key: cord-0894896-zjx76ony
authors: Belhassine, Olfa; Karamti, Chiraz
title: Contagion and portfolio management in times of COVID-19
date: 2021-08-05
journal: Econ Anal Policy
DOI: 10.1016/j.eap.2021.07.010
sha: 5ee60fa8a80288a3ff2452102839c689ee404f1a
doc_id: 894896
cord_uid: zjx76ony

This paper aims to investigate the COVID-19 pandemic impacts on the interconnectedness between the Chinese stock market and major financial and commodity markets—gold, silver, Bitcoin, WTI, S&P 500, and Euro STOXX 50—and analyze the portfolio design implications. Using daily data from 2018 to 2021, we first apply the wavelet power spectrum (WPS) to visualize volatility shifts. In contrast to previous research, we empirically identify the precise COVID-19 outbreak dates for each market using the Perron (1997) breakpoint test. Finally, we employ the bivariate DCC-GARCH model to analyze the connectedness between markets. The findings reveal that the COVID-19 pandemic caused volatility shifts of different intensities for all of the studied markets. Moreover, each return series exhibits one break date, which is specific to each market and corresponds to a distinct COVID-19-related event. Correlations, hedge ratios, and optimal portfolio weights changed significantly after the COVID-19 outbreak. There is evidence of contagion effects between the Chinese stock market and S&P 500, Euro STOXX 50, gold, and silver. Interestingly, the latter two assets lost their safe haven property with SSE. However, WTI and Bitcoin act as safe havens against SSE risks.

Catastrophes, terrorist events, wars, and crises are turbulences that severely hit economies as well as financial markets. There is a plethora of research on the effect of such major events and financial crises on financial markets. For instance, Kollias et al. (2013) showed that war significantly affects the oil-stock market relationship. Nasir and Du (2018) found that the global financial crisis (GFC) changed the interrelation among the global financial markets. Belhassine and Ben Bouzid (2019) found evidence that both the subprime and Euro debt crises altered the relationship between the oil market and the Eurozone sectors. COVID-19 (also referred to as coronavirus disease) is this century's first major global pandemic. An unseen, microscopic virus termed SARS-CoV-2 has led to tremendous costs for all people worldwide and at all levels. Being so devastating, this virus has also resulted in plummets and changes in the financial markets. The worldwide spread of COVID-19 has heightened market risk aversion to levels not seen since the GFC. Around the world, low economic growth and considerable financial instability are caused by this dramatic increase in uncertainty. Such issues first affected China's stock markets, one of the largest economies in the world, and then the remaining stock markets around the globe. Lyócsa et al. (2020) showed that during the COVID-19 period, fear of the virus, proxied by the excess Google search volume, Our dataset covers the period 2018-2021. We collect daily data for the Shanghai Stock Exchange (SSE) Composite Index as a benchmark for the Chinese stock market and major international assets that are commonly used by portfolio managers, namely WTI, gold, silver, Bitcoin, Euro STOXX 50, and S&P 500. We use the wavelet power spectrum (WPS) to visualize volatility shifts and the Perron (1997) breakpoint test to locate the precise COVID-19 break dates. Then, we employ the bivariate DCC-GARCH model of Engle (2002) to estimate the time-varying correlations between SSE and the other assets under study. Our results show that the COVID-19 pandemic unevenly increased the volatility in the studied markets. The pandemic break dates are specific to each market and correspond to distinct COVID-19-related events. Moreover, the dynamic conditional correlations (DCCs), hedge ratios (HRs), and optimal portfolio weights (OPWs) changed significantly after the pandemic's outbreak. Specifically, there is evidence of contagion effects between the Chinese stock market and S&P 500, Euro STOXX 50, gold, and silver. Interestingly, gold and silver lost their safe haven role in the COVID-19 pandemic. However, WTI and Bitcoin act as safe haven against SSE risks. These results are useful for regulators and policymakers to plan policies that allow them to cope with financial contagion. They are also valuable for portfolio and risk managers, particularly because the pandemic operates in waves.

The remainder of this paper is as follows. Section 2 describes the data. Section 3 outlines the methodology. Section 4 reports and discusses the results. Finally, Section 5 concludes.

