A description of the COVID-19 outbreak role in financial risk forecasting

Abstract

This study aims to describe the risk of the system composed on the market indexes of the countries that were more affected by COVID-19. Our sample encompasses the thirty-five countries with more cases and/or deaths caused by COVID-19 until November 2020. As a second contribution, we describe the risk of each market index individually. As a general pattern, we note that losses and individual and systemic risks peaked in March 2020. We verify that countries that were epicenters of the COVID-19 pandemic experienced critical levels of risk, which is partially explained by more stringent confinement measures since these are the ones whose labor markets will suffer more in the medium and long run. We perceived a market recovery, arguably due to the low-interest rates and expansive actions taken by central banks. Nonetheless, we also observed that the systemic risk returned to pre-pandemic levels at the end of 2020.

1. Introduction

With the outbreak of the COVID-19 pandemic, economies worldwide have entered an unprecedented, sour chapter. According to the data collected by Organization for Economic Cooperation and Development (OECD) (OECD, 2021), three European economies stand out among the worst gross domestic product (GDP) results in 2020: France (−8.2%), United Kingdom (−9.9%), and Spain (−11%). The decline of the United States GDP, −3.5%, is the worst since the Second World War (Crutsinger, 2021). Although more encouraging, the positive result of China (GDP of 2.3%) is the lowest since 1976 (Trading Economics, 2021). At the aggregated level, the global economy shrank by 3.3% in 2020 (International Monetary Fund, 2021). The pandemic period was also accompanied by a sharp increase in wage inequality and unemployment rate and loss of full-time jobs (Aspachs et al., 2021, International Monetary Fund, 2020, Mazur et al., 2021). Moreover, extreme poverty increased for the first time since 1988 (World Bank, 2020). The shortage of demand, the disruption of production chains, and social distancing measures are often pointed to as the mechanism through which COVID-19 affected the real economy (Baker et al., 2020, Carlsson-Szlezak et al., 2020a, Carlsson-Szlezak et al., 2020b). Baldwin and Di Mauro (2020) also comment that panic among consumers and businesses has distorted usual consumption patterns and created market anomalies, contributing to negative effects on economies.

Global financial markets were also severely hit. In March 2020, the slump in stock exchanges was deep and synchronous across several countries, with circuit breaks and bans on short sales being widespread triggered (Kodres, 2020, Nunn and Kulam, 2021). The United States, for instance, hit the circuit break level four times in ten days, the first occurring on March 9, 2020 (Zhang, Hu, & Ji, 2020). The day before it, the escalating Saudi-Russian oil price war facilitated a quarterly drop of 65% on the oil price (Jacobs, 2020). This shock resonated on a stressed market, leading the S&P 500 to drop by 7.6% on March 9, 2020, which triggered the circuit breaker (Jason, 2020). Before this date, the circuit breaker had only ever been triggered once. This fateful day, dubbed Black Monday, was followed by daily price rebounds in various international markets, reflecting their skyrocketing volatility (Abuzayed, Bouri, Al-Fayoumi, & Jalkh, 2021). The VIX index recorded its all-time high on March 16, 2020 (Wagner, 2020), and the volatility of the S&P 500 in March 2020 was the third-highest since 1900 (Baker et al., 2020). The stock market collapse due to the pandemic is already similar to that faced during the Subprime crisis (Rout, Das, & Inamdar, 2020). It is undoubtedly the biggest due to infectious diseases (Baker et al., 2020, Velde, 2020). Studies of the impact of previous epidemics on the economic and financial sectors are, for instance, Chen et al., 2007, Chen et al., 2018, Del Giudice and Paltrinieri, 2017, Ichev and Marinč, 2018, Lee et al., 2004.

When economic downturns and financial distresses are combined, the usual result is that both the real (economic) sector as well as the financial sector take longer to recover (Reinhart & Rogoff, 2009). In the long-run, adverse economic consequences of COVID-19 will be felt, for instance, in the form of losses of human capital accumulation. For instance, Fuchs-Schündeln, Krueger, Ludwig, and Popova (2020) used a structural life-cycle model to assess the long-term consequences of school closures due to the COVID-19 pandemic. They found that younger children could be more affected by school closures because of the self-productive component of human capital accumulation. Coibion, Gorodnichenko, and Weber (2020) found a direct association between the early adoption of confinement measures and citizens’ pessimism about economic performance in the short and long-run. Through a survey with more than 10,000 respondents, they found that, to the households’ eyes, a V-shape recovery is unlikely. The heterogeneous aspect of the economic consequences of the COVID-19 pandemic was recognized, for instance, in Fana, Pérez, and Fernández-Macías (2020), that argued that countries and economic sectors that underwent more stringent confinement measures would possibly be the ones whose labor markets will suffer more in the medium and long run. In this regard, see also Breugem, Corvino, Marfè, and Schoenleber (2020). On the macro-financial side, the accentuated increase of the sovereign debt risk in countries with small fiscal space is a recurrent concern. For instance, Andrieś, Ongena, and Sprincean (2021) found that economies with small fiscal space have a limited capacity to issue new debt and, therefore, a small capacity to adopt fiscal and monetary responses to the economic downturn. Therefore, small fiscal capacity makes economies more vulnerable (Augustin, Sokolovski, Subrahmanyam, & Tomio, 2022). A theoretical discussion focused on the incentives of emerging economies in repaying their debts is carried out in Rogoff (2022). On the financial side, the long-term impact of the COVID-19 crisis was reflected by a sharp increase in the premiums required by long-term investors. By analyzing the yield of European corporate bonds of several maturities (financial and non-financial sectors), Ettmeier, Kim, and Kriwoluzky (2020) observed that the premium for long-term bonds increased much more than that of short-term bonds.

Given this background, the objective of this study is twofold. Our first goal is to assess the single-index risk1 of thirty-five of the countries most exposed to COVID-19: Argentina, Austria, Bangladesh, Belgium, Brazil, Canada, Chile, China, Czechia, Egypt, France, Germany, India, Indonesia, Iraq, Israel, Italy, Mexico, Morocco, Nepal, Netherlands, Pakistan, Philippines, Poland, Portugal, Romania, Russia, Saudi Arabia, South Africa, Spain, Sweden, Switzerland, Turkey, United Kingdom (UK), and United States of America (USA). We selected these countries because they had the highest total number of confirmed cases and/or deaths caused by COVID-19 until November 2020. We use both variables to select countries because (Al-Awadhi, Alsaifi, Al-Awadhi, & Alhammadi, 2020) found that they exert a significant adverse effect on stock market returns. We quantify the single-index risk using the following single component risk measures2 : Value at Risk (VaR), Expected Shortfall (ES), Expected Loss (EL), Expectile Value at Risk (EVaR), Mean plus Semi-Deviation (MSD), and Maximum Loss (ML). We use each country’s daily stock market index data from November 17, 2018, to October 25, 2021.

As a second and main task, we analyze the risk of the system composed of the thirty-five countries investigated in this work. The theoretical foundation of the systemic risk measures we use was developed in Chen, Iyengar, and Moallemi (2013) and extended by Kromer, Overbeck, and Zilch (2016). A systemic risk measure is determined by two fundamental elements: an aggregation function and a single component risk measure. The aggregation function uses data from the individual indexes to create a new series representing the whole system. Then, we quantify the systemic risk by applying the single component risk measures to the aggregate indexes.

We consider three aggregation functions; each one is a weighted mean of the returns of the individual indexes and provides a different picture of the system. We use a naive aggregation function that gives equal weights to each index as a benchmark. This aggregation function, applied to returns, is equivalent to the sum aggregation function of the profits and losses suggested by Chen et al. (2013). We also use two aggregation functions that weigh the individual indexes according to the number of cases and deaths from coronavirus (COVID-19) in each country. We use both indexes because previous studies show that the market has reacted negatively to the number of cases (Ashraf, 2020, Xu, 2021) and to the number of cases and deaths by COVID-19 (Al-Awadhi et al., 2020, Andrieś et al., 2021). As a byproduct, these aggregation functions provide three dynamic pictures of the global financial system during the time of our sample. We provide descriptive statistics of the aggregate indexes series and explore the relationship between them and the descriptive statistics of the individual indexes.

We consider six single component risk measures, whence reflect six alternative views on the financial risk of the system. VaR, ES, EVaR, and ML are tail risk measures focusing on extreme losses. The EL is a measure of the central tendency of the loss, and the MSD adds to the EL a variability component, which is specially adequate in our context of high variability due to the COVID-19 crisis. Therefore, we study both dimensions of the risk (loss and variability) (Righi, 2019, Righi and Borenstein, 2018).

