Modeling the Linkages between Bitcoin, Gold, Dollar, Crude Oil, and Stock Markets: A GARCH-EVT-Copula Approach

Table 7

Results of VaR and ES backtesting.

	Portfolio 1			Portfolio 2			Portfolio 3
	VaR		ES	VaR		ES	VaR		ES
Test			McNeil			McNeil			McNeil
Panel A: the whole sample
90%	0.8818	0.9876	0.4601	0.2761	0.5408	0.3311	0.8123	0.7888	0.1304
95%	0.8364	0.9673	0.3800	0.5471	0.3671	0.0919	0.7493	0.8044	0.1442
97.5%	0.8868	0.6991	0.2460	0.1656	0.2601	0.7326	0.3925	0.5375	0.1858
99%	0.2149	0.4068	0.9904	0.1038	0.2370	0.9998	0.0733	0.1767	0.6055
Panel B: without the COVID-19
90%	0.1478	0.1099	0.3379	0.2319	0.4770	0.1812	0.5784	0.8485	0.2590
95%	0.2393	0.3926	0.3134	0.6267	0.5925	0.1166	0.8529	0.7138	0.1839
97.5%	0.5644	0.7834	0.4697	0.7458	0.7946	0.1570	0.8971	0.8881	0.1607
99%	0.5576	0.8060	0.8942	0.2414	0.4657	0.2653	0.2786	0.5227	0.4108
Panel C: within the COVID-19
90%	0.3142	0.5646	0.9524	0.0313	0.0975	0.9961	0.6826	0.9185	0.4415
95%	0.7732	0.5354	0.7085	0.4092	0.2479	0.9929	0.1777	0.1134	0.7451
97.5%	0.5650	0.6567	0.9897	0.5650	0.6567	0.9999	0.1970	0.2912	0.9863
99%	0.8077	0.9373	0.9999	0.6967	0.9125	0.9999	0.8077	0.9373	0.9996

Note. The weights of bitcoin, gold, dollar, crude oil, and stock in portfolio 1 are 20%, 20%, 20%, 20%, and 20%. The weights in portfolio 2 are 10%, 10%, 10%, 10%, and 60%, respectively. The weights in portfolio 3 are 10%, 10%, 10%, 35%, and 35%, respectively.