We collect data on daily frequency from January 2, 2018, to June 7, 2021. To represent the Chinese stock market, we choose the Shanghai Stock Exchange (SSE) Composite Index. Because the disease epicenter moved from China to Europe and then to the US, we consider two stock indices, namely the S&P 500 as a proxy for the US stock market and Euro STOXX 50 representing the Eurozone. We use the West Texas Intermediate (WTI) crude oil price as a proxy for the world oil price level and the London Bullion Market Association (LBMA) gold fixing price as a proxy for gold prices. Finally, we utilize the most important cryptocurrency, which is Bitcoin. The SSE, Euro STOXX 50, and S&P 500 data are sourced from Yahoo Finance, whereas the WTI, gold, silver, and Bitcoin data are collected from the Federal Reserve Economic Database (fred.stlouisfed.org). We have an initial sample of 834 daily observations. All data are synchronized as the SSE index, and the other assets are traded on different stock markets that operate with different holidays. For each data series, daily returns (r it ) are calculated as Ln (P it /P it−1 ) × 100, where P it is the daily closing price. Table 1 displays the descriptive statistics for the series under investigation. All standard deviations are relatively high. WTI and Bitcoin have standard deviations that are considerably higher than any of the other financial assets examined. Bitcoin exhibits the highest average return. Moreover, all the kurtosis statistics are higher than 3, suggesting that all the returns are leptokurtic. The skewness statistics show that all return series are negatively skewed, except for gold. Finally, the JB test statistics show that all series are not normally distributed. Unit root tests indicate that all return series are stationary at conventional levels.

The first step of the study is to detect if the COVID-19 pandemic caused volatility shifts in the variance for the considered return series. To do so, we utilize the wavelet power spectrum (WPS) plots. This technique is used to illustrate the local volatility of the analyzed series x(t) at each scale and at each time (Torrence and Webster, 1999) . The WPS is defined as:

with W X (τ , s) the continuous wavelet transform of the time series for a mother wavelet ψ given by:

where s is the scaling factor that determines the length of the wavelet by dilating (|s| > 1) and compressing (|s| < 1) the series, τ the translation parameter that represents its location, and asterisk denotes complex conjugation. The mother wavelet ψ(t) is used to generate other window functions at a location center τ . As the window shifts through time, time information is obtained in the transformed domain. Then, we test each return series for the presence of structural break. We identify the exact break dates by employing the Perron (1997) break date test, applying the mixed IO (innovational outlier) model. 1 The determined break date for each market will be used as the starting point for the post-COVID-19 period.

We use the bivariate DCC-GARCH model of (Engle, 2002) to estimate the time-varying correlations of SSE-Asset (A i ) pairs. This methodology is widely used to assess the dynamic correlations between different assets (Akhtaruzzaman et al., 2020; Dutta et al., 2020) . It is a two steps estimation technique. Let r t = (r 1t , r 2t ) denote the vector of the observed data at time t. First, the GARCH parameters are estimated by an ARMA(0, 0) − GARCH(1, 1) 2 model for the univariate process

where µ i is the mean of the process r it , h it represents the conditional variance of asset i, the parameters α and β are non-negative (with α + β < 1) and represent the short-and long-run persistence of shocks to conditional variance, respectively. Then, the dynamic conditional correlation is estimated through the conditional variance-covariance matrix H t of the residuals in the DCC.

D t is the 2 × 2 diagonal matrix of time-varying standard deviations from the univariate GARCH models. R t is the conditional correlation matrix of the standardized residuals.

The multivariate DCC-GARCH models are estimated by quasi-maximum likelihood estimation (QMLE) using the BFGS algorithm.

We compute W Ai/SSE t , the OPW of asset A i in a one-dollar SSE/A i portfolio subject to a no-shorting constraint, where A i can be gold, silver, oil, Bitcoin, Euro STOXX 50, or S&P 500. Assuming zero expected returns and a mean-variance utility function, the risk-minimizing OPW proposed by Kroner and Ng (1998) is given by:

with h SSE/Ai t the conditional covariance between SSE Index and the asset A i returns at time t, and h Ai t and h SSE t are the conditional variances of asset A i and the SSE Index at time t, respectively.

