The Volatility In Financial Markets During The Covid-19 Pandemic

CONTENTS

1 Introduction

2 Background

3 Data

4 Method

5 Results and Discussion

6 Conclusion

References

Appendices

a Imputed Data

b DCC Diagrams

LIST OF FIGURES

Figure 1 Absolute Returns

Figure 2 DCC of FTSE 100

Figure 3 Imputed Price Data

Figure 4 Dynamic Conditional Correlation

LIST OF TABLES

Table 1 Summary Statistics

Table 2 Univariate GARCH Results

1 INTRODUCTION

Covid-19 is a contagious disease, which manifests itself as pneumonia in humans (see Sohrabi et al. 2020 for a medical overview). The first cases were reported in late December 2019 in Wuhan, one of the most populous cities in China. Due to its infectiousness, the WHO declared a Public Health Emergency of International Concern on January 30th, 2020. In the 100 days that followed, the virus infected more than 1 million people with an initial mortality rate of approximately 5% (Ali et al 2020). On March 11th, 2020, the WHO declared Covid-19 a pandemic. As of now (February 2022) Covid-19 has taken more than 5.9 million lives and infected more than 424 million people worldwide.

Initial reactions of many governments around the world were aimed at limiting - or at least slowing - the rate of infection. These practices amplified the uncertainty already inherent in the pandemic itself (e.g. uncertainties with respect to the in­fectiousness and lethality of the virus, the capacities of the healthcare systems, the development of vaccines, . . . ) by uncertainties related to the survival of businesses, effects on the accumulation of human capital (especially formal education), persis­tence of governmental policies, et cetera (see Baker et al. 2020). Combined, this has led to a unique disruption of life on our planet.

While Covid-19 had immediate effects on the real economy, delays in the availabil­ity of data makes the study of financial markets - as a leading indicator - important (Bai et al. 2020). Furthermore, financial markets and their volatility are intimately connected with the real economy, affecting anything from risk management to invest­ment and consumption plans to regulatory decisions (Baker et al. 2020). Especially in the early periods of the pandemic, the ample slowdown in economic activity dev­astated global financial markets; skyrocketing volatility, battering asset prices, and eliminating trillions in wealth (see e.g. Ali et al. 2020, Barro et al. 2020, Bickley et al. 2020, Chevallier 2020, Aslam et al. 2021, Awan et al. 2021). This turmoil in the financial markets had (negative) repurcussions on the real economy, leading to even more turbulences in financial markets (Corbet et al. 2021), starting a vicious cycle.

The objective of this essay is to investigate the effects of Covid-19 on the volatility of individual asset markets as well as the correlation between those markets. The investigated assets are the major world equity indices, as well as Oil, Gold, and Bitcoin. I have found significant volatility clustering over the entire spectrum of assets, as well as increases in the correlation between assets during the initial phase of the Covid-19 pandemic. There is clear evidence of financial contagion. Furthermore - from a portfolio perspective - Gold and interestingly Bitcoin show relatively low correlation with the investigated equity markets and may hence act as important ingredients to a robust portfolio.

The remainder of this paper proceeds as follows. Section 2 is going to dive deeper into the literature on financial markets with a particular focus on how the pandemic influenced them. It will also discuss some of the policy reactions by monetary and fiscal agencies. The third section introduces the data used in the empirical part of this paper. Section 4 will give a brief overview of (multivariate) volatility modelling and the method used in this analysis. Finally, section 5 will present the results of the empirical investigation, while section 6 concludes.

2 BACKGROUND

Traditionally, the literature assumed financial markets to display independent and random price fluctuations as described by the random-walk hypothesis (see Bickley et al. 2020 for a more detailed overview). Such theories, however, are challenged by market discontinuities like those recently provoked by the Covid-19 pandemic. Such anomalies have given rise to numerous different approaches to modelling financial markets, which are increasingly analyzed as complex systems with vast interactions between a large number of highly complex individual agents (Bickley et al. 2020). These agents respond to market outcomes and learn from both internal feedback processes as well as external factors (Filimonov and Sornette 2012), like the recent pandemic and, more directly, the news surrounding it.

