Covid-19 pandemic and tail-dependency networks of financial assets.

This study provides evidence on the frequency-based dependency networks of various financial assets in the tails of return distributions given the extreme price movements under the exceptional circumstance of the Covid-19 pandemic, qualified by the IMF as the Great Lockdown. Our results from the quantile cross-spectral analysis and tail-dependency networks show increases in the network density in both lower and upper joint distributions of asset returns. Particularly, we observe an asymmetric impact of the Covid-19 because the left-tail dependencies become stronger and more prevalent than the right-tail dependencies. The cross-asset tail-dependency of equity, currency and commodity also increases considerably, especially in the left-tail, implying a higher degree of tail contagion effects. Meanwhile, Bitcoin and US Treasury bonds are disconnected from both tail-dependency networks, which suggests their safe-haven characteristics.

Introduction

Since its first case was officially reported in China in late December 2019, the Covid-19 disease has spread rapidly worldwide and was declared as a global pandemic in March 2020. Its severity has resulted in an unprecedented impact on financial markets, where investors have panic-sold out of fears. Panic trading has caused several significant drops in various markets (Zhang, Hu, Ji, 2020, Shehzad, Xiaoxing, Kazouz, 2020). For example, the U.S. stock markets had to activate the market-wide circuit-breakers four times since the outbreak of the Covid-19 pandemic, with respect to the S&P 500 Index drops, in an effort to calm the panic-trading. Baker et al. (2020a) assess that over the last century, no other pandemic has had such an effect on international financial markets like the Covid-19. Not only stock markets, but also other asset markets such as currencies and commodities have been affected significantly. Global travel restrictions have caused significant drops in oil prices due to lower demand for oil (leading to negative crude oil futures prices for the first time in the history) and put pressure on the commodity-based currencies, such as the Canadian dollar. Also, limited trade routes and tourism badly affected several countries, such as Australia and New Zealand, causing their currencies to weaken. On the other hand, gold prices hit all-time high levels due to concerns that an economic recovery from the coronavirus pandemic might be weakening in the United States and elsewhere. As the majority of financial markets continue to experience extreme movements and are likely interconnected, investors are left with questions about portfolio diversification and potential shifts in asset allocation. Our current study thus aims to shed a light on these issues before and during the Covid-19 outbreak, while considering a large and comprehensive set of assets and asset classes that are of common interest for portfolio management due to their different risk-return characteristics.1

More precisely, we investigate the Covid-19 effects on the dependency network of equity, currency, commodity, bond, and Bitcoin markets. Our focus is on the tail-dependency network for each pair of the assets using quantile cross-spectral analysis proposed by Baruník and Kley (2019). We analyse two quantiles that represent the left tail (0.05) and the right tail (0.95) of the joint distribution. Previous studies have shown evidence of the asymmetry in tail-dependence structure in various asset markets (i.e., the effect in the left tail is stronger and more prevalent than in the right tail). For example, Okimoto (2008) and Jondeau (2016) find an asymmetric behaviour of the tail-dependence in equity portfolios, especially in the bear markets. Wang et al. (2013) document this asymmetry in the tail-dependence structure between stock and currency markets. Hammoudeh et al. (2014) confirm asymmetric tail dependence between stock and commodity futures markets. Mensi et al. (2017) provide evidence on time-varying asymmetric tail dependence in commodity markets. Following the literature, we analyse both tails of the distribution with a conjecture that there exists asymmetric behaviour in the tail-dependency network, and our empirical results confirm this hypothesis. In particular, among different types of assets, the connectivity of the tail-dependency networks among equities and commodities has increased the most due to Covid-19. We, however, find a notable result that Bitcoin and US Treasury (UST) bonds are disconnected from other assets, making them a safe haven for the investors during the Covid-19 crisis.

