Information transmission and hedging effectiveness for the pairs crude oil-gold and crude oil-Bitcoin during the COVID-19 outbreak

Figures & data

Figure 1. Hourly prices of oil, gold, and Bitcoin.

Source: Authors' calculations.

Figure 2. Hourly returns of oil, gold, and Bitcoin.

Source: Authors' calculations.

Table 1. Descriptive statistics.

	Panel A: Pre-COVID-19 period (May 21, 2019 to December 31, 2019)
	Mean	Maximum	Minimum	Std. Dev.	Skewness	Kurtosis	Jarque-Bera	Q-stat (18)	ARCH	ADF
OIL	−0.0024	12.687	−6.009	0.460	4.824	179.844	462794^a	54.873 ^a	12.464^b	−58.764^a
GOLD	0.0050	1.372	−2.276	0.181	−0.294	18.451	35276.2^a	29.356^b	130.652^a	−60.976^a
BTC	−0.0029	9.342	−13.691	0.983	−0.855	34.027	142468^a	38.433^a	13.552^a	−58.625^a
	Panel B: COVID-19 period (May 1, 2020 to May 20, 2020)
	Mean	Maximum	Minimum	Std. Dev.	Skewness	Kurtosis	Jarque-Bera	Q-stat (18)	ARCH	ADF
OIL	−0.0303	16.375	−23.503	1.415	−1.095	56.883	262708^a	57.044^a	18.630^a	−45.965^a
GOLD	0.0061	2.677	−3.174	0.312	−0.351	16.469	16431.9^a	65.529^a	70.709^a	−47.759^a
BTC	0.0142	18.352	−18.772	1.311	−2.491	74.703	466677^a	140.99^a	49.369^a	−10.121^a

Notes: BTC (Bitcoin). Q-stat denotes the Ljung–Box Q-statistics. ARCH test refers to the LM-ARCH test of Engle (1982). ADF refers to the augmented Dickey-Fuller test. ^a,^b,^c indicate statistical significance at 1%, 5% and 10% respectively.

Source: Authors' calculations.

Table 2. Correlation matrix.

Pre-COVID-19 period (May 21, 2019 to December 31, 2019)				COVID-19 period (May 1, 2020 to May 20, 2020)
	OIL	GOLD	BTC		OIL	GOLD	BTC
OIL	1			OIL	1
GOLD	−0.124^a	1		GOLD	−0.029^a	1
BTC	0.026^a	0.028^a	1	BTC	0.115^a	−0.047^a	1

Notes: BTC (Bitcoin). ^a,b,c indicate statistical significance at 1%, 5%, and 10% respectively.

Source: Authors' calculations.

Table 3. Return and volatility spill-overs for the pair oil-gold in the pre-COVID-19 period (May 21, 2019 to December 31, 2019).

	DCC-GARCH		VAR-GARCH		BEKK-GARCH
	OIL	GOLD	OIL	GOLD		OIL	GOLD
Panel A. Mean Equation
Constant	−0.003	0.004^b	−0.002	0.004^b	Constant	−0.002	0.004^c
	0.503	0.040	0.699	0.045		0.725	0.061
$r_{t-1}^o$	−0.007	0.008	−0.006	0.008	$r_{t-1}^o$	−0.012	0.006
	0.698	0.344	0.749	0.216		0.423	0.406
$r_{t-1}^g$	−0.078^c	−0.002	−0.071	−0.002	$r_{t-1}^g$	−0.094^b	0.003
	0.067	0.902	0.102	0.922		0.033	0.881
Panel B. Variance Equation
					C	0.174^a
						0.000
Constant	0.025^a	0.003^a	0.025^a	0.003^a		−0.015^a	0.008^a
	0.000	0.007	0.000	0.000		0.000	0.000
${(e_{t-1}^o)}^2$	0.163^a	1.080^a	0.165^a	1.094^a	A	0.397^a	0.008
	0.000	0.000	0.000	0.000		0.000	0.389
${(e_{t-1}^g)}^2$	0.018^a	0.134^a	0.017^a	0.129^a		0.564^a	0.170^a
	0.000	0.000	0.000	0.000		0.000	0.000
$h_{t-1}^o$	0.439^a	0.186	0.462^a	0.067	B	0.741^a	0.017
	0.000	0.618	0.000	0.683		0.000	0.500
$h_{t-1}^g$	−0.060^a	0.997^a	−0.054^a	0.981^a		−0.057^a	0.986^a
	0.000	0.000	0.000	0.000		0.000	0.000
Correlations
${\varnothing }_1$	0.005^a		−0.182^1
	0.000		0.000
${\varnothing }_2$	0.993^a
	0.000
Panel D. Diagnostic Tests
LogL	678.145		663.095			503.301
AIC	6.824		6.826			6.155
$\mathrm{Q}\left[20\right]$	39.091^a	11.729	38.807	11.609		39.714	11.287
	0.007	0.925	0.007	0.929		0.005	0.938
$Q^2\left[20\right]$	7.913^a	31.595	7.432	33.041		8.582	38.575
	0.273	0.048	0.268	0.033		0.280	0.000