In the study of financial markets, a particular focus lies on the dispersion of re­turns, that is, on asset volatility. According to Poon and Granger (2003), volatility can be interpreted as uncertainty, which is an important determinant of a variety of intertemporal decisions, including consumption plans, portfolio allocations, and so on. The importance of volatility has also been recognized by regulators, who, for example, compel financial institutions to produce volatility forecasts (see Basel Accord 1996 and also Poon and Granger 2003 for a more detailed overview).

While there exists an extensive literature that (statistically) models and forecasts the volatility of financial markets (see Clements et al. 2015 for an overview), there exists only a poor theoretical understanding of how volatility comes to be, which factors drive and which restrain it, and how the transmission of volatility between financial markets works.

With respect to the current crisis, the literature has identified several factors that may have impacted volatility levels. Haroon and Risvi (2020) have shown that the Covid-19 news coverage increased the volatility in equity markets, particularly of those sectors, which were perceived to be most at risk. Similarly, Lycosa and Molnar (2020) found that Coronavirus related Google searches increased financial market volatility. Zaremba et al. (2020) analyzed the effect of governments' social distancing measures and found a negative correlation between the citizens' mobility and market volatility. Sansa (2020) used bivariate regressions and found a significant positive relationship between Covid-19 cases and stock market volatilities.

Conceptually, all the aforementioned factors worsen agents' perception of the state of the world (i.e. their sentiment) and hence increase their degree of risk aversion. In response, agents may rebalance their portfolios, increasing volatility in the process, which further affects market sentiment (see Bollverslev et al. 2018). These portfolio changes, however, do not necessarily have to be rational. Some stocks, for example those containing parts of the word “corona” suffered substantially larger losses than the market as a whole (Corbet et al. 2021).

In the past decades, financial markets have become significantly more integrated due to globalization, securitization, and advancements in technology (Farid et al. 2021). Furthermore, since the volatilities of different assets tend to behave similarly (Bollverslev et al. 2018), there has been a quest for alternative, safe-haven invest­ments, which are ideally uncorrelated with the rest of the market. One example for this is the financialization of commodity markets, which has led to an increasing integration between traditional financial markets and commodity markets like those for agricultural resources. As a consequence, studies that focus on the interconnect­edness between different financial markets (see e.g. Louzis 2013) have increased in popularity. Creti et al. (2013), for example, find time varying correlations between commodity and stock market returns. Junttila et al. (2018) support these findings and further suggest that correlations between commodities and equities are affected by economic downturns. Sadorsky (2014) finds that there exist strong volatility spillovers (i.e. high return correlation) between commodities and equity markets in emerging economies. Akhtaruzzaman et al. (2021) further find that financial firms played a critical role in financial contagion during the pandemic.

Due to the integration of the global financial system, a shock in just a part of a market or region may be sufficient to infect the entire system with increased volatil­ity and, as a consequence, accentuate the global systemic risk (Junior and Franca 2012, Baker and Bloom 2013, Chevallier 2020).

Governing bodies around the world have enacted a multitude of different policies aimed at mitigating the economic turmoil caused by the pandemic. The stimulus package in the US alone exceeds USD 3 trillion, with additional loans and guar­antees amounting to more than USD 4.5 trillion (see Akhtaruzzaman et al. 2021). Central banks around the world have lowered their interest rates and, particularly in the cases of the Federal Reserve and the European Central Bank, implemented massive Quantitative Easing (QE) programs, collectively worth trillions of USD. Fur­ther responses in monetary policies include lower reserve requirements, additional financing facilities, and relaxed capital buffers (Zhang et al. 2020). From a financial perspective, these policies try to provide sufficient liqudity to the market, which is regarded as key to curtail excess volatility and volatility spillovers (Corbert et al. 2021). Yet, these policies - especially the virtually unlimited QE - may introduce further uncertainty in the markets and consequently amplify the systemic risk in the future (see Yang and Zhou 2017, who analyzed QE after the 2008 financial crisis).

While the individual and collective fiscal and monetary policy responses will doubtlessly play an important part in managing the current crisis, making finan­cial markets more anti-fragile through systemic risk management will also be crucial (Chevallier 2020). Ideally, one would like a financial system that is mostly unaffected by a crisis (i.e. no sharp increases in volatility and few volatility transmissions) while also efficiently providing the necessary intermediation services to the economy. It remains to see, whether the Covid-19 pandemic will lead to lasting changes in the financial system. Bitcoin, on which many hopes were pinned before the pandemic, has thus far been seen critically, with some authors finding that it suffered from the same volatility contagion as the rest of the financial markets (e.g. Corbet et al. 2020). The performance of Bitcoin will be revisited in the empirical part of this essay.