Our study contributes to the literature in many aspects. Firstly, we provide fresh evidence regarding the impact of Covid-19 on the tail-dependency network of financial assets. Although earlier studies have investigated the dynamics of cross-asset relations during Covid-19 period (Rizwan, Ahmad, Ashraf, 2020, Gharib, Mefteh-Wali, Jabeur, 2020, Sharif, Aloui, Yarovaya, 2020, Akhtaruzzaman, Boubaker, Sensoy, 2020), no study has been done on these relations in a network framework. This approach provides us a powerful tool to analyse an extended set of assets at once and make inference via visual analysis. Secondly, we demonstrate how the Covid-19 pandemic can amplify the asymmetry of the tail-dependency network, which is the difference between the left and the right tail of the asset return distribution. This is especially important in a period where financial markets experience extreme downturns with increased volatility due to the pandemic (Mazur, Dang, Vega, 2020, Baig, Butt, Haroon, Rizvi, 2020, Albulescu, 2020, Bai, Wei, Wei, Li, Zhang, 2020, Baker, Bloom, Davis, Kost, Sammon, Viratyosin, 2020). Lastly, since the Covid-19 pandemic started, fear and uncertainty have taken control in the financial markets (Lyocsa and Molnar, 2020) where investors started panic trading (Ortmann et al., 2020) and changed their economic behaviour (Baker et al., 2020b). Naturally, academics are still looking for strategies for risk management (Ji, Zhang, Zhao, 2020, Conlon, McGee, 2020, Corbet, Larkin, Lucey, 2020) or assets that perform relatively better than others during the crisis period (Broadstock et al., 2020). While these studies argue that Bitcoin do not act as hedge or safe haven during the pandemic period, and support the safe-haven role of gold during the same time, our findings provide an important implication for financial risk management by showing the diversification benefit of Bitcoin and UST bond during the alike Covid-19 crisis.

Data and methodology

Data

We utilise daily prices of 51 international assets from Dukascopy Bank SA, a Swiss forex bank and an ECN broker with its headquarters in Geneva. In particular, our dataset consists of 23 spot exchange rates against the US dollar and the Dollar index, contracts for the difference on 11 commodities (2 precious metals, 5 agriculture and 4 energy), contracts for the difference on 14 international equity indices, contract for difference on UST bonds (30 years to maturity), and contract for difference on Bitcoin.2 As we look at the impact of the Covid-19 pandemic on the tail dependency between financial assets, our dataset spans the period from January 1, 2019 to April 30, 2020. To capture the impacts of the Covid-19 to the tail dependency between international assets, we break our sample into two sub-samples. The without Covid-19 sample consists of observations before January, 1 2020, whereas we employ the whole sample to account for the impacts Covid-19 as the first case was officially reported in China in late December 2019.3 Table 1 provides the list of sample assets with their summary statistics. Panel B of Table 1, which corresponds to the sample with the Covid-19 pandemic, reveals that the volatility and kurtosis of all asset returns increase substantially, indicating a high level of uncertainty associated with the nature of the pandemic.

Table 1

Summary statistics of sample assets.