Notes: The number of lags for VAR is decided using SIC and AIC criteria. Q(20), and Q²(20) indicate the empirical statistics of Ljung-Box Q statistics of order 20 for autocorrelation applied to the standardised residuals and squared standardised residuals, respectively. Values in parentheses are the P-values. ^a,^b,^c indicate statistical significance at 1%, 5% and 10% respectively.

Constant conditional correlation

Source: Authors' calculations.

Table 4. Return and volatility spill-overs for the pair oil-gold during the COVID-19 period (January 1, 2020 to May 20, 2020).

	DCC-GARCH		VAR-GARCH			BEKK-GARCH
	OIL	GOLD	OIL	GOLD		OIL	GOLD
Panel A. Mean Equation
Constant	−0.016	0.006	−0.015	0.008	Constant	−0.018	0.008^c
	0.249	0.139	0.173	0.121		0.187	0.091
$r_{t-1}^o$	−0.003	−0.003	−0.009	−0.001	$r_{t-1}^o$	0.001	−0.004
	0.889	0.522	0.784	0.940		0.965	0.418
$r_{t-1}^g$	−0.004	−0.080^a	−0.022	−0.074^a	$r_{t-1}^g$	0.018	−0.077^a
	0.954	0.000	0.747	0.006		0.771	0.007
Panel B. Variance Equation
					C	0.012
						0.759
Constant	0.002	0.000	0.002	0.000		0.001	0.016^a
	0.213	0.135	0.183	0.063		0.953	0.000
${(e_{t-1}^o)}^2$	0.037^b	0.243^b	0.036^a	0.232^b	A	0.177^a	0.015
	0.019	0.026	0.003	0.011		0.000	0.252
${(e_{t-1}^g)}^2$	0.000	0.036^a	0.000	0.033^a		0.014	0.200^a
	0.198	0.001	0.220	0.000		0.189	0.000
$h_{t-1}^o$	0.960^a	−0.202^c	0.961^a	−0.200^c	B	0.985^a	−0.002^b
	0.000	0.094	0.000	0.080		0.000	0.049
$h_{t-1}^g$	0.000	0.960^a	0.000	0.963^a		0.032^b	0.978^a
	0.266	0.000	0.300	0.000		0.022	0.000
Panel C. Correlations
${\varnothing }_1$	−0.032^a		−0.034
	0.000		0.253
${\varnothing }_2$	0.966^a
	0.000
Panel D. Diagnostic Tests
LogL	−2481.2		−2555.5			−2488.6
AIC	6.270		6.271			6.273
$Q\left[20\right]$	39.248^a	24.511	39.604^a	24.218		38.182^a	23.193
	0.006	0.221	0.006	0.233		0.008	0.279
$Q^2\left[20\right]$	10.943	20.874	11.081	21.849		15.511	21.337
	0.948	0.405	0.944	0.349		0.746	0.378

Notes: The lag length for VAR is decided using SIC and AIC criteria. Q(20), and Q²(20) indicate the empirical statistics of Ljung-Box Q statistics of order 20 for autocorrelation applied to the standardised residuals and squared standardised residuals, respectively. Values in parentheses are the P-values. ^a,^b,^c indicate statistical significance at 1%, 5% and 10% respectively.

Source: Authors' calculations.

Table 5. Return and volatility linkages for the pair oil-BTC during the pre-COVID-19 period (May 21, 2019 to December 31, 2019).