3 DATA

To analyze the volatility in financial markets during the pandemic, I have gathered data from various sources, which can be grouped into two categories: financial data and data on Covid-19.

The financial data has been collected from Refinitiv Eikon Datastream in the form of daily price data for the period between January 1st, 2020 and February 14th, 2022. This time span allows me to not only analyze the immediate effect of the pandemic, but to also inspect the medium-run consequences. In particular, I collected price data on equity markets, commodities, and cryptocurrency.

The considered equity markets are those of the G7 member states (Canada, France, Germany, Italy, Japan, United Kingdom, and United States) and the BRIC countries (Brazil, Russia, India, and China). For each nation, I have gleaned information on the dominant stock indices, which act as a benchmark for the equity market of the country (see Table 1 for an overview). The reason for choosing these markets is that they are (1) the largest in the world, and (2) geographically diverse in the sense that they represent countries in Asia, Europe, and the Americas, which were hit at different times with the Covid-19 pandemic and experienced differing evolutions of it. Furthermore, these countries have implemented distinct policy responses, such that

- as already argued by Haldar and Sethi (2021) - the volatilities they experienced may differ.

The selected commodities are Gold and Oil (WTI). Gold is traditionally seen as a safe-haven asset in times of economic turmoil and hence widely used in the study of financial markets. Oil is interesting due to two factors. First, Oil is - after Gold

- one of the main hedging assets used against shocks in equity markets (see e.g. Corbet et al. 2021). Secondly, the social distancing policies implemented around the world led to a significant decrease in the demand for Oil. In fact, the Covid-19 pandemic had such significant effects on the oil markets that the WTI crude oil futures uniquely plunged below zero im mid-April 2020 (Awan et al. 2021). My analysis uses the WTI grade, as it acts as a benchmark for the world oil market (see Zhang and Hamori 2021). For both commodities, I used a continuous futures price series provided by Refinitiv Eikon. This continuous price series is build by choosing the nearest-to-maturity futures contract available as a starting point and - as it reaches its expiry date - rolling it over to the next available contract, thereby creating “an artificial asset that tracks price changes” (Hamilton and Wu 2015, p. 188). I did not include further rare earth commodities (like silver or platinum), because they are typically highly correlated with Gold and Oil (Song et al. 2021). An extension to, for example, agricultural commodities, is beyond the scope of this essay.

The final asset considered is Bitcoin, which “remains synonymous with the market leading cryptocurrency in terms of both market capitalization and trading liquidity” (Corbet et al. 2021, p. 78). The current pandemic can be seen as a first major test of whether Bitcoin acts as the much promised safe-haven or whether it is just as affected by the turmoil as equity markets and commodities. The precise data used, is the Gemini Bitcoin Trade Price Index, which gives a continuous price (in USD) for one Bitcoin.

Obviously, the financial dataset covers only days at which trading took place. One problem are national holidays, during which the markets are closed in one corner of the world, but not in others. As a consequence there is some missing data. Standard procedure will commonly omit all observations (i.e. trading days) during which not all markets are open. However, due to the fact that the sample is relatively short, cutting it by even just a few percent does not seem to be the optimal procedure. Instead, I have used Kalman smoothing to fill any missing data points (see Moritz 2021). Appendix A provides an overview of the price data and highlights all those data points, which have been imputed. It also gives an overview of the performance of the assets during the pandemic.

For the further analysis, the price data has been converted into log first differences. Descriptive statistics of these returns can be taken from Table 1:

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As can be seen, the mean return of all assets is zero. The importance of this will be shown in the next section. The Jarque-Bera test quantifies that the distribution of the return series is not normally distributed. The skewness is less than -1 for most assets, implying that the return distribution is highly skewed left. All assets have positive excess kurtosis, meaning the series have fat tails (which is to be expected in financial data). The results of the Augmented-Dickey-Fuller (1979), the Phillips- Perron (1988), and the Kwiatkowski et al. (1992) tests indicate that all return series are stationary.