	Panel A: Without Covid-19 period				Panel B: With Covid-19 period
	Mean	Std.Dev.	Skewness	Kurtosis	Mean	Std.Dev.	Skewness	Kurtosis
Equity
AUSTRALIA200	0.070	0.712	-1.387	7.568	-0.012	1.760	-0.333	17.279
CHINA-A50	0.132	1.275	0.223	2.920	0.072	1.619	-0.866	7.752
EUROSTOXX50	0.087	0.828	-0.570	2.427	-0.009	1.895	-2.267	18.778
FRANCE40	0.099	0.820	-0.818	2.336	-0.007	1.906	-2.377	19.029
GERMANY30	0.086	0.953	-0.710	3.799	0.006	1.805	-1.898	17.372
HONGKONG40	0.047	1.105	-0.343	1.445	-0.006	1.471	-1.159	5.871
INDIA50	0.046	0.904	1.211	5.932	-0.038	1.858	-1.532	16.306
JAPAN225	0.074	0.918	-0.308	2.950	0.008	1.559	-1.196	14.110
NETHERLANDS25	0.085	0.779	-0.777	2.281	0.012	1.718	-2.022	15.766
SINGAPORE	0.035	0.791	-1.034	4.358	-0.039	1.428	-1.069	10.696
SPAIN35	0.046	0.795	-0.385	1.159	-0.067	1.721	-2.454	19.406
SWITZERLAND20	0.092	0.720	-0.750	1.791	0.039	1.621	-1.371	15.453
UK100	0.047	0.792	-0.953	4.844	-0.039	1.576	-1.690	14.340
USA500	0.104	0.844	-1.030	7.595	0.045	1.693	-0.794	15.882
Currency
AUDUSD	0.005	0.444	0.092	1.215	-0.018	0.624	-0.463	5.608
DOLLAR INDEX	-0.001	0.292	-0.304	0.680	0.008	0.395	0.602	5.369
EURUSD	-0.004	0.313	0.161	0.912	-0.010	0.396	-0.638	6.324
GBPUSD	0.022	0.522	0.767	1.742	0.002	0.636	-0.439	7.612
NZDUSD	0.006	0.469	-0.231	0.931	-0.023	0.594	-0.789	7.570
USDCAD	-0.019	0.328	-0.234	0.830	0.007	0.424	0.584	3.522
USDCHF	-0.009	0.347	-0.338	1.099	-0.007	0.407	0.058	2.968
USDCNH	0.004	0.318	0.811	9.572	0.009	0.319	0.862	7.690
USDCZK	-0.002	0.357	-0.097	0.701	0.024	0.620	1.756	17.927
USDDKK	0.004	0.312	-0.212	1.006	0.009	0.398	0.596	6.150
USDHKD	-0.002	0.045	-0.931	5.029	-0.003	0.046	-0.846	3.938
USDHUF	0.013	0.480	-0.173	0.330	0.036	0.628	0.728	6.549
USDILS	-0.032	0.308	0.152	0.498	-0.021	0.473	0.631	11.763
USDJPY	0.004	0.337	-0.394	1.149	0.000	0.483	0.719	8.652
USDMXN	-0.014	0.539	0.313	2.241	0.061	0.850	0.789	4.573
USDNOK	-0.001	0.472	-0.114	0.369	0.045	0.861	1.727	15.348
USDPLN	-0.001	0.415	0.058	0.151	0.026	0.554	1.129	10.982
USDRON	0.015	0.340	0.059	1.349	0.021	0.418	0.276	2.575
USDRUB	-0.040	0.477	-0.034	1.035	0.023	0.936	3.001	26.479
USDSEK	0.013	0.449	0.178	0.485	0.022	0.558	0.866	4.722
USDSGD	-0.007	0.195	-0.079	0.428	0.009	0.255	0.244	3.245
USDTHB	-0.032	0.273	-0.372	2.301	0.002	0.317	0.450	3.087
USDTRY	0.030	0.880	0.347	7.257	0.070	0.827	0.246	7.176
USDZAR	-0.016	0.816	-0.044	0.345	0.070	0.936	0.160	0.515
Commodity
BRENT	0.083	2.040	-0.356	10.208	-0.224	3.982	-2.115	20.247
COCOA	0.021	1.492	0.041	-0.043	0.000	1.551	0.135	0.258
COFFEE	0.108	2.061	0.020	0.787	0.020	2.210	0.064	0.488
COTTON	-0.011	1.338	-0.130	1.120	-0.066	1.472	-0.088	1.090
GASOIL	0.082	1.596	0.675	5.876	-0.234	2.838	-1.677	14.504
NATURAL GAS	-0.119	2.431	0.752	5.440	-0.124	2.792	0.800	3.233
SOYBEAN	0.020	1.002	0.566	1.163	-0.019	0.991	0.446	1.184
SUGAR	0.036	1.184	0.643	1.465	0.007	1.328	0.306	1.049
WTI	0.113	1.939	0.504	5.114	-0.249	4.849	-2.572	25.651
SILVER	0.055	1.188	-0.104	2.554	-0.010	1.714	-0.850	12.048
GOLD	0.064	0.741	0.380	1.700	0.080	0.966	0.130	3.841
Bond
USTBOND	0.035	0.544	-0.136	0.995	0.076	0.729	-0.414	7.650
Bitcoin
BTCUSD	0.239	4.408	0.562	4.429	0.234	5.151	-2.239	25.600
Average	0.034	0.861	-0.095	2.625	-0.004	1.317	-0.330	9.906