On the methodological side, we contribute to the literature by taking a view on the systemic risk that was not previously employed to measure risk during the pandemic period. Within the framework of Chen et al. (2013), we considered a total of 18 systemic risk measures,3 therefore providing the literature with a fairly comprehensible application of the general theory (as far as we are aware of, no previous work has considered such diversity of systemic risk measures to analyze the pandemic period). This theory is based on the idea of “aggregating the components of the system, and then measuring the risk of the aggregate index”. This is one possible manner of measuring the risk of a system. For instance, a concurrent approach would be to “measure the risk of each of the system components, and then aggregating the risks”. The difference between these two approaches is discussed thoroughly in Doldi and Frittelli (2021) and Biagini, Fouque, Frittelli, and Meyer-Brandis (2019). Both approaches can be viewed as extensions of the basic theory developed in Artzner, Delbaen, Eber, and Heath (1999). As such, they can be used by supervisory authorities interested in assessing systemic risk and by risk managers interested in controlling the risk of portfolios of global stock market indexes.

To better contextualize the place of our methodological choices within the literature, we should notice that, in addition to the axiomatic approaches mentioned in the last paragraph, there is a vast literature of specific measures designed to explore specific aspects of systemic risk. Notably, the CoVaR proposed in Tobias and Brunnermeier (2016) allows us to measure the influence of each of the systems’ components on systemic risk. Conversely, the Systemic expected shortfall proposed in Acharya, Pedersen, Philippon, and Richardson (2017) gives us a measure of how each institution in the system is affected by the system. Following an alternative strategy, Huang, Zhou, and Zhu (2012) propose an index of systemic risk based on the (hypothetical) risk-neutral premium against systemic financial distress.

Our empirical analysis shows that the stock markets in the countries more exposed to COVID-19 presented synchronous dynamics following March 9, 2020, when several markets presented their minimum returns. We divided our sample into a pre-COVID-19 sub-sample and a second sub-sample representing the pandemic period. The contrast between the stability of the pre-pandemic period and the meltdown of March 2020 provides an opportunity to evaluate the behavior of our measures to quantify systemic risk in two very different scenarios (a similar strategy was employed, for instance, in Akhtaruzzaman, Boubaker, Nguyen, and Rahman (2022) and Abuzayed et al. (2021)). In addition to the large losses, the variability of the returns during the pandemic sub-sample is consistently higher for all countries. Fortunately, the markets have recovered after the March shock, so the mean return for the second sub-sample was not considerably smaller than that of the pre-COVID sub-sample. The increase of the single-indexes’ losses and variability was previously reported in several papers (see, for instance, Al-Awadhi et al., 2020, Ashraf, 2020, Li et al., 2021, Vasileiou et al., 2021, Xu, 2021 and Zhang et al., 2020). Therefore, in what losses and variability are regarded, our contribution is limited to providing information about losses and variability during the COVID-19 period for a larger set of countries.

On the practical side, our main contribution is to the growing literature analyzing the impact of COVID-19 on the single-index and systemic risk of the financial system. We observed a sharp increase in the risk in the individual markets during March 2020, with a posterior recovery. However, as a general trend, the market risks did not retract to pre-pandemic levels until near the end of 2020. Our results indicate a similar pattern for systemic risk. For most systemic risk measures we used, the systemic risk peaked around March 2020 and remained above the pre-pandemic level for most of 2020. Quantifying the effect of pandemics on systemic risk is an elementary task that any regulatory agency should perform. We compare the systemic risk before and after the shock of March 9 through several lenses, providing support for regulatory agencies and financial agents to get better informed about the possible financial consequences of COVID-19 variants. These findings are directly applicable and useful for distinct agents, such as market investors, policymakers, and regulatory agencies, for monitoring and managing both single-market and systemic risk in times of huge distress, as is the case for the COVID-19 pandemic.

Our empirical findings relate closely to Abuzayed et al. (2021), Lai and Hu (2021), Akhtaruzzaman, Benkraiem, et al., 2022, Akhtaruzzaman, Boubaker, et al., 2022 and Zhang et al. (2020). However, different from ours, much of this literature is focused on studying contagion among countries (Akhtaruzzaman, Benkraiem, et al., 2022), cryptocurrencies (Akhtaruzzaman, Boubaker, et al., 2022), or financial institutions (Akhtaruzzaman, Boubaker, and Sensoy, 2021, Baumöhl et al., 2020, Borri and Di Giorgio, 2021, Rizwan et al., 2020). For instance, Abuzayed et al. (2021) studied the tail-risk spillovers from the financial system and each of the fourteen countries most exposed to COVID-19. They found that the spillovers were considerably higher in their sample of the pandemic period (February 2020 to July 2020) than in their stable period (January 2016 to February 2020). In particular, they noticed that the increase of risk spillover was remarkably high for the European countries more exposed to the pandemic. We complement their findings by showing that, for the several risk measures we considered, the single-index risk of the most affected European countries increased dramatically, especially in the week of March 9, 2020. Also, we consider a larger set of countries and provide more up-to-date information since our sample goes until October 2021.

The remainder of this paper is structured as follows: Section 2 presents the theoretical background of single component risk measures and summarizes the approach of Chen et al. (2013) and Kromer et al. (2016) to measure systemic risk; Section 3 describes the data and the methodology, including descriptive data analysis, models, and risk estimation procedures. Section 4 presents single-index and systemic risk results, and Section 5 summarizes and concludes the paper. The study also has an Appendix that describes additional results.

2. Background

In this section, we present the theoretical framework underlying the systemic risk measures that we adopt. This section’s main goal is to show that the systemic risk measures we use reflect systemic risk in a meaningful manner. We also introduce the single component risk measures that we use and present a general form for the aggregation functions.

The return of a financial position is represented by a random variable $X$, which is defined on a probability space $(\Omega ,\mathcal{F},\mathbb{P})$. Accordingly, $X\left(\omega \right)>0$ represents a gain (when the state $\omega \in \Omega$ occurs) and $X\left(\omega \right)<0$ a loss. Kromer et al. (2016) generalized the approach of Chen et al. (2013) to the very general setting of locally convex solid Riesz spaces. On the other hand, our goal is to provide a more direct presentation. Therefore, we consider the special case where $\mathcal{X}≔L^2(\Omega ,\mathcal{F},\mathbb{P})$, that is, we work with random variables satisfying ${\int }_{\Omega }{X}^{2}d\mathbb{P}<\infty$. We denote vectors and random vectors as $\mathbf{x}≔(x_1,\dots ,x_n)\in {\mathbb{R}}^n$ and $\mathbf{X}≔(X_1,\dots ,X_n)\in {\mathcal{X}}^n$, respectively. All equalities and inequalities between random variables should be understood in the $\mathbb{P}$-a.s. sense. We identify $\mathbb{P}$-a.s. constant random variables (vectors, respectively) with real numbers (vectors, respectively), i.e., we adopt the identities $\mathbb{R}\equiv {\cup }_{c\in \mathbb{R}}\{X\in \mathcal{X}:X=c\}$ and ${\mathbb{R}}^n\equiv {\cup }_{\mathbf{c}\in {\mathbb{R}}^n}\{\mathbf{X}\in {\mathcal{X}}^n:\mathbf{X}=\mathbf{c}\}$, where $\mathbf{c}=(c_1,\dots ,c_n)$. The positive and negative parts, the expected value, the cumulative distribution function, and the left quantile of a random variable $X\in \mathcal{X}$ are defined, respectively, as $X^{+}≔max\{X,0\}$, $X^{-}≔max\{-X,0\}$, $E\left[X\right]≔{\int }_{\Omega }Xd\mathbb{P}$, $F_X\left(x\right)≔\mathbb{P}(X\le x)$ for $x\in \mathbb{R}$ and, $F_X^{-1}\left(\alpha \right)=inf\{x\in \mathbb{R}:F_X\left(x\right)\ge \alpha \}$ for $\alpha \in [0,1]$, respectively.

We measure systemic risk by first aggregating the system’s components and then applying a single component risk measure to the aggregate index. Accordingly, we begin by presenting the aggregation functions and, after that, the risk measures.

Our system is defined as a collection of $n\in \mathbb{N}$ market indexes. The system is represented by a random vector $\mathbf{X}=(X_1,X_2,\dots ,X_n)\in {\mathcal{X}}^n$. Notice that each $\omega \in \Omega$ defines a cross-sectional profile $\mathbf{X}\left(w\right)=(X_1\left(\omega \right),X_2\left(\omega \right),\dots ,X_n\left(\omega \right))$ of gains and losses across the components of the system. In what follows, $\mathbf{X}\ge \mathbf{Y}$ means that $X_i\ge Y_i$ for all $i\in \{1,2,\dots ,n\}$, and $\mathbf{1}\in {\mathcal{X}}^n$ is defined (with a slight abuse of notation) as $\mathbf{1}≔(1,1,\dots ,1)$.