We also determine the risk-minimizing HR (β * Ai/SSE,t ) for each SSE/A i portfolio. A long (buy) position of one USD in the asset A i should be hedged with a short (sell) position of β * Ai/SSE,t USD in the SSE Index. Kroner and Sultan (1993) define this ratio as:

1 See Perron (1997) for more details on test statistics which allow for different forms of structural breaks.

2 We estimated several GARCH type specifications (EGARCH, AGARCH, GJR-GARCH etc.) and we used for each returns series the most appropriate one judging by the information criteria. Fig. 1 illustrates the local variance evolution of each return series with respect to the frequency-time domains. The x-axis shows the period under study. The y-axis represents the frequency level, covering short-(high-frequency) to longterm (low-frequency) horizons. The color code represents the volatility spectrum, ranging from blue (low volatility) to red (high volatility) 3 (Grinsted et al., 2004) . Fig. 1 shows that for all time scales and the full sample period, there is evidence of low volatility because shades of blue dominate, except for the early 2020s when the virus began to spread. This statistically significant and highly volatile period is common to all return series, but its intensity differs from one asset to the other. When comparing the hot-colored areas, we note that WTI, S&P 500, and Euro STOXX 50 are the most affected markets by the COVID-19 pandemic, particularly in the long run. As for gold, during the same volatile period, red-shaded areas spread only up to 32 days. However, SEE seems the least affected stock market by the COVID-19 outbreak, which is surprising because China was at the forefront of the pandemic exposure. Moreover, the WPS plot suggests that Bitcoin experienced very low volatility over the short-term horizons, denoted by the dark blue shading throughout the sample period, except some moderate volatility at the medium and low frequencies as evident from the yellow and orange islands hanging over the turmoil period.

To summarize, all studied markets experienced higher volatility localized at the beginning of 2020 and coinciding with the COVID-19 outbreak. China and Bitcoin are the markets that seem to be the least affected by the pandemic. It is well documented that China, despite being first to be hit by the virus, was also the first to contain it and limit its consequences, in contrast to other countries. For instance, in August 2021, the Chinese reported that cases were substantially below all the other countries. 4

After finding evidence that COVID-19 caused high volatility for all markets under study, we identify the COVID-19 break dates for each series. Table 2 summarizes the precise break date for each financial market and its corresponding event. 5 Interestingly, all the identified structural breaks correspond to a distinct COVID-19-related event. The pandemic triggering event is specific to each return series, suggesting that the onset of COVID-19 is specific to each market. For the Bitcoin market, the break date is March 10, 2020, which is one day before the WHO declared COVID-19 to be a global pandemic, indicating that the Bitcoin market was able to anticipate the WHO announcement. The gold and silver markets were most likely affected by the travel restrictions imposed by the US president, which affected all mining industries because they caused a supply-chain disruption (Corbet et al., 2020b; Jowitt, 2020) . Regarding Euro STOXX 50, the break date occurs on the day on which the European Commission (EC) finally announced the first measures and recommendations to face the pandemic. Indeed, on March 17, 2020, EC president Ursula von der Leyen acknowledged that COVID-19 was underestimated and declared the urgent need to unify efforts to face the pandemic. Regarding the oil market, the identified date coincides with the oil market turmoil period. On April 12, 2020, Saudi Arabia and Russia agreed to cut oil supplies because the demand was extremely low and the tanks were full. On April 15, 2020, the Energy Information Administration (EIA) released its monthly report describing and analyzing the devastating effects of the pandemic on oil demands. Consequently, on April 20, 2020, all the world was astonished by the never-seen-before, negative price of WTI closing at -$37.63 per barrel.

We use the identified break dates to divide our full sample for each return series into pre-and post-COVID-19 onset periods. Table 3 displays the descriptive statistics for each series in the two sub-periods. It shows that all the average returns and almost all volatilities increased, whereas the minimum values are lower in the post-COVID-19 period, suggesting higher risks in all markets. The highest volatility in the post-COVID-19 sub-period is detected for WTI. Interestingly, the Chinese stock market is the only market displaying a volatility decrease. All series, except for Euro STOXX 50, are negatively skewed and display higher kurtosis statistics after the break date, indicating that the distributions have heavy tails and that the assets are riskier. Finally, the Jarque-Bera statistic indicates that none of the returns are normally distributed.

3 The null hypothesis of a steady estate is compared with WPS to determine the statistical significance of the volatility. The WPS significance level of 5% is represented by the black contour. 