This table presents the summary statistics of daily returns on 14 international equity indices, 24 currency exchange, 11 commodity contracts, the 30 years US government bond and Bitcoin. Panel A shows the summary statistics of sample assets before the Covid-19 pandemic (1/1/2019 - 31/12/2019), whereas the statistics for the period including the Covid-19 pandemic (1/1/2019 - 28/04/2020) is presented in Panel B.

Methodology

We employ the quantile cross-spectral analysis proposed by Baruník and Kley (2019) to investigate the dependencies in the tails of the joint distribution for each pair of assets. This method allows direct estimates of extreme co-movements between asset returns that are independent of the joint moments across the frequency domain.4 This is of particular interest for economic agents as the dependencies between assets tend to increase significantly during the time of distress (Akhtaruzzaman et al., 2020).

Let and be two stationary processes. The marginal distribution of is denoted by and the corresponding quantile function is . The matrix of quantile cross-covariance kernels, which measures the serial and cross-dependency structure between and is defined as:where and is indicator function. In the frequency domain, this yields the matrix of quantile cross-spectral density kernels, where:Finally, the quantile coherency kernel that measures the dynamic dependency between two processes () and () across frequency (by choosing appropriate ) and the quantiles (by choosing appropriate and ), can be defined as follows:where captures the real part of the complex conjugate . The quantile coherency kernel is estimated via the smoothed rank-based copula cross-periodograms (see Baruník and Kley, 2019, for more details).

In this study, we address the tail dependency structure for both the extreme left tail (5%) and right tail (95%) of the joint distribution for each pair of assets’ returns. We compute daily returns for each assets, as the natural logarithm difference between closing prices of two consecutive trading days, i.e. where is the closing price of asset on day . We follow Baruník and Kley (2019)and use returns standardized by its conditional volatility estimated by a GARCH(1,1) model of Bollerslev (1987). By doing so, we are able to focus on the tail-dependence structure between the joint distribution of asset returns without strong common factors in volatility (see, e.g., Barigozzi, Brownlees, Gallo, Veredas, 2014, Žikeš, Baruník, 2016, for evidence of common volatility factors and its impacts on the conditional return quantiles).5 Given the rapid spread of the Covid-19’s dramatic shock to almost all financial markets, we are particularly interested in its instantaneous impact on the tail-dependency network of financial assets by considering 1-day frequency in the time domain. The estimated quantile coherency is then used as inputs to the adjacency matrix in order to build a tail-dependency network using the force-directed layout algorithm proposed by Fruchterman and Reingold (1991).

Results

Table 2 reports the average return coherency between assets grouped by asset classes. We focus on two quantiles that present the extreme left tail (5%) and right tail (95%) of the return joint distribution. The Covid-19 pandemic significantly increases the dependence between asset classes in both lower and upper tails of the joint distribution, except for average return coherency of currency (commodity) at the lower (upper) tail. The joint dependence between commodities increase the most, particularly in the extreme negative returns.

Table 2

Average return coherency between selected assets.

	Without Covid-19 period		With Covid-19 period
	0.05	0.95	0.05	0.95
Equity	0.629	0.153	0.699	0.217
Currency	0.247	0.098	0.159	0.231
Commodity	0.045	0.099	0.218	0.083
Bond	-0.103	0.083	-0.070	0.159
Bitcoin	-0.054	0.041	0.091	0.027
Average	0.079	0.054	0.177	0.102

This table reports the average return coherency in two quantiles, namely 0.05 and 0.95, between individual assets grouped under the same asset class, except for ‘Bond‘ and ‘Bitcoin‘ where the average correlations to other assets in the sample are reported.

