^{2}$	0.2981	0.1419	5.2800	0.0397	0.5856	6.0737	45.1464
$σ_{G J R, t + 1}^{2}$	0.2792	0.1654	3.3902	0.0422	0.4441	5.4099	35.8330
$σ_{I V, t + 1}^{2}$	4.1351	2.6569	35.8681	0.9044	4.6218	3.8514	21.5677

Panel B: High uncertainty periods with positive FEPU_t (79 monthly observations)
R_t+1	0.3097	0.8423	10.7706	−16.9984	4.9157	−0.6526	4.0718
$σ_{R W, t + 1}^{2}$	0.4727	0.2281	5.4539	0.0446	0.8283	4.2532	22.8819
$σ_{M, t + 1}^{2}$	0.5140	0.2069	8.7049	0.0573	1.1509	5.4612	35.9613
$σ_{G, t + 1}^{2}$	0.4566	0.1986	5.2800	0.0584	0.8441	4.2677	21.9725
$σ_{G J R, t + 1}^{2}$	0.4285	0.2456	3.3902	0.0623	0.6349	3.7371	17.0246
$σ_{I V, t + 1}^{2}$	5.9205	3.9402	35.8681	1.1707	6.1749	2.8557	12.1809

Panel B: High uncertainty periods with positive FEPU_t (79 monthly observations)
R_t+1	0.3097	0.8423	10.7706	−16.9984	4.9157	−0.6526	4.0718
$σ_{R W, t + 1}^{2}$	0.4727	0.2281	5.4539	0.0446	0.8283	4.2532	22.8819
$σ_{M, t + 1}^{2}$	0.5140	0.2069	8.7049	0.0573	1.1509	5.4612	35.9613
$σ_{G, t + 1}^{2}$	0.4566	0.1986	5.2800	0.0584	0.8441	4.2677	21.9725
$σ_{G J R, t + 1}^{2}$	0.4285	0.2456	3.3902	0.0623	0.6349	3.7371	17.0246
$σ_{I V, t + 1}^{2}$	5.9205	3.9402	35.8681	1.1707	6.1749	2.8557	12.1809

Panel C: Low uncertainty periods with negative FEPU_t (112 monthly observations)
R_t+1	0.6963	1.0166	9.3792	−9.3764	2.9412	−0.6396	4.4701
$σ_{R W, t + 1}^{2}$	0.1442	0.0914	1.9980	0.0138	0.2188	6.0243	48.2440
$σ_{M, t + 1}^{2}$	0.2270	0.1275	1.5481	0.0391	0.2699	3.1271	12.9936
$σ_{G, t + 1}^{2}$	0.1863	0.1191	2.0411	0.0397	0.2363	5.2797	37.3554
$σ_{G J R, t + 1}^{2}$	0.1739	0.1322	1.4297	0.0422	0.1653	4.8534	33.3487
$σ_{I V, t + 1}^{2}$	2.8758	2.0867	19.4834	0.9044	2.4292	3.9540	23.8663

Panel C: Low uncertainty periods with negative FEPU_t (112 monthly observations)
R_t+1	0.6963	1.0166	9.3792	−9.3764	2.9412	−0.6396	4.4701
$σ_{R W, t + 1}^{2}$	0.1442	0.0914	1.9980	0.0138	0.2188	6.0243	48.2440
$σ_{M, t + 1}^{2}$	0.2270	0.1275	1.5481	0.0391	0.2699	3.1271	12.9936
$σ_{G, t + 1}^{2}$	0.1863	0.1191	2.0411	0.0397	0.2363	5.2797	37.3554
$σ_{G J R, t + 1}^{2}$	0.1739	0.1322	1.4297	0.0422	0.1653	4.8534	33.3487
$σ_{I V, t + 1}^{2}$	2.8758	2.0867	19.4834	0.9044	2.4292	3.9540	23.8663