Figure 1 gives an overview of the absolute returns of all assets. One can im­mediately notive the large increase in volatility after the WHO's declaration of a pandemic on March 11th, 2020. After this, volatility decreased and stayed compar­atively low during most of 2021. At the moment, volatilities are increasing again. Note especially the volatility spike in Russia's MOEX Index. Figure 1 gives first indications of volatiltiy clustering in all of the markets.

The second data category is comprised of Covid-19 related data. The current literature on financial market volatility and Covid-19 uses two kinds of exogenous variables: those relating to the directly experienceable consequences of the virus (e.g. number of new cases, movement restrictions due to social distancing policies, number of deaths) and those relating to news about Covid-19. Thi s investigation focusses on the former and neglects the latter. The reason behind this is that, for example, data on web search volumes would require the definition of keyword­categories, which have to be translated into all the languages used in my sample. Such an implementation is beyond the scope of this essay (see e.g. Costola et al. 2021 for an implementation). The variables I do use, come from two sources.

The first source is the Community Mobility Report from Google (Google LLC 2022), containing variables which measure how the movements of citizens of differ­ent nations have changed over the time of the pandemic. The report does hence effectively measure the real, tangible effects of government's social distancing inter- ventions on the mobility of its citizens. The data starts in February 2020 and gives daily changes in movement relative to a baseline. For the analysis in this essay, I will only use movement data for retail and recreation areas, which were - and in some cases still are - the most severely affected by social distancing policies. The choice of the mobility report was inspired by Bickley et al. (2020), who used data on the residential category and only considered a much shorter time span.

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One downside of this dataset is, that the mobility data does not cover China. Instead of excluding China from my analysis, I will omit these regressors in the specification for China.

The second dataset is sourced from the website ourworldindata.com (Ritchie et al. 2022) and provides daily statistics on an array of Covid-19 related variables. For this essay, I have chosen the number of new cases per million and the number of new deaths per million. To improve the interpretability of the results, I also needed to re-scale the data: instead of looking at new cases and new deaths per million, I multiplied both data columns by 0.01 to get new cases and new deaths per one hun­dred million. This adjustment was necessary, because the effect of these variables on the returns, while statistically significant, is rather small in absolute terms.

One complication with these Covid-19 variables arises from the fact that I have included global assets (Bitcoin, WTI, and Gold) in my sample. To still be able to in­clude the predictors in their respective models, I have simply taken the average of all three variables as a global proxy for the state of the pandemic and the governments' responses.

Another factor that must be mentioned, is that there are many other factors that influence the price volatility of the considered assets. Corbet et al. (2021), for example, find that Bitcoin has experienced significant increases in volatility during the pandemic, however, they also point out that there are other confounding factors (e.g. increased regulatory efforts) that have affected the Bitcoin market. This holds true for all other assets as well. Particularly macroeconomic events like the current Ukraine crisis - which overlaps with my sample period - will affect financial markets severely. For this reason, any results obtained from this data must be interpreted with great care: not all the observed volatility can necessarily be attributed to the pandemic.

4 METHOD

The (volatility) modelling of financial data poses several challenges, including the non-stationarity of the time series (which was already addresed by using log first differences), strong autocorrelation of the absolute returns (i.e. volatility clustering) and leptokurticity (Poon and Granger 2003, Franq and Zakoian 2019). Furthermore, since the focus of this essay lies beyond analyzing the volatility of each individual asset, I face further restrictions regarding the selection of a model. As will be shown in this section, I have chosen to apply the DCC-GARCH model of Engle (2002) - an extension to the widely used univariate GARCH models - that allows to analyze the conditional covariance structure of the entire portfolio (here the world's equity mar­kets, Gold, Oil, and Bitcoin) instead of just the risk/uncertainty associated with any given asset (see Franq and Zakoian 2019). Before presenting the model specification used in the empirical analysis, I am going to briefly reflect on volatility modelling.

The unconditional volatility of a market is given by the standard deviation of its return series. This measure, however, is not all too useful, since it gives a single volatility value for the entire time series. Conditional volatility gives a more dynamic picture by computing a time-varying volatility value. The simplest example of such a conditional volatility model is the moving average. Assuming that the returns have a mean of zero, such a model is given by:

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Note that this model assumes equal weights, regardless of how distant the lag of a squared return may be. A generalization to this approach is the autoregressive conditional heteroskedasticity ARC H( p) model, which models volatility as a weighted average of the past p returns (Engle 1982):

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