Fig. 1 displays the two networks of extreme negative return coherency. The period without the Covid-19 pandemic is presented in the left plot, whereas the period with the Covid-19 pandemic is in the right plot. In each network, we only present the significant tail dependencies that are stronger than 0.6, in which the blue (red) lines show the positive (negative) quantile coherency. We observe considerable increase in the dependency between assets at the extreme negative return coherency. Almost all 0.05 quantile coherency between assets are positive, which is in line with the literature that assets returns tend to co-move in distress periods (Okorie and Lin, 2020). The Covid-19 pandemic also increases the left-tail dependency between equity indices significantly, whereas the within-asset left-tail correlations between currencies are weaker. The cross-asset return coherency also increases notably by the inclusion of the Covid-19 period.

Fig. 1

Left-tail Dependency Network This network is built using the force-directed layout proposed by Fruchterman and Reingold (1991) with the adjacency matrix being built from the 0.05-quantile coherency measures. Red nodes present equity indices (14 indices), light-blue being exchange rates (24 exchange rates), orange being commodity (11 commodities), yellow being Bitcoin and blue being the UST bond. Green lines indicate positive coherency, whereas red lines present negaitve coherency. The left-plot is the network without the Covid-19 sample and the right-plot is the network with the Covid-19 pandemic. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

In a similar structure, Fig. 2 presents the networks of extreme positive return coherency. Before the Covid-19 pandemic, the right-tail connectedness between assets is much less significant, while there are several negative tail-correlations for some pairs of assets. The inclusion of Covid-19 pandemic changes, however, the network structure dramatically, with a substantial increase in the right-tail dependence, especially between currencies.

Fig. 2

Right-tail Dependency Network This network is built using the force-directed layout proposed by Fruchterman and Reingold (1991) with the adjacency matrix being built from the 0.95-quantile coherency measures. Red nodes present equity indices (14 indices), light-blue being exchange rates (24 exchange rates), orange being commodity (11 commodities), yellow being Bitcoin and blue being the UST bond. Green lines indicate positive coherency, whereas red lines present negaitve coherency. The left-plot is the network without the Covid-19 sample and the right-plot is the network with the Covid-19 pandemic. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

One notable finding is the role of Bitcoin and UST bond in the two networks. While these two assets are almost disconnected vertices in the extreme negative return coherency, they are positively correlated with other assets in the extreme positive return coherency. Thus, they can act as safe-haven assets for international investors with well diversified portfolios.

In Table 3 , we provide information on the density and centrality of the networks. Panel A reports the two centrality measures for each node, namely the strength and closeness centrality, with the average and standard deviation of centrality scores of all nodes being reported at the bottom of Panel A.6 On the other hand, Panel B reports the network’s density and the average clustering coefficients.7 As expected, the strength and closeness centrality increase considerably in the extreme negative return coherency, especially in the equity and commodity indices. The average strength increases from 12.637 to 13.441 with the inclusion of the Covid-19 pandemic. The most significant changes at the individual asset level are for the Spanish and Japanese equity indices, and for Brent and gas oil in the commodities. The strength of centrality also increases in the extreme positive return coherency, from 9.874 before the Covid-19 to 10.490 after the inclusion of the pandemic. Looking at the individual assets, however, the picture is quite different to that of the left-tail dependence. The most significant changes in strength and closeness are recorded in the foreign exchange rates and UST bond, where the strength of the Dollar index increases significantly from 8.745 to 14.051 and that of the UST bond from 9.377 to 14.127.

Table 3

Network Centrality and Density.