The DCC parameter estimates and the model diagnosis tests for the two sub-periods are presented in Table 4 . Fig. 2 displays the DCC conditional correlations for the SSE/A i pairs. It shows that the COVID-19 pandemic caused a significant change in the correlation patterns for all pairs. Table 5 , Panel A presents the mean and standard deviations of the SSE/A i correlations for the two sub-periods and the mean and variance equality tests. It indicates that S&P 500 and Euro STOXX 50 correlations decreased significantly, although remaining positive, indicating that these assets are diversifiers for SSE risks. The same table shows that gold and silver average correlations increased significantly after the COVID-19 onset, suggesting significant financial contagion effects between the Chinese financial market and these markets. Moreover, gold and silver had near-to-zero average correlations with SSE before the COVID-19 onset, meaning that they were weak hedges for SSE. After the crisis, these assets changed to become diversifiers for SSE and lost their hedging property. It is worth noting that our results for gold are specific to the COVID-19 crisis because gold has always been considered a universal safe haven (Baur and Lucey, 2010; Dutta et al., 2020) . This result agrees with Bȩ dowska-Sójka and Kliber (2021), who found that the COVID-19 pandemic made gold lose its safe haven property against US and European indices' risks. One possible explanation for this conflicting finding is that, in contrast to previous turmoil, COVID-19 deeply affected the mining industry by restricting travel across countries causing stock, gold, and silver markets to move in the same path. Moreover, China was the first gold producer 6 and the third silver 7 producer in 2019. Table 5 Panel A shows that for WTI, the average correlation with SSE decreased significantly to become negative. WTI, which was positively correlated with SSE before the COVID-19 onset, became a strong safe haven for SSE after the crisis. A tentative explanation for this correlation shift could be that China is the first crude oil-importer; hence, it likely profited from the unprecedented oil price plummet after the COVID-19 onset. Indeed, the Chinese domestic oil products pricing mechanism sets the refined petroleum products' retail prices to a minimum of 40$ per barrel if the international crude oil prices are equal to or lower than that level. Therefore, China has kept its retail petrol prices unchanged from March 18, 2020 to June 29, 2020, 8 reducing the uncertainty of its domestic oil products, while the international crude oil prices were lower than 40$/b. Oil product producers were asked to pay their additional earnings to the Chinese government ''Price Adjustment Risk Fund'', and the government has no more subsidies to pay to the refining firms. Therefore, the international crude oil price plunge after the COVID-19 outbreak helped the Chinese economy. This was not the case before the pandemic when oil prices were higher than 40$ per barrel, and the Chinese government had to adjust domestic retail oil prices and pay subsidies to refined product companies to compensate for their losses. 

ρ This table reports the results for the DCC-GARCH estimations for each A i /SSE pair over the pre-and post-COVID-19 periods. McLeod and Li (1983) test for a lag of 30 on both standardized and squared standardized residuals. *Denotes significance at 10% level. **Denotes significance at 5% level. ***Denotes significance at 1% level. Regarding Bitcoin, Table 5 Panel A shows that the average correlation with SSE decreased significantly, and Fig. 2 shows that it became almost flat after the pandemic onset. Bitcoin was a weak hedge for SSE during the normal market conditions and is a weak safe heaven after the COVID-19 onset. These results are consistent with those of and Bouri et al. (2017) , both of whom found that Bitcoin has safe heaven properties for China and Asia pacific stocks, respectively.

Finally, we conclude that investors should avoid holding portfolios containing S&P 500, Euro STOXX 50, gold, or silver with SSE during the post-COVID-19 outbreak period. However, they can minimize SSE risks if they hold Bitcoin or oil assets.