	DCC-GARCH		VAR-GARCH			BEKK-GARCH
	OIL	BTC	OIL	BTC		OIL	BTC
Panel A. Mean Equation
Constant	0.000	−0.012	0.000	−0.015	Constant	0.001	−0.014
	0.826	0.179	0.962	0.181		0.897	0.244
$r_{t-1}^o$	0.000	0.051^c	0.001	0.060^b	$r_{t-1}^o$	0.005	0.040
	0.772	0.064	0.950	0.030		0.789	0.117
$r_{t-1}^b$	0.001	−0.026	0.003	−0.025	$r_{t-1}^b$	0.004	−0.019
	0.734	0.359	0.687	0.360		0.512	0.367
Panel B. Variance Equation
					C	0.187^a
						0.000
Constant	0.031^a	−0.011^b	0.032^a	−0.012^c		−0.041	0.069^b
	0.000	0.035	0.000	0.069		0.280	0.042
${(e_{t-1}^o)}^2$	0.226^a	0.001	0.228^a	0.003	A	0.456^a	−0.075
	0.000	0.187	0.000	0.358		0.000	0.110
${(e_{t-1}^b)}^2$	−0.125^a	0.027^a	−0.126^a	0.028^a		−0.035^b	0.168^a
	0.000	0.000	0.000	0.005		0.022	0.000
$h_{t-1}^o$	0.536^a	0.000	0.531^a	0.000	B	0.728^a	0.087
	0.000	0.861	0.000	0.964		0.000	0.361
$h_{t-1}^b$	0.263^a	0.958^a	0.264^a	0.959^a		0.013^b	0.978^a
	0.000	0.000	0.000	0.000		0.023	0.000
Correlations
${\varnothing }_1$	−0.018^a		0.019
	0.000		0.224
${\varnothing }_2$	−0.050
	0.168
Panel D. Diagnostic Tests
LogL	−5076.453		−5088.395			−5097.360
AIC	6.154		6.298			6.155
$Q\left[20\right]$	45.005^a	16.196	44.911^a	15.964		44.369^a	15.686
	0.001	0.704	0.001	0.719		0.001	0.736
$Q^2\left[20\right]$	13.968	17.898	14.353	17.950		17.226	18.377
	0.387	0.594	0.371	0.591		0.368	0.563

Notes: lag length for VAR is decided using SIC and AIC criteria. Q(20), and Q²(20) indicate the empirical statistics of Ljung-Box Q statistics of order 20 for autocorrelation applied to the standardised residuals and squared standardised residuals, respectively. Values in parentheses are the P-values. ^a,^b,^c indicate statistical significance at 1%, 5% and 10% respectively.

Source: Authors' calculations.

Table 6. Return and volatility linkages for the pair oil-BTC during the COVID-19 period (January 1, 2020 to May 20, 2020).

	DCC-GARCH		VAR-GARCH					BEKK-GARCH
	OIL	BTC	OIL		BTC			OIL	BTC
Panel A. Mean Equation
Constant	−0.012	0.027^c	−0.013	0.020			Constant	−0.014	0.035^b
	0.367	0.071	0.270	0.118				0.254	0.026
$r_{t-1}^o$	0.001	−0.009	−0.016	−0.009			$r_{t-1}^o$	−0.004	−0.009
	0.968	0.571	0.600	0.705				0.848	0.486
$r_{t-1}^b$	0.054^a	−0.023	0.049^a	−0.017			$r_{t-1}^b$	0.052^a	−0.012
	0.000	0.335	0.009	0.528				0.000	0.640
Panel B. Variance Equation
							C	−0.046^b
								0.011
Constant	−0.004	0.058	0.000	0.074				0.055	0.162
	0.566	0.191	0.937	0.209				0.297	0.314
${(e_{t-1}^o)}^2$	0.060^a	−0.007	0.028^b	−0.001			A	0.232^a	−0.003
	0.000	0.270	0.029	0.860				0.000	0.923
${(e_{t-1}^b)}^2$	−0.010^a	0.102^c	−0.016^c	0.054				−0.012	0.231
	0.002	0.077	0.059	0.110				0.115	0.160
$h_{t-1}^o$	0.938^a	0.020	0.951^a	0.003			B	0.974^a	0.002
	0.000	0.338	0.000	0.763				0.000	0.808
$h_{t-1}^b$	0.022	0.793^a	0.050	0.788^a				0.005	0.950^a
	0.264	0.000	0.387	0.000				0.426	0.000
Correlations
${\varnothing }_1$	0.028^a		0.042
	0.000		0.146
${\varnothing }_2$	0.185
	0.584
Panel D. Diagnostic Tests
LogL	−5231.772		−5225.422					−5261.267
AIC	7.656		7.659					7.658
$Q\left[20\right]$	35.596^b	14.638	35.143^b	14.887				36.077^b	13.710
	0.017	0.797	0.019	0.782				0.015	0.845
$Q^2\left[20\right]$	7.245	5.833	7.151	5.951				7.997	7.112
	0.996	0.999	0.996	0.998				0.992	0.996