Definition 1

An aggregation function is a map $\Lambda :{\mathbb{R}}^n\to \mathbb{R}$. For two cross-sectional profiles $\mathbf{X}\left(\omega \right)$ and $\mathbf{X}\left({\omega }^{\prime }\right)$, consider the following useful properties that $\Lambda$ might satisfy:

• •(Monotonicity) $\Lambda$ is monotone if $\mathbf{X}\left(\omega \right)\ge \mathbf{X}\left({\omega }^{\prime }\right)$ implies $\Lambda \left(\mathbf{X}\left(\omega \right)\right)\ge \Lambda \left(\mathbf{X}\left({\omega }^{\prime }\right)\right)$.
• •(Concavity) $\Lambda$ is concave if for all $0\le \alpha \le 1$ we have that $\Lambda (\alpha \mathbf{X}\left(\omega \right)+(1-\alpha )\mathbf{X}\left({\omega }^{\prime }\right))\ge \alpha \Lambda \left(\mathbf{X}\left(\omega \right)\right)+(1-\alpha )\Lambda \left(\mathbf{X}\left({\omega }^{\prime }\right)\right)$.
• •(Surjectivity) $\Lambda \left({\mathbb{R}}^n\right)=\mathbb{R}$.
• •($\mathcal{X}$-restricted) $\Lambda \left({\mathcal{X}}^n\right)=\mathcal{X}$.

Aggregation functions reflect – or can be thought of as reflecting – a regulator’s view of the system. In this sense, the monotonicity property can be interpreted as saying that if all system components are better off on the state $\omega$ than on the state ${\omega }^{\prime }$, then the regulator would also prefer the state $\omega$ to ${\omega }^{\prime }$. The property of concavity can be thought of as reflecting the regulator’s risk aversion: it prefers the average of the cross-sectional profiles $\mathbf{X}\left(\omega \right)$ and $\mathbf{X}\left({\omega }^{\prime }\right)$ than to bet on one of them. Aggregation functions satisfying monotonicity, concavity, and surjectivity are named concave aggregation functions. For the property of $\mathcal{X}$-restrictedness, notice that, for $\mathbf{X}\in {\mathcal{X}}^n$, the term $\Lambda \left(\mathbf{X}\right)$ is a random variable. With this in mind, the property of $\mathcal{X}$-restrictedness tells us that the function $\Lambda$ is, on the one hand, rich enough to generate all random variables in $\mathcal{X}$, i.e., $\Lambda \left({\mathcal{X}}^n\right)\supseteq \mathcal{X}$ and; on the other hand, it maintains the square-integrability of the random variables, i.e., $\Lambda \left({\mathcal{X}}^n\right)\subseteq \mathcal{X}$.

As we explain in Section 3, the aggregation functions we use are weighted means of the individual market indexes, that is, for $x=(x_1,\dots ,x_n)$ they take the form $\Lambda \left(x\right)={\sum }_{i=1}^n{\theta }_i{x}_i$, where $({\theta }_1,{\theta }_2,\dots ,{\theta }_n)\in {[0,1]}^n$ and ${\sum }_{i=1}^n{\theta }_i=1$. Presenting the specific functional forms of the aggregation functions we use requires first a description of our data-set structure. Therefore we postpone the presentation of the specific aggregation functions to Section 3. These weighted-means aggregation functions allow the regulator to weigh the components of the system differently. Yet, they satisfy monotonicity, concavity, and surjectivity, i.e., they are concave aggregation functions. To see that weighted means also satisfy $\mathcal{X}$-restrictedness (for $\mathcal{X}=L^2(\Omega ,\mathcal{F},\mathbb{P})$), see Lemma 1 of Kromer et al. (2016).

Definition 2

A single component risk measure is a functional ${\rho }_0:\mathcal{X}\to \mathbb{R}\cup \{+\infty \}$, which might fulfill the following proprieties4 :

• •(Monotonicity) If $X\ge Y$, then ${\rho }_0\left(X\right)\le {\rho }_0\left(Y\right)$, $\forall X,Y\in \mathcal{X}$.
• •(Convexity) ${\rho }_0(\lambda X+(1-\lambda )Y)\le \lambda {\rho }_0\left(X\right)+(1-\lambda ){\rho }_0\left(Y\right)$, $\forall \lambda \in [0,1]$ and $\forall X,Y\in \mathcal{X}$.
• •(Constancy) ${\rho }_0\left(a\right)=-a$ for $a\in \mathbb{R}$.

Monotonicity indicates that if the value of a financial position $X$ is always greater or equal to the value of $Y$, then the risk of $X$ must be smaller than or equal to the risk of $Y$. Convexity captures the notion that diversification does not create additional risk. The constancy property gives a single component risk measure a monetary facet related to the axiomatic formulation of Artzner et al. (1999). Notice that if ${\rho }_0$ fulfills constancy, then the risk of a certain loss, let us say a real number $a<0$, is represented by the size of the loss, i.e., $\left|a\right|=-a$. As proposed in Kromer et al. (2016), single component risk measures satisfying monotonicity, convexity, and constancy are called convex single component risk measures. This is the case for all single component risk measures we use, except the Value at Risk, which is not convex.

• •Value at Risk (VaR): This measure is defined as $Va{R}^{\alpha }\left(X\right)=-F_X^{-1}\left(\alpha \right),\alpha \in [0,1)$. The significance level $\alpha$ can be thought of as an (inverse) security level. This measure represents the maximum loss for a given period and significance level. It is the most common in the financial industry and academy.
• •Expected Loss (EL): This risk measure is defined as $EL\left(X\right)=-E\left[X\right]$. It is the most parsimonious one, indicating a loss’s expected value (mean).
• •Mean plus Semi-Deviation (MSD): This risk measure is defined as $MS{D}^{\beta }\left(X\right)=-E\left[X\right]+\beta \sqrt{E\left[{\left({(X-E\left[X\right])}^{-}\right)}^2\right]},0\le \beta \le 1$. It has the advantage of reflecting the losses explicitly (with EL) and the variability for values below $E\left[X\right]$.
• •Expected Shortfall (ES): This risk measure is defined as $E{S}^{\alpha }\left(X\right)=-\frac{1}{\alpha }{\int }_0^{\alpha }{F}_X^{-1}\left(s\right)ds,0<\alpha \le 1$. It quantifies the expected value of losses given that they are larger than $Va{R}^{\alpha }$.
• •Expectile Value at Risk (EVaR): This measure links to the concept of an expectile, given by $EVa{R}^{\alpha }\left(X\right)=-{arg\; min}_{x\in \mathbb{R}}E[\alpha {\left({(X-x)}^{+}\right)}^2+(1-\alpha ){\left({(X-x)}^{-}\right)}^2],0<\alpha \le 0.5$.  Bellini and Di Bernardino (2017) points out that according to EVaR, the position is acceptable when the ratio of expected gain to expected loss is sufficiently high.
• •Maximum loss (ML): This is an extreme risk measure that can be defined as $ML\left(X\right)=-ess\; infX=-sup\{m\in \mathbb{R}:\mathbb{P}(X<m)=0\}$. Such a risk measure leads to more protective situations. In fact, for any single component risk measure ${\rho }_0$ satisfying monotonicity, constancy and such that ${\rho }_0\left(0\right)=0$, it follows that ${\rho }_0\left(X\right)\le ML\left(X\right)$ for all $X\in \mathcal{X}$. We adopt here the convention that $sup0̸=-\infty$, so it follows that $ML\left(\cdot \right)$ takes values on $\mathbb{R}\cup \{+\infty \}$.

The reader will find mathematical and conceptual discussions about the above risk measures in Acerbi and Tasche, 2002, Bellini and Di Bernardino, 2017, Föllmer and Schied, 2016 and Righi (2019). Making use of the convention ${\mathbb{R}}^n\equiv {\cup }_{\mathbf{c}\in {\mathbb{R}}^n}\{\mathbf{X}\in {\mathcal{X}}^n:\mathbf{X}=\mathbf{c}\}$, we denote the restriction of a functional $\rho :{\mathcal{X}}^n\to \mathbb{R}\cup \{+\infty \}$ to the set of $\mathbb{P}$-a.s. constant random vectors as ${\rho }_{|{\mathbb{R}}^n}$. Therefore, it holds that ${\rho }_{|{\mathbb{R}}^n}:{\mathbb{R}}^n\to \mathbb{R}$ is defined as ${\rho }_{|{\mathbb{R}}^n}\left(\mathbf{x}\right)=\rho \left(\mathbf{x}\right)$ for all $\mathbf{x}\in {\mathbb{R}}^n$.