The OPW (Eq. (6)) and HR (Eq. (8)) were estimated using the time-varying variances and covariances obtained through the DCC-GARCH model. Panel B of Table 5 displays the average OPW of assets (A i ) in the pre-and post-COVID-19 onset periods and their standard deviations. We also perform mean and variance equality tests for the pre-and post-event series. We can see that the OPW of S&P 500, Euro STOXX 50, gold, and silver are higher than 50% before the COVID-19 onset, meaning that the risk-minimizing portfolio should hold more of these assets than SSE. These average OPWs decreased significantly in the post-COVID-19 onset period to be less than 50%. The lowest average value is recorded for silver, which shifted from 56.58% to 15.20%. These findings indicate that investors should rebalance their risk minimizing portfolio by decreasing these asset holdings after the crisis. Regarding the average OPW of Bitcoin, it was 7.20% in the stable period and increased significantly in the post-COVID-19 period to 16.51%. However, we can observe a drastic and significant decrease in the Bitcoin OPW standard deviation, meaning that Bitcoin is the cheapest safe haven for SEE because it does not require frequent portfolio rebalancing that could be expensive (Belhassine, 2020; Junttila et al., 2018; Olson et al., 2017) . Fig. 3 displays the optimal HR plots over the full sample period. It shows that all HRs are time varying. In addition, there is a noticeable change in all HR patterns after the COVID-19 onset. The optimal HR averages and standard deviations are presented in Panel C of Table 5 . We can notice that the average HR for S&P 500, gold, and silver increased significantly after the onset of COVID-19. After the crisis, investors need to short more SSE contracts to hedge a long position of 1 USD of the considered assets, meaning that the pandemic induced higher hedging costs for these assets. This result is consistent with Akhtaruzzaman et al. (2020) , who studied the COVID-19 crisis effects on HR of financial and non-financial Chinese firms with G7 countries. Batten et al. (2019) and Belhassine (2020) also found that the GFC increased the studied HRs. Euro STOXX 50 only showed an increase in its HR standard deviation, suggesting that hedging activity has become more expensive after the crisis. However, for WTI, the average HR with SSE decreased significantly and became negative after the COVID-19 onset, meaning that investors should take long positions on SSE contracts to hedge oil risk. The SSE index should be used to hedge oil portfolios. As for Bitcoin, the average HR and its standard deviation decreased significantly to become more stable after the pandemic onset. This result suggests that the relationship between the Chinese stock market and Bitcoin became more stable, and hedges are less responsive because investors are not constrained to rebalance their portfolios constantly, as is the case for the other studied markets. Interestingly, Bitcoin is the only asset that witnessed a significant decrease in its HR standard deviation with SSE, meaning that hedging Bitcoin risk with SSE became more attractive and less expensive to investors after the COVID-19 onset because the portfolios do not need to be frequently rebalanced.

This study provides insights into how the COVID-19 pandemic impacts the interconnectedness between the Chinese stock market and major financial and commodity markets (gold, silver, Bitcoin, WTI, S&P 500, and Euro STOXX 50). Our goal was to model volatility spillovers, explore the dynamics of conditional correlations, and estimate optimal hedge ratios to find the assets with the best hedge efficacy for the Chinese stock market returns (SSE).

Our findings suggest that COVID-19 significantly affected the volatility of the different studied markets. However, the Chinese stock market seems to be the least affected, even though China reported the first viral infections. This result could suggest that the Chinese government was able to contain the pandemic impacts both sanitarily and economically. Indeed, it is of common knowledge that COVID-19 operates in waves. However, in contrast to all the other countries, China was the only one that witnessed only a first wave in the first quarter of 2020. Therefore, it would be interesting to examine the real causes behind the Chinese effectiveness in containing the crisis. Another original result of this study is that the pandemic caused a discernable breakpoint in all the studied return series. Interestingly, we found that there is a unique and specific breakpoint for each asset, coinciding with a specific Covid-19-related event. Therefore, we recommend that future studies consider these specific dates instead of common dates in the COVID-19 timeline when studying the pandemic impacts.

Finally, the findings show the existence of co-movements between the Chinese stock market and the major financial markets. There is evidence of significant contagion effects between the Chinese stock market and S&P 500, Euro STOXX 50, gold, and silver. S&P 500 and Euro STOXX 50 kept their diversifier property with the SSE index. Investors and policymakers should be cautious with the price behavior of these markets after the crisis. Portfolio managers should revise their holding of these assets downwards and possess more SSE index. However, investors must be aware that gold and silver lost their safe haven property. Holding these assets with SSE in the COVID-19 pandemic could lead to tremendous losses in bearish market conditions. Interestingly, we found that Bitcoin is displacing gold as the most cost-effective hedge against Chinese stock market volatility amid the COVID-19 outbreak. This is a new and interesting finding. It contradicts most recent studies on hedging Chinese equities, which claim that commodity markets, particularly gold, are the strongest risk-hedging assets (Ming et al., 2020; Shahzad et al., 2020) . Contrary to these studies, we uncover how the hedging effectiveness of gold against the Chinese stock market is shaped by the COVID-19 outbreak. Moreover, the results show that the pandemic stabilized the co-movements between the Chinese stock market and Bitcoin. In the post-COVID-19 period, WTI and Bitcoin act as safe havens against SSE risk, with Bitcoin being a cheap safe haven for SEE because it does not require frequent portfolio rebalancing that could be expensive. Therefore, we would recommend that investors use these assets to hedge SSE risks in the post-COVID-19 period.

Our findings provide interesting insights for portfolio design in times of the COVID-19 pandemic. They are important to financial market investors, risk managers, and portfolio managers, all of whom should pay increased attention to risk management during periods of severe risks, such as the COVID-19 crisis, particularly because the pandemic operates in waves.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.