Panel D: High uncertainty periods with positive FVOV_t (68 monthly observations)
R_t+1	0.3887	0.7338	10.7706	−16.9984	4.6578	−0.7512	5.0119
$σ_{R W, t + 1}^{2}$	0.4810	0.2253	5.4539	0.0267	0.8679	4.2022	21.8380
$σ_{M, t + 1}^{2}$	0.5232	0.1813	8.7049	0.0869	1.2324	5.1580	31.7502
$σ_{G, t + 1}^{2}$	0.4675	0.1689	5.2800	0.0826	0.9037	4.0162	19.3136
$σ_{G J R, t + 1}^{2}$	0.4405	0.2190	3.3902	0.0831	0.6782	3.5215	14.9894
$σ_{I V, t + 1}^{2}$	6.0566	3.8133	35.8681	1.4496	6.4383	2.8337	11.6743

Panel D: High uncertainty periods with positive FVOV_t (68 monthly observations)
R_t+1	0.3887	0.7338	10.7706	−16.9984	4.6578	−0.7512	5.0119
$σ_{R W, t + 1}^{2}$	0.4810	0.2253	5.4539	0.0267	0.8679	4.2022	21.8380
$σ_{M, t + 1}^{2}$	0.5232	0.1813	8.7049	0.0869	1.2324	5.1580	31.7502
$σ_{G, t + 1}^{2}$	0.4675	0.1689	5.2800	0.0826	0.9037	4.0162	19.3136
$σ_{G J R, t + 1}^{2}$	0.4405	0.2190	3.3902	0.0831	0.6782	3.5215	14.9894
$σ_{I V, t + 1}^{2}$	6.0566	3.8133	35.8681	1.4496	6.4383	2.8337	11.6743

Panel E: Low uncertainty periods with negative FVOV_t (123 monthly observations)
R_t+1	0.6181	1.0554	9.3792	−9.3764	3.3827	−0.6968	4.2307
$σ_{R W, t + 1}^{2}$	0.1690	0.0934	2.0075	0.0138	0.2732	5.2131	34.0925
$σ_{M, t + 1}^{2}$	0.2476	0.1393	1.5481	0.0391	0.2882	2.7451	10.3425
$σ_{G, t + 1}^{2}$	0.2045	0.1254	2.0411	0.0397	0.2465	4.4355	28.5622
$σ_{G J R, t + 1}^{2}$	0.1901	0.1356	1.4297	0.0422	0.1789	3.8126	22.4139
$σ_{I V, t + 1}^{2}$	3.0729	2.1433	19.4834	0.9044	2.7033	3.4404	17.9136

Panel E: Low uncertainty periods with negative FVOV_t (123 monthly observations)
R_t+1	0.6181	1.0554	9.3792	−9.3764	3.3827	−0.6968	4.2307
$σ_{R W, t + 1}^{2}$	0.1690	0.0934	2.0075	0.0138	0.2732	5.2131	34.0925
$σ_{M, t + 1}^{2}$	0.2476	0.1393	1.5481	0.0391	0.2882	2.7451	10.3425
$σ_{G, t + 1}^{2}$	0.2045	0.1254	2.0411	0.0397	0.2465	4.4355	28.5622
$σ_{G J R, t + 1}^{2}$	0.1901	0.1356	1.4297	0.0422	0.1789	3.8126	22.4139
$σ_{I V, t + 1}^{2}$	3.0729	2.1433	19.4834	0.9044	2.7033	3.4404	17.9136

Note(s): The table reports descriptive statistics of monthly excess stock market returns, conditional variances, and implied variance. R_t+1 is the monthly excess stock market returns in month t+1. $σ_{R W, t + 1}^{2}$ is the conditional variance in month t+1 estimated by the rolling window model. $σ_{M, t + 1}^{2}$ is the conditional variance in month t+1 estimated by the MIDAS. $σ_{G, t + 1}^{2}$ is the conditional variance in month t+1 estimated by the GARCH(1,1). $σ_{G J R, t + 1}^{2}$ is the conditional variance in month t+1 estimated by the GJR-GARCH(1,1). $σ_{I V, t + 1}^{2}$ is the implied variance in month t+1 calculated by the square of VIX_t. Panel A reports the descriptive statistics during the whole sample period. Panel B and Panel D report the descriptive statistics during high uncertainty periods with positive FEPU_t and positive FVOV_t, respectively. Panel C and Panel E report the descriptive statistics during low uncertainty periods with negative FEPU_t and negative FVOV_t, respectively. The sample period is from January 2003 to November 2018

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