Definition 3

A systemic risk measure is a functional $\rho :{\mathcal{X}}^n\to \mathbb{R}\cup \{+\infty \}$, which might satisfy some or all of the following properties:

• •(Monotonicity) If $\mathbf{X}\ge \mathbf{Y}$, then $\rho \left(\mathbf{X}\right)\le \rho \left(\mathbf{Y}\right)$, $\forall \mathbf{X},\mathbf{Y}\in {\mathcal{X}}^n$.
• •(Preference Consistency) If $\rho \left(\mathbf{X}\left(w\right)\right)\le \rho \left(\mathbf{Y}\left(w\right)\right)$ for almost all $w\in \Omega$, then $\rho \left(\mathbf{X}\right)\le \rho \left(\mathbf{Y}\right)$, $\forall \mathbf{X},\mathbf{Y}\in {\mathcal{X}}^n$.
• •(Outcome Convexity) For a system $\mathbf{Z}=\lambda \mathbf{X}+(1-\lambda )\mathbf{Y}$, where $\lambda \in [0,1]$, we have $\rho \left(\mathbf{Z}\right)\le \lambda \rho \left(\mathbf{X}\right)+(1-\lambda )\rho \left(\mathbf{Y}\right)$, $\forall ,\mathbf{X},\mathbf{Y},\mathbf{Z}\in {\mathcal{X}}^n$.
• •(Risk Convexity) Let $\mathbf{X},\mathbf{Y},\mathbf{Z}\in {\mathcal{X}}^n$. Suppose $\rho \left(\mathbf{Z}\left(w\right)\right)=\lambda \rho \left(\mathbf{X}\left(w\right)\right)+(1-\lambda )\rho \left(\mathbf{Y}\left(w\right)\right)$ for a given scalar $\lambda \in [0,1]$ and almost all $w\in \Omega$. Then $\rho \left(\mathbf{Z}\right)\le \lambda \rho \left(\mathbf{X}\right)+(1-\lambda )\rho \left(\mathbf{Y}\right)$.
• •(Surjectivity) $\rho \left({\mathbb{R}}^n\right)=\mathbb{R}$.
• •(Magnitude Preserving) ${\rho }_{|{\mathbb{R}}^n}\left({\mathcal{X}}^n\right)\subseteq \mathcal{X}$.

The monotonicity property for $\rho$ has the same intuition as that for ${\rho }_0$. The property of preference consistency says that, if $\mathbf{X}$ and $\mathbf{Y}$ are two systems such that, for almost all $\omega \in \Omega$, the risk of the constant systems satisfy $\rho \left((X_1\left(\omega \right),\dots ,X_n\left(\omega \right))\right)\le \rho \left((Y_1\left(\omega \right),\dots ,Y_n\left(\omega \right))\right)$, then the risk $\rho \left(\mathbf{X}\right)$ of the random system $\mathbf{X}$ must be not greater than $\rho \left(\mathbf{Y}\right)$. Outcome convexity is the natural extension of convexity for risk measures. Risk convexity was proposed initially by Chen et al. (2013). To gain intuition, take $\mathbf{Z}\in {\mathcal{X}}^n$ and look at $\rho \left(\mathbf{Z}\left(\omega \right)\right)$ as the ex-post risk, that is, the risk of the system after the state $\omega \in \Omega$ had been revealed. Now, if the ex-post risk of the system $\mathbf{Z}$ is always the same convex combination of the ex-post risk of the systems $\mathbf{X}$ and $\mathbf{Y}$, then the ex-ante risk of $\mathbf{Z}$ must be given by this same convex combination, that is, $\rho \left(\mathbf{Z}\right)=\lambda \rho \left(\mathbf{X}\right)+(1-\lambda )\rho \left(\mathbf{Y}\right)$. Of course, this would be stronger than risk convexity. This interpretation for risk convexity is related to the axiom of time consistency for dynamic risk measures and is different from the interpretations provided in Chen et al. (2013) and Kromer et al. (2016). The properties of surjectivity and magnitude preserving are important for Theorem 1 and Proposition 1. All of the mentioned properties are used in Kromer et al. (2016), and systemic risk measures satisfying them are called convex systemic risk measures.

The following Theorem 1 of Kromer et al. (2016) guarantees that by combining concave aggregation functions with convex single component risk measures, one obtains convex systemic risk measures.

Theorem 1

(Kromer et al., 2016 ). A functional $\rho :{\mathcal{X}}^n\to \mathbb{R}\cup \{+\infty \}$ is a convex systemic risk measure if, and only if, there is a convex single component risk measure ${\rho }_0:\mathcal{X}\to \mathbb{R}\cup \{+\infty \}$ and a concave aggregation function $\Lambda :{\mathbb{R}}^n\to \mathbb{R}$ , such that $\rho \left(\mathbf{X}\right)=({\rho }_0\circ \Lambda )\left(\mathbf{X}\right),\forall \mathbf{X}\in {\mathcal{X}}^n$ .

This theorem guarantees that the functionals we use to measure the systemic risk consistently, except when VaR is used as a single component risk measure. Chen et al. (2013) proved an analog theorem for positive homogeneous single component risk measures, which are not convex, as the VaR. However, our application does not fit their theorem because the aggregation functions we use do not satisfy their normalization property, which requires $\Lambda \left(\mathbf{1}\right)=n$. This fact, however, poses no conflict between, on the one hand, systemic risk measures with desirable properties and, on the other hand, compositions of the form $Va{R}^{\alpha }\left(\Lambda \left(\cdot \right)\right)$, where $\Lambda$ is a weighted mean. First, as VaR is not convex, it is natural that it generates nonconvex systemic risk measures. Second, compositions in the form $Va{R}^{\alpha }\left(\Lambda \left(\cdot \right)\right)$, where $\Lambda$ is a weighted mean, satisfy all the desirable properties of Definition 3, except outcome and risk convexity, and yet, they are positive homogeneous in the sense of the following proposition.

Proposition 1

Fix $\alpha \in [0,1)$ and consider a vector $\mathit{\theta }=({\theta }_1,\dots ,{\theta }_n)\in {\mathbb{R}}^n$ satisfying ${\sum }_{i=1}^n{\theta }_i=1$ and ${\theta }_i\ge 0$ for all $1\le i\le n$ . Let $\rho :{\mathcal{X}}^n\to \mathbb{R}\cup \{+\infty \}$ be defined as $\rho \left(\mathbf{X}\right)=Va{R}^{\alpha }\left(\Lambda \left(\mathbf{X}\right)\right)$ , where $\Lambda :{\mathbb{R}}^n\to \mathbb{R}$ is an aggregation function defined as $\Lambda \left(\mathbf{x}\right)={\sum }_{i=1}^n{x}_i{\theta }_i$ for all $\mathbf{x}\in {\mathbb{R}}^n$ . Then $\rho$ satisfies monotonicity, preference consistency, surjectivity, and magnitude preserving. Moreover, it is positive homogeneous, that is, $\rho \left(\lambda \mathbf{X}\right)=\lambda \rho \left(\mathbf{X}\right)$ for $\lambda \ge 0$ and all $\mathbf{X}\in {\mathcal{X}}^n$ .

Proof

For monotonicity, notice that if $\mathbf{X}\ge \mathbf{Y}$, then $\Lambda \left(\mathbf{X}\right)\ge \Lambda \left(\mathbf{Y}\right)$. Since VaR is a monotonic single component risk measure, it follows that $Va{R}^{\alpha }\left(\Lambda \left(\mathbf{X}\right)\right)\le Va{R}^{\alpha }\left(\Lambda \left(\mathbf{Y}\right)\right)$.

For preference consistency, take $\mathbf{X}$ and $\mathbf{Y}$ such that $Va{R}^{\alpha }\left({\sum }_{i=1}^n{\theta }_i{X}_i\left(\omega \right)\right)\le Va{R}^{\alpha }\left({\sum }_{i=1}^n{\theta }_i{Y}_i\left(\omega \right)\right)$ $\mathbb{P}$-a.s. Notice that VaR satisfies constancy, therefore we have ${\sum }_{i=1}^n{\theta }_i{X}_i\left(\omega \right)\ge {\sum }_{i=1}^n{\theta }_i{Y}_i\left(\omega \right)$ $\mathbb{P}$-a.s. This implies that $\Lambda \left(X\right)\ge \Lambda \left(Y\right)$, whence we have $Va{R}^{\alpha }\left(\Lambda \left(X\right)\right)\le Va{R}^{\alpha }\left(\Lambda \left(Y\right)\right)$.