	Left-tail return coherencey				Right-tail return coherencey
	Without Covid-19		With Covid-19		Without Covid-19		With Covid-19
Panel A: Node Strength
	Strength	Closeness	Strength	Closeness	Strength	Closeness	Strength	Closeness
Equity
AUSTRALIA200	12.815	0.548	21.266	0.741	10.312	0.463	8.445	0.438
CHINA	12.268	0.516	18.284	0.681	7.421	0.396	6.792	0.376
EUROSTOXX50	16.564	0.622	18.374	0.627	9.346	0.456	10.666	0.462
FRANCE40	16.947	0.626	18.286	0.617	9.007	0.440	9.401	0.446
GERMANY30	16.910	0.638	17.548	0.615	8.313	0.430	11.637	0.497
HONGKONG40	14.965	0.591	18.914	0.693	10.268	0.476	8.358	0.431
INDIA50	14.398	0.609	19.761	0.726	11.141	0.505	7.920	0.425
JAPAN225	15.778	0.615	20.387	0.712	11.165	0.502	10.094	0.476
NETHERLANDS25	15.753	0.601	17.422	0.631	7.972	0.419	8.959	0.432
SINGAPORE	16.663	0.654	19.407	0.663	7.104	0.366	8.949	0.411
SPAIN35	17.407	0.650	20.617	0.719	10.808	0.480	10.276	0.468
SWITZERLAND20	14.554	0.592	17.077	0.618	10.454	0.487	8.037	0.389
UK100	12.961	0.558	19.049	0.657	10.231	0.472	11.244	0.489
USA500	13.585	0.567	19.046	0.659	9.815	0.475	11.041	0.475
Currency
AUDUSD	12.013	0.540	16.523	0.626	12.032	0.527	10.472	0.452
DOLLAR INDEX	13.345	0.553	14.300	0.563	8.745	0.449	14.051	0.522
EURUSD	8.843	0.458	6.875	0.387	14.023	0.549	9.708	0.484
GBPUSD	7.066	0.425	11.203	0.500	9.527	0.469	8.506	0.442
NZDUSD	7.719	0.441	16.751	0.617	11.387	0.508	10.768	0.478
USDCAD	14.761	0.588	8.968	0.482	8.730	0.457	14.523	0.556
USDCHF	15.467	0.641	15.070	0.603	11.181	0.503	10.385	0.486
USDCNH	9.495	0.485	8.574	0.514	7.986	0.429	12.000	0.489
USDCZK	15.155	0.595	9.450	0.468	11.188	0.499	14.305	0.557
USDDKK	15.106	0.574	15.978	0.612	11.540	0.528	10.467	0.485
USDHKD	10.868	0.507	9.637	0.458	8.180	0.413	8.490	0.413
USDHUF	11.719	0.516	9.181	0.483	9.856	0.488	8.647	0.446
USDILS	12.122	0.561	6.416	0.386	9.931	0.462	13.846	0.529
USDJPY	14.607	0.619	18.110	0.663	9.890	0.451	11.284	0.480
USDMXN	12.361	0.533	8.221	0.422	10.922	0.490	14.033	0.528
USDNOK	11.789	0.510	8.303	0.391	13.191	0.549	13.492	0.526
USDPLN	13.604	0.578	10.636	0.502	12.057	0.496	12.316	0.496
USDRON	15.149	0.572	15.046	0.603	9.479	0.459	12.336	0.493
USDRUB	13.639	0.563	12.745	0.538	12.168	0.510	12.812	0.512
USDSEK	13.953	0.598	7.911	0.452	14.071	0.548	14.092	0.540
USDSGD	16.687	0.623	8.808	0.411	10.141	0.466	11.373	0.476
USDTHB	15.614	0.615	9.348	0.474	9.199	0.463	11.680	0.477
USDTRY	9.991	0.490	7.747	0.426	8.756	0.418	11.115	0.481
USDZAR	15.523	0.611	9.133	0.464	10.532	0.496	10.953	0.482
Commodity
BRENT	8.512	0.421	15.195	0.593	9.733	0.453	9.626	0.436
COCOA	8.807	0.457	9.614	0.497	7.306	0.397	6.766	0.365
COFFEE	10.644	0.521	9.751	0.463	10.709	0.495	11.110	0.514
COTTON	12.436	0.528	14.116	0.595	7.491	0.388	9.359	0.459
GASOIL	11.711	0.514	15.818	0.604	10.651	0.488	10.058	0.435
NATURALGAS	8.117	0.446	9.964	0.459	10.548	0.515	11.190	0.496
SOYBEAN	9.995	0.472	14.356	0.566	6.775	0.373	7.691	0.418
SUGAR	8.865	0.469	13.384	0.549	8.287	0.437	8.012	0.418
WTI	9.410	0.465	14.712	0.576	9.002	0.462	8.326	0.417
SILVER	8.779	0.488	14.430	0.577	7.981	0.422	7.019	0.422
GOLD	11.195	0.521	6.392	0.374	7.624	0.427	11.047	0.486
Bond
USTBOND	11.401	0.518	9.514	0.473	10.001	0.475	14.127	0.548
Bitcoin
BTCUSD	6.428	0.418	7.851	0.423	6.428	0.418	7.851	0.423
Average	12.637	0.545	13.441	0.552	9.874	0.466	10.490	0.467
Std.dev	2.948	0.066	4.521	0.102	1.692	0.044	2.166	0.047
Panel B: Network Density
	Density	UCC	Density	UCC	Density	UCC	Density	UCC
Network Density	0.165	0.479	0.182	0.374	0.081	0.186	0.101	0.244
*