Notes: The number of lags for VAR is decided using SIC and AIC criteria. Q(20), and Q²(20) indicate the empirical statistics of Ljung-Box Q statistics of order 20 for autocorrelation applied to the standardised residuals and squared standardised residuals, respectively.

Values in parentheses are the P-values. ^a,^b,^c indicate statistical significance at 1%, 5% and 10% respectively.

Source: Authors' calculations.

Figure 3. Pairwise dynamic conditional correlations.

Source: Authors' calculations.

Table 7. Optimal weights and hedge ratios.

	OIL/GOLD				OIL/BTC
	DCC-GARCH	VAR-GARCH	BEKK-GARCH		DCC-GARCH	VAR-GARCH	BEKK-GARCH
Panel A: Pre-COVID-19 (May 21, 2019 to December 31, 2019)				Panel C: Pre-COVID-19 (May 21, 2019 to December 31, 2019)
$w_t^{OG}$	0.20	0.20	0.21	$w_t^{OB}$	0.79	0.79	0.80
${\beta }_t^{OG}$	−0.41	−0.43	−0.44	${\beta }_t^{OB}$	0.01	0.01	0.00
Panel B: COVID-19 (May 1, 2020 to May 20, 2020)				Panel D: COVID-19 (May 1, 2020 to May 20, 2020)
$w_t^{OG}$	0.09	0.09	0.10	$w_t^{OB}$	0.47	0.47	0.47
${\beta }_t^{OG}$	0.07	0.06	0.04	${\beta }_t^{OB}$	0.03	0.01	0.02

Note: $w_t$ and ${\beta }_t$ refer to the optimal weights and hedge ratios, respectively. In superscript, O, G, B represent oil, gold, and Bitcoin, respectively.

Source: Authors' calculations.

Figure 4. Time-varying hedge ratio.

Source: Authors' calculations.

Table 8. Hedging effectiveness (HE) results.

	OIL/GOLD				OIL/BTC
	DCC-GARCH	VAR-GARCH	BEKK-GARCH		DCC-GARCH	VAR-GARCH	BEKK-GARCH
Panel A: Pre-COVID-19 (May 21, 2019 to December 31, 2019)				Panel C: Pre-COVID-19 (May 21, 2019 to December 31, 2019)
HE (%)	86.85	86.88	86.78	HE (%)	17.69	17.28	17.66
Panel B: COVID-19 (May 1, 2020 to May 20, 2020)				Panel D: COVID-19 (May 1, 2020 to May 20, 2020)
HE (%)	94.10	94.05	94.02	HE (%)	61.04	60.56	61.02

Note: This table presents the results of hedging effectiveness (HE) of gold and Bitcoin for the oil market in both periods.

Source: Authors' calculations.

Table 9. Estimation results for the hedge and safe haven properties of gold and Bitcoin against oil during the COVID-19 period.

	Hedge ( ${\gamma }_0)$	Safe haven ( ${\gamma }_1)$
Gold	−0.124^a	−0.122^a
Bitcoin	0.084^a	0.002

Note: The results reported in this table are estimated based on Equation (13)(13) $${\mathit{DCC}}_t=\mathrm{}{\gamma }_0+\mathrm{}{\gamma }_{1}D(\mathit{COVID}-19)$$(13) . ^a indicates statistical significance at the 1% level.

Source: Authors' calculations.

Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the econometric society, 987–1007.

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