The property of positive homogeneity for the systemic risk measure $\rho \left(\cdot \right)=Va{R}^{\alpha }\left(\Lambda \left(\cdot \right)\right)$ follows from the fact that, for $\mathbf{X}\in {\mathcal{X}}^n$ and $\lambda \ge 0$, we have $\Lambda \left(\lambda \mathbf{X}\right)=\lambda \Lambda \left(\mathbf{X}\right)$ and that, in addition, it holds that $Va{R}^{\alpha }\left(\lambda X\right)=\lambda Va{R}^{\alpha }\left(X\right)$, for all $\lambda \ge 0$ and for all $X\in \mathcal{X}$. Therefore it holds that $Va{R}^{\alpha }\left(\Lambda \left(\lambda \mathbf{X}\right)\right)=Va{R}^{\alpha }\left(\lambda \Lambda \left(\mathbf{X}\right)\right)=\lambda Va{R}^{\alpha }\left(\Lambda \left(\mathbf{X}\right)\right)$ for all $\lambda \ge 0$ and $\mathbf{X}\in {\mathcal{X}}^n$.

The property of surjectivity requires $\rho \left(\cdot \right)$ to cover all the real line using only vectors with non-random components (see item 5 of Definition 3). But this is the case for $Va{R}^{\alpha }\left(\Lambda \left(\cdot \right)\right)$ because $Va{R}^{\alpha }\left(\Lambda \left((x,x,\dots ,x)\right)\right)=-x$, for all $x\in \mathbb{R}$ and, therefore, $Va{R}^{\alpha }\left(\Lambda \left({\mathbb{R}}^n\right)\right)=\mathbb{R}$.

For magnitude preserving, recall that ${\rho }_{|{\mathbb{R}}^n}:{\mathbb{R}}^n\to \mathbb{R}$ is defined as ${\rho }_{|{\mathbb{R}}^n}\left(\mathbf{x}\right)=\rho \left(\mathbf{x}\right)$ for all $\mathbf{x}\in {\mathbb{R}}^n$. If a systemic risk measure is of the form $\rho \left(\cdot \right)={\rho }_0\left(\Lambda \left(\cdot \right)\right)$, where ${\rho }_0$ is a single component risk measure satisfying constancy, then ${\rho }_{|{\mathbb{R}}^n}\left(\mathbf{x}\right)={\rho }_0\left(\Lambda \left(\mathbf{x}\right)\right)=-\Lambda \left(\mathbf{x}\right)$ for all $\mathbf{x}\in {\mathbb{R}}^n$. In particular, for the case of $\rho \left(\cdot \right)=Va{R}^{\alpha }\left(\Lambda \left(\cdot \right)\right)$ we have that $Va{R}_{|{\mathbb{R}}^n}^{\alpha }\left(\mathbf{x}\right)=Va{R}^{\alpha }\left(\Lambda \left(\mathbf{x}\right)\right)=-\Lambda \left(\mathbf{x}\right)$ for all $x\in {\mathbb{R}}^n$.

Now, notice that, when ${\rho }_{|{\mathbb{R}}^n}$ is applied to a random vector $\mathbf{X}\in {\mathcal{X}}^n$, we have that ${\rho }_{|{\mathbb{R}}^n}\left(\mathbf{X}\right)$ is a random variable. Similarly, ${\rho }_{0|{\mathbb{R}}^n}$ goes from ${\mathbb{R}}^n$ to $\mathbb{R}$, so that ${\rho }_{0|{\mathbb{R}}^n}\left(\mathbf{X}\right)$ is a random variable for all $\mathbf{X}\in {\mathcal{X}}^n$. In the case that $\rho \left(\cdot \right)={\rho }_0\left(\Lambda \left(\cdot \right)\right)$, it holds that, ${\rho }_{|{\mathbb{R}}^n}\left(\mathbf{X}\right)={\rho }_{0|{\mathbb{R}}^n}\left(\Lambda \left(\mathbf{X}\right)\right)$ for all $\mathbf{X}\in {\mathcal{X}}^n$. It is easy to verify that, if ${\rho }_0$ fulfills constancy, then the same holds for ${\rho }_{0|{\mathbb{R}}^n}$. This implies, in view of the last paragraph, that if ${\rho }_0$ fulfills constancy, then ${\rho }_{0|{\mathbb{R}}^n}\left(\Lambda \left(\mathbf{X}\right)\right)=-\Lambda \left(\mathbf{X}\right)$ for all $\mathbf{X}\in {\mathcal{X}}^n$. Since $Va{R}^{\alpha }$ fulfills constancy, we can apply the equality ${\rho }_{0|{\mathbb{R}}^n}\left(\Lambda \left(\mathit{\cdot }\right)\right)=-\Lambda \left(\mathit{\cdot }\right)$ to the systemic risk measure $\rho \left(\mathit{\cdot }\right)=Va{R}^{\alpha }\left(\Lambda \left(\mathit{\cdot }\right)\right)$. By proceeding in this manner, we conclude that $Va{R}_{|{\mathbb{R}}^n}^{\alpha }\left(\Lambda \left(\mathbf{X}\right)\right)=-\Lambda \left(\mathbf{X}\right)$ for all $\mathbf{X}\in {\mathcal{X}}^n$. But $\Lambda \left(\cdot \right)$ is $\mathcal{X}$-restricted and, therefore, we conclude that $Va{R}_{|{\mathbb{R}}^n}^{\alpha }\left(\Lambda \left({\mathcal{X}}^n\right)\right)=-\Lambda \left({\mathcal{X}}^n\right)\subseteq \mathcal{X}$. □

3. Data and methodology

This section describes the data, the aggregation functions, and the risk estimation procedures.

3.1. Data and descriptive analysis

We selected two sets of countries: the top 40 with the highest number of COVID-19 cases until November 11, 2020, and the top 40 with the highest number of death by COVID-19 until November 11, 2020 (COVID-19 Coronavirus, 2020).5 Only four countries do not belong to both sets. This selection criterion was motivated by the evidence showing that stock markets react negatively to the number of cases and deaths caused by COVID-19. For instance, Al-Awadhi et al. (2020), and Xu (2021) found that market returns decreased in response to new cases and deaths by COVID-19, while Andrieś et al. (2021) and Zhang et al. (2020) showed that cases and deaths by COVID-19 are associated with the increase of financial risk. Also, other studies analyzing the impact of the pandemic on financial markets have considered cases and deaths caused by COVID-19 as the criterion for selecting the countries to be studied. See, for example, Zhang et al. (2020). We excluded from our sample the countries that do not have the price available in Quandl (Dotson, McTaggart, Daroczi, & Leung, 2019), or quantmod (Ryan et al., 2020).6 Our dataset contains data from 35 countries, which are among the top 40 with the highest number of COVID-19 cases and/or deaths.

In Table 1, we describe the countries and market indexes considered in the study. We selected the market indexes by their representativeness in the country and the available data in the databases consulted. We also report the absolute number of COVID-19 cases and deaths per country and the percentage of COVID-19 cases and deaths. Notice that our dataset contains the countries with the largest stock exchanges in the world, including, for example, the United States, China, India, 16 of the G20 countries (Argentina, Brazil, Canada, China, France, Germany, India, Indonesia, Italy, Mexico, Russia, Saudi Arabia, South Africa, Turkey, UK, and the USA), and Spain that is a guest member of G20.7 The representativeness of these economies, and the pandemic’s severe impact on them, justifies the study of the system they compose and, in particular, how COVID-19 affected the risk of the system. Moreover, the analysis of the systemic and single-index risk of the markets considered allows us to have a rough idea of the financial risk on a global scale.

Table 1.

Market index, the absolute number of COVID-19 cases (Abs. Cases), and deaths (Abs. Deaths) until November 11, 2020, per country. Besides, this table describes the percentage of COVID-19 cases ($c_i^{\ast }$ (%) ) and deaths ($d_i^{\ast }$ (%)), by country.