This table presents the network centrality and density for the extreme return coherency. The first four columns report results for the left-tail dependency, whereas the last four columns report results for the right-tail dependency network. In Panel A, we report the strength and closeness of the node centrality. Higher values indicate greater centrality in the network. At the bottom of Panel A, we present the average centrality scores and their standard deviations. Panel B provides information on the network density and its connectivity under the columns ‘Density‘ and ’UCC’ respectively where ‘UCC‘ is the average undirected clustering coefficient of the nodes in the network.

As expected, the network density increases considerably in both the extreme negative (from 0.165 to 0.182) and positive return coherency (from 0.081 to 0.101) in the Covid-19 sample. Interestingly, the clustering coefficients decrease from 0.479 to 0.374 in the left-tail dependency network, but it increases from 0.186 to 0.244 in the right-tail dependency network. This finding indicates that the Covid-19 induces a wider-spread network in the left-tail dependence, whereas the pandemic leads to a more compact network in the right-tail dependence.

Conclusion

Using tail-dependency networks constructed by quantile cross-spectral analysis (Baruník and Kley, 2019), we explore the asymmetric effects of the Covid-19 outbreak on the tail dependencies of a wide range of assets, which is crucial for asset and risk management during the pandemic. As it is found out earlier for the US equities (Azimli, 2020), we show that there exists an asymmetric response in the tail dependencies to the Covid-19 crisis for various asset classes, where the effect in the left tail is stronger and more prevalent than in the right tail. Moreover, the connectivity of tail-dependency networks among equities and commodities have increased the most during the pandemic period compared to other asset groups, showing a higher tail contagion effect for these specific assets. Conlon and McGee (2020) and Corbet et al. (2020b) argue that cryptocurrencies, Bitcoin in particular, do not act as hedges, or safe havens during the pandemic, but perhaps rather as amplifiers of contagion. While this might be true for these studies due to their shorter sample periods or their focus on the whole series (not the tail behaviour), we contrarily reveal that Bitcoin, in addition to US Treasury bond, is disconnected from other assets in tail-dependency networks, making it a safe-haven asset for international investors during the extreme periods of the Covid-19 crisis, which is in line with the findings of Goodell and Goutte (2020).

CRediT authorship contribution statement

Trung Hai Le: Conceptualization, Software, Methodology, Visualization, Writing - original draft, Data curation. Hung Xuan Do: Conceptualization, Investigation, Methodology, Writing - original draft. Duc Khuong Nguyen: Conceptualization, Investigation, Methodology, Writing - review & editing, Supervision. Ahmet Sensoy: Conceptualization, Investigation, Methodology, Visualization, Writing - review & editing, Data curation.