Countries	Market index	Abs. Cases	$c_i^{\ast }$ (%)	Abs. Deaths	$d_i^{\ast }$ (%)
Argentina	MERVAL	1262476	2.858	34183	3.167
Austria	ATX	172380	0.390	1564	0.145
Bangladesh	DSEX	425353	0.963	6127	0.568
Belgium	BEL 20	507475	1.149	13561	1.256
Brazil	IBOVESPA	5701283	12.908	162842	15.087
Canada	S&P/TSX	273037	0.618	10632	0.985
Chile	IPSA	523907	1.186	14611	1.354
China	SSE	86284	0.195	4634	0.429
Czechia	PX	429880	0.973	5323	0.493
Egypt	EGX 30	109654	0.248	6394	0.592
France	CAC 40	1829659	4.142	42207	3.911
Germany	DAX	707550	1.602	11881	1.101
India	S&P BSE Sensex	8636974	19.554	127630	11.825
Indonesia	IDX	448118	1.015	14836	1.375
Iraq	ISX60	508508	1.151	11482	1.064
Israel	TA-100	320912	0.727	2684	0.249
Italy	FTSE MIB	995463	2.254	42330	3.922
Mexico	IPC	978531	2.215	95842	8.880
Morocco	MASI	265165	0.600	4425	0.410
Nepal	NEPSE	202329	0.458	1174	0.109
Netherlands	AEX	424819	0.962	8215	0.761
Pakistan	KSE 100	348184	0.788	7021	0.651
Philippines	PSEI	401416	0.909	7710	0.714
Poland	WIG	618813	1.401	8805	0.816
Portugal	PSI-20	187237	0.424	3021	0.280
Romania	BET	324094	0.734	8389	0.777
Russia	MOEX	1836960	4.159	31593	2.927
Saudi Arabia	TASI	351849	0.797	5590	0.518
South Africa	FTSE/JSE Top 40	740254	1.676	19951	1.848
Spain	IBEX 35	1443997	3.269	39756	3.683
Sweden	OMX-S30	166707	0.377	6082	0.564
Switzerland	SMI	243472	0.551	3087	0.286
Turkey	BIST 100	399360	0.904	11059	1.025
UK	FTSE 250	1233775	2.793	49770	4.611
USA	S&P 500	10573090	23.938	245963	22.789

Note: Abs. Cases, $c_i^{\ast }$, Abs. Deaths and $d_i^{\ast }$ refer to the absolute number of COVID-19 cases, percentage of COVID-19 cases, the absolute number of COVID-19 deaths, and the percentage of COVID-19 deaths, respectively. The percentage of COVID-19 cases ($c_i^{\ast }$ (%)) and deaths ($d_i^{\ast }$ (%)), by country, are computed based on the total number of cases and deaths from COVID-19 registered by the countries that make up our sample.

The sample period analyzed comprises November 17, 2018, to October 25, 2021. We selected this period because it contains a pre-pandemic period, which comprises the beginning of the sample until the first case of COVID-19 registered in Wuhan, China, on November 17, 2019, and an extended period of the pandemic.8 Throughout the text, the complete sample will be named as full sample. To compare risk behavior before and after the beginning of the pandemic, we divided the sample into two periods. The first period goes from November 17, 2018, to November 16, 2019, and it is named sub-sample 1. The second period goes from November 17, 2019, to October 25, 2021, and it is named sub-sample 2. Our choice of the breakpoint generates a sub-sample 1, which is free of any influence from the COVID-19 pandemic, and a sub-sample 2 reflects this influence from the beginning of the pandemic until the end of the sample. Therefore, by choosing the first case of COVID-19 as the breakpoint, we can describe how the systemic risk – and the risk of individual countries – evolved during the COVID-19 pandemic.

The market indexes of each country considered in the study are indexed as $\mathcal{I}≔\{1,\dots ,n\}$ and the periods are denoted by $\mathcal{T}≔\{1,\dots ,T\}$. For each market index, we computed log-returns using close-to-close daily prices,9 which are defined as $X_{t,i}=ln{P}_{t+1,i}-ln{P}_{t,i}$, where $P_{t,i}$ refers to the price of the market index $i\in \mathcal{I}$ at period $t\in \mathcal{T}$. For days when the market has not opened, we replaced the market index price with the value of the previous trading day. It is noteworthy that closing times vary between countries because international stock markets have different trading hours. However, given the variety of existing financial data synchronization methods (Bühlmann and Audrino, 2007, Burns et al., 1998), we chose to use close-to-close log-returns, as performed by Silva Filho, Ziegelmann, and Dueker (2014). We have postponed the investigation of different synchronization methods to estimate single-index and systemic risk for future work.

For descriptive analysis of log-returns of the market indexes, we computed the average (Mean), minimum (Min), maximum (Max), standard deviation (SD), asymmetry (Skew), and kurtosis (Kurt)10 of the full sample and sub-samples. These descriptive statistics are presented in Table 2. We observed that most markets underwent similar changes between sub-samples 1 and 2. The only descriptive statistic that did not change systematically between the sub-samples was the mean of the log-returns, which is close to zero for all market indexes and samples. This result was expected for sub-sample 1 because near-zero average returns are a common feature of financial series, and sub-sample 1 is a period of relative stability. For sub-sample 2, the near-zero mean return for most countries is explained by the recovery that followed the shock of March 2020 (this is illustrated in Fig. 1). We employed a bi-tailed and the right one-tailed Mann–Whitney test to verify if there are differences in the average ranks of both sub-samples. We consider the Mann–Whitney test because it is a non-parametric test, i.e., a distribution-free test. The results of the tests are in Appendix. Overall, the tests do not reject the null hypothesis at a 10% significance level, i.e., the median return of both sub-samples is equal. This finding corroborates our descriptive analysis of average returns.

Table 2.

Descriptive statistics of the log-returns (in %) of market indexes of thirty-five countries with most cases and/or deaths by COVID-19. The full sample period refers from November 17, 2018, to October 25, 2021. Sub-sample 1 comprehends data from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends data from November 17, 2019, to October 25, 2021.

Countries	Full sample						Sub-sample 1						Sub-sample 2
	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt
Argentina	0.114	−47.692	9.773	2.893	−5.241	82.438	0.008	−47.692	9.731	3.618	−7.393	95.280	0.169	−15.629	9.773	2.442	−0.792	7.005
Austria	0.021	−14.675	10.206	1.420	−1.679	24.113	0.006	−3.338	3.092	0.893	−0.218	1.442	0.028	−14.675	10.206	1.626	−1.683	20.688
Bangladesh	0.030	−6.737	9.798	0.890	1.065	23.763	−0.034	−1.908	2.315	0.623	0.592	2.023	0.062	−6.737	9.798	0.999	1.007	22.037
Belgium	0.019	−15.328	7.361	1.291	−2.248	26.882	0.031	−3.481	2.923	0.847	−0.700	1.966	0.013	−15.328	7.361	1.468	−2.235	23.723
Brazil	0.022	−15.994	13.023	1.724	−1.831	24.173	0.059	−3.810	3.494	1.046	−0.301	1.649	0.003	−15.994	13.023	1.984	−1.774	20.183
Canada	0.037	−13.176	11.294	1.176	−2.209	47.291	0.037	−1.882	2.756	0.518	−0.078	3.468	0.037	−13.176	11.294	1.399	−1.984	34.982
Chile	−0.024	−15.216	7.759	1.446	−2.073	24.587	−0.021	−4.716	7.759	0.892	1.404	20.488	−0.025	−15.216	7.594	1.660	−2.181	19.995
China	0.032	−8.039	5.554	1.009	−0.651	8.607	0.024	−5.745	5.449	1.041	−0.107	6.124	0.036	−8.039	5.554	0.993	−0.968	10.076
Czechia	0.023	−8.160	7.369	0.963	−1.400	18.938	0.001	−2.079	1.618	0.572	−0.666	1.699	0.035	−8.160	7.369	1.112	−1.353	15.575
Egypt	−0.022	−9.808	5.753	1.132	−1.467	13.316	0.020	−5.464	3.256	0.978	−0.699	5.146	−0.043	−9.808	5.753	1.203	−1.635	14.402
France	0.031	−13.098	8.056	1.255	−1.561	20.467	0.054	−3.635	2.688	0.818	−0.737	3.074	0.020	−13.098	8.056	1.428	−1.515	17.773
Germany	0.035	−13.055	10.414	1.278	−1.142	20.381	0.050	−3.537	3.314	0.860	−0.437	2.689	0.027	−13.055	10.414	1.446	−1.134	18.154
India	0.059	−14.102	8.595	1.252	−1.872	27.227	0.041	−2.084	5.186	0.795	1.120	6.709	0.068	−14.102	8.595	1.431	−2.006	23.355
Indonesia	0.011	−6.805	9.704	1.036	0.068	14.200	0.006	−2.628	1.916	0.639	−0.163	1.214	0.013	−6.805	9.704	1.190	0.077	11.788
Iraq	0.016	−3.844	6.885	0.742	1.991	19.870	−0.014	−2.254	2.095	0.541	0.030	3.036	0.032	−3.844	6.885	0.825	2.147	18.789
Israel	0.030	−6.857	7.228	1.070	−0.774	10.114	0.022	−4.839	2.008	0.750	−1.438	6.891	0.033	−6.857	7.228	1.202	−0.652	8.694
Italy	0.038	−18.541	8.549	1.383	−3.275	43.571	0.071	−3.608	3.311	0.912	−0.383	2.078	0.021	−18.541	8.549	1.570	−3.321	38.892
Mexico	0.022	−6.638	4.744	1.045	−0.502	4.994	0.008	−4.263	2.927	0.798	−0.202	3.406	0.029	−6.638	4.744	1.151	−0.543	4.448
Morocco	0.019	−9.232	5.305	0.751	−2.983	41.774	0.014	−1.642	1.955	0.439	0.214	3.263	0.022	−9.232	5.305	0.869	−2.936	34.640
Nepal	0.086	−6.226	5.885	1.222	0.005	6.843	−0.019	−2.130	2.725	0.703	0.803	2.127	0.140	−6.226	5.885	1.413	−0.131	5.178
Netherlands	0.048	−11.376	8.591	1.125	−1.391	18.903	0.044	−3.374	2.386	0.737	−0.889	3.356	0.050	−11.376	8.591	1.279	−1.346	16.453
Pakistan	0.009	−7.102	4.684	1.101	−0.794	6.750	−0.033	−3.353	3.511	1.021	0.160	1.289	0.031	−7.102	4.684	1.141	−1.151	8.495
Philippines	0.002	−14.322	7.172	1.329	−1.962	22.834	0.036	−2.995	2.785	0.838	0.164	1.537	−0.016	−14.322	7.172	1.520	−1.971	19.496
Poland	0.031	−13.579	5.705	1.195	−1.867	22.300	0.020	−2.515	2.651	0.783	0.051	1.415	0.037	−13.579	5.705	1.359	−1.933	19.653
Portugal	0.017	−10.267	7.532	1.099	−1.295	16.636	0.022	−2.215	2.783	0.734	−0.181	0.976	0.014	−10.267	7.532	1.245	−1.322	14.740
Romania	0.044	−11.892	6.817	1.107	−2.486	29.536	0.039	−11.892	6.817	1.149	−3.217	41.461	0.046	−10.075	5.973	1.087	−2.032	21.637
Russia	0.063	−8.646	7.435	1.039	−0.971	16.504	0.068	−2.018	2.395	0.681	0.158	0.782	0.061	−8.646	7.435	1.181	−1.010	14.422
Saudi Arabia	0.048	−8.685	6.831	0.961	−2.021	21.565	0.011	−3.615	2.123	0.796	−0.463	1.552	0.067	−8.685	6.831	1.035	−2.358	23.910
South Africa	0.030	−10.450	9.057	1.253	−0.738	14.588	0.026	−3.078	3.077	0.840	−0.408	1.827	0.032	−10.450	9.057	1.419	−0.727	12.859
Spain	−0.002	−15.151	8.225	1.309	−1.781	25.910	0.007	−2.807	2.485	0.757	−0.413	1.558	−0.006	−15.151	8.225	1.516	−1.700	21.110
Sweden	0.048	−11.173	6.849	1.158	−1.191	13.114	0.051	−2.902	2.953	0.864	−0.432	1.260	0.046	−11.173	6.849	1.283	−1.253	12.694
Switzerland	0.033	−10.134	6.780	0.951	−1.509	20.914	0.047	−3.181	2.811	0.702	−0.474	3.118	0.026	−10.134	6.780	1.057	−1.582	20.089
Turkey	0.051	−10.307	5.810	1.284	−1.387	9.866	0.038	−5.840	4.043	1.190	−0.411	3.420	0.057	−10.307	5.810	1.331	−1.736	11.795
UK	0.023	−9.820	8.039	1.152	−0.889	15.644	0.030	−2.875	4.105	0.695	0.220	4.811	0.019	−9.820	8.039	1.326	−0.890	12.709
USA	0.056	−12.765	8.968	1.308	−1.135	22.054	0.042	−3.290	4.840	0.867	−0.215	5.228	0.062	−12.765	8.968	1.484	−1.161	19.364
Average	0.031	−11.968	7.764	1.210	−1.406	22.305	0.023	−4.762	3.437	0.884	−0.449	7.068	0.036	−11.000	7.736	1.334	−1.308	17.709

Note: Min, Max, SD, Skew, and Kurt are, respectively, minimum, maximum, standard deviation, skewness, and kurtosis of the log-returns of the market indexes of countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020. Average refers to the average value of descriptive statistics of log-returns.

Fig. 1.

Historical evolution of the market indexes prices for November 17, 2018, to October 25, 2021. The dotted grey line indicates November 17, 2019, and the dotted red line indicates March 9, 2020. Note: This figure illustrates the historical evolution of the closing prices of market indexes of countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The standard deviation of log-returns increased from sub-sample 1 to sub-sample 2 for all countries except Argentina, China, and Romania. This increase is illustrated in Fig. 2, which shows that the variability peaked during March 2020 and kept at high levels until the end of the sample. As mentioned above, March 2020 also presents the largest drop for most indexes. In this way, we can observe that despite the pandemic having reached countries at different periods,11Fig. 1 shows that the reaction of stock markets to COVID-19 took place in a similar or very close period. We also note a delay between the first COVID case diagnosed on November 17, 2020, and the market reaction. Ashraf (2020) points out that the decline in market returns occurred mainly as the number of confirmed cases of the disease increased, which happened around March 2020. In this period, the World Health Organization (WHO) officially declared the COVID-19 outbreak to be a global pandemic (WHO, World Health Organization, 2020), which may also justify the market’s reaction to the virus. Vasileiou et al. (2021) identify a period of a sharp decline in the stock market when COVID-19 was declared a pandemic.

Fig. 2.

Historical evolution of log-returns of the market indexes (in %). The period refers from November 17, 2018, to October 25, 2021. The dotted grey line indicates November 17, 2019, and the dotted red line indicates March 9, 2020. Note: This figure illustrates the historical evolution of the log-returns of the market indexes (in %) of countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020. We obtain log-returns considering the closing prices of each market index.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The descriptive statistics of minimum returns of the indexes also reflect the adverse shock around March 2020. Except for Argentina, Iraq, Romania, and Turkey, all countries had their minimum returns in March 2020. More specifically, the week of March 9, 2020, concentrates on the minimum returns of 21 countries. The strong recovery that took place after the shock caused the maximum returns of the countries to be registered within sub-sample 2, except for Chile and Romania.12 In Section 4.1, we mention some particularities of these countries that might account for some of their descriptive statistics’ dissonance with the other countries. Also, comparing the range between the minimum and maximum returns during the sub-samples helps characterize the increased variability during the pandemic. The average (across countries) of the minimum and maximum returns during sub-sample 1 was −4.76% and 3.44%, respectively. In sub-sample 2, this gap became more expansive, the average minimum return was −11.00%, and the average maximum return was 7.74%.

The skewness is negative for most countries in both sub-samples, being more predominantly negative in sub-sample 2. The negative asymmetry indicates values concentrated in the left tail of the density. By its definition, the skewness is non-linearly affected by the observations. This finding explains why the effect of the extreme losses around March 9, 2020, was stronger than the effect of the trend of high positive returns that followed the shock. Notwithstanding, the recovery after the shock presumably caused the right tail in sub-sample 2 to become heavier than in sub-sample 1. In addition to that, the kurtosis also increased from sub-sample 1 to sub-sample 2. This increase indicates that the distribution tails become heavier than sub-sample 1.

3.2. Aggregate indexes

We use the returns of the market indexes to generate three aggregate indexes. These aggregate indexes are constructed through three different aggregation functions, which provide concise pictures of how the financial markets were exposed to the COVID-19 pandemic. Our three aggregation functions differ in how they assign weights to the individual indexes. For the definition of the aggregate indexes, we adopt the following notation: the return of the market index $i\in I$ at $t\in \mathcal{T}$ is denoted as $X_{t,i}$ and $X_t=(X_{t,1},X_{t,2},\dots ,X_{t,n})$; the elements in $C≔\{c_1,\dots ,c_n\}$ and $D≔\{d_1,\dots ,d_n\}$ represent the absolute values of COVID-19 cases and deaths, respectively, recorded in each country until November 11, 2020 (these values are reported in Table 1). The first aggregate index, which we use as a benchmark, is the naive portfolio, which weights the market indexes equally:

$${\Lambda }_N\left(X_t\right)≔\sum _{i=1}^n{X}_{t,i}\times \frac{1}{n},$$

where $n$ refers to the number of countries, i.e., 35 countries.

The second and third procedures use information about the COVID-19 cases and deaths toll in each country. The second procedure weighs the individual markets by the percentage of coronavirus cases in the respective country:

$${\Lambda }_C\left(X_t\right)≔\sum _{i=1}^n{X}_{t,i}\times c_i^{\ast },$$

where $c_i^{\ast }=\frac{c_i}{{\sum }_{i=1}^n{c}_i}$, $c_i\in C$, is the country $i$’s percentage of the total COVID-19 cases until November 11, 2020 (among the countries in our sample). The following function weights the return of each country $i\in \mathcal{I}$ with $i$’s percentage of the total deaths by COVID-19 until November 11, 2020 (among the countries in our sample).

$${\Lambda }_D\left(X_t\right)≔\sum _{i=1}^n{X}_{t,i}\times d_i^{\ast },$$

where $d_i^{\ast }=\frac{d_i}{{\sum }_{i=1}^n{d}_i}$, $d_i\in D$, is the percentage of COVID-19 deaths for each $i\in \mathcal{I}$. As can be seen in Table 1, the values of $d_i^{\ast }$ and $c_i^{\ast }$ differ, which justifies considering both weightings instead of one.13 As mentioned in the introduction, we consider both aggregation functions because of the evidence that the market reacted negatively to the number of cases and deaths caused by COVID-1914 . See, for instance,  Al-Awadhi et al., 2020, Andrieś et al., 2021, Ashraf, 2020 and Xu (2021). We do not include financial variables for weighting, such as trading volume, so we do not give more weight to countries with high volume and low risk.

The aggregated indexes were also divided into two sub-samples, one containing data before the first coronavirus case and the other with data during the pandemic. For the full sample and sub-samples, we quantify descriptive statistics in Table 3. We should emphasize that the descriptive statistics of the aggregated indexes provide information that could not be extracted by analyzing the descriptive statistics of the individual indexes. For instance, looking at Table 2, one could conclude nothing about what the system looked like in its worst period. In particular, one would not obtain a realistic image of the system’s worst period by averaging the countries’ minimum returns (last line, second column of Table 2). This follows because of the fact that

$$min\left\{{\Lambda }_{\theta }\left(X_t\right):t\in \mathcal{T}\right\}=min\left\{\sum _{i=1}^n{\theta }_i{X}_{i,t}:t\in \mathcal{T}\right\}\ge \sum _{i=1}^n{\theta }_{i}min\left\{X_{i,t}:t\in \mathcal{T}\right\},$$ (1)

where $\theta \in \left\{N,C,D\right\}$ represents the aggregation function and ${\theta }_i\in \left\{n^{-1},c_i^{\ast },d_i^{\ast }\right\}$ is the country, $i$’s weight. The left-hand side of Eq. (1) stands for the worst return of the system, as represented by an aggregation function ${\Lambda }_{\theta }\left(\cdot \right)$. The right-hand side stands for the average of the countries’ worst returns. The above equation is an example of how aggregation functions can be useful in assessing the performance of a system composed of several financial entities. The next equation further illustrates this argument, this time considering the best period of the system, as represented by the naive aggregation function.

$$max\left\{{\Lambda }_N\left(X_t\right):t\in \mathcal{T}\right\}=max\left\{\frac{1}{n}\sum _{i=1}^n{X}_{i,t}:t\in \mathcal{T}\right\}\le \frac{1}{n}\sum _{i=1}^{n}max\left\{X_{i,t}:t\in \mathcal{T}\right\}$$ (2)

To illustrate how large the gap in the previous inequality can be, we note that $max\left\{{\Lambda }_N\left(X_t\right):t\in \mathcal{T}\right\}=4$.788% in sub-sample 2, which is lower than $max\left\{X_{i,t}:t\in \mathcal{T}\right\}$ for almost all countries, whose average in sub-sample 2 equals 7.736% (see Table 2).

Table 3.

Descriptive statistics of the aggregated indexes. The full sample period refers from November 17, 2018, to October 25, 2021. Sub-sample 1 comprehends data from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends data from November 17, 2019, to October 25, 2021.

	Full sample
Indexes	Mean	Min	Max	SD	Skew	Kurt
${\Lambda }_C$	0.042	−10.343	6.156	0.952	−2.984	34.305
${\Lambda }_D$	0.038	−10.493	6.449	0.974	−2.776	32.518
${\Lambda }_N$	0.031	−8.744	4.788	0.759	−3.277	35.511
Average	0.037	−9.860	5.798	0.895	−3.012	34.111
	Sub-sample 1
Indexes	Mean	Min	Max	SD	Skew	Kurt
${\Lambda }_C$	0.037	−2.063	1.739	0.524	−0.675	1.914
${\Lambda }_D$	0.036	−2.364	1.800	0.547	−0.762	2.317
${\Lambda }_N$	0.023	−1.702	1.546	0.432	−0.656	2.269
Average	0.032	−2.043	1.695	0.501	−0.698	2.167
	Sub-sample 2
Indexes	Mean	Min	Max	SD	Skew	Kurt
${\Lambda }_C$	0.045	−10.343	6.156	1.110	−2.819	27.487
${\Lambda }_D$	0.040	−10.493	6.449	1.132	−2.630	26.269
${\Lambda }_N$	0.036	−8.744	4.788	0.881	−3.141	28.998
Average	0.040	−9.860	5.798	1.041	−2.863	27.585

Note: Min, Max, SD, Skew, and Kurt are, respectively, minimum, maximum, standard deviation, skewness, and kurtosis of the aggregated indexes. ${\Lambda }_N$, ${\Lambda }_C$ and ${\Lambda }_D$ are the aggregated indexes. ${\Lambda }_N$ is the naive aggregation (equally weighted); ${\Lambda }_C$ is based on the number of cases (weights returns by the percentage of COVID-19 cases); and ${\Lambda }_D$ is based on the number of deaths (weights returns by the percentage of COVID-19 deaths). Aggregate indexes are built using log-returns from 35 countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020. Average refers to the average value of descriptive statistics of aggregated indexes.

The point of inequalities (1), (2) is to establish the notion that the aggregated indexes are diversified portfolios and, as such, their minimum and maximum returns are “moderate”. Moreover, since the aggregated indexes are diversified portfolios, their standard deviations are also expected to be smaller than those of the individual markets. Formally, for any weights ${\theta }_i\in \left\{n^{-1},c_i^{\ast },d_i^{\ast }\right\}$ we have

$$SD\left(\sum _{i=1}^n{\theta }_i{X}_i\right)\le \sum _{i=1}^n{\theta }_{i}SD\left(X_i\right),$$ (3)

where $SD\left(\cdot \right)$ stands for the standard deviation and $X_i$ represents the theoretical counter-part of the return of the country $i$’s market index (see Section 2 for details). The difference between the left and right-hand sides of inequality (3) can be very substantial. For instance, the standard deviation of the naive portfolio in sub-sample 1, which equals 0.432, is smaller than the standard deviation of all the individual markets in the same sub-sample, whose average equals 0.884 (see Table 2). Last, we have the following equality between the mean return of the aggregate indexes and the weighted mean returns of the individual indexes

$$\frac{1}{T}\sum _{t=1}^T{\Lambda }_{\theta }\left(X_t\right)=\frac{1}{T}\sum _{t=1}^T\left(\sum _{i=1}^n{\theta }_i{X}_{i,t}\right)=\sum _{i=1}^n{\theta }_i\left(\frac{1}{T}\sum _{t=1}^T{X}_{i,t}\right)$$ (4)

which holds for $\theta \in \{N,C,D\}$ and ${\theta }_i\in \left\{n^{-1},c_i^{\ast },d_i^{\ast }\right\}$. Notice that Eq. (4) provides an opportunity to check the consistency of our data by comparing the mean of ${\Lambda }_N$ in each sample (Table 3) with the average of the mean returns of the individual indexes (last line of Table 2).

The above inequalities and equality establish a guide to compare the descriptive statistics of the aggregated indexes with the mean of the respective statistics among the individual indexes. Let us now focus on how the aggregated indexes changed between the sub-samples. Some patterns found for the individual indexes also hold for the aggregated indexes. For instance, the mean of the aggregated indexes is close to zero in all samples. This result is a consequence of the mean of the individual indexes being close to zero15 and of Eq. (4). We applied the bilateral (and right one-tailed) Mann–Whitney test to check whether the location parameter of sub-sample 2 is different than (higher than, respectively) that of sub-sample 1. The p-values of the tests are in Appendix. As expected (given the results for the market indexes), the tests do not generally reject the null hypothesis, indicating that the median returns did not change significantly between the sub-samples. This result reflects the characteristics observed in daily returns (close to zero) and a reversal of returns, both individual and aggregated indexes, to a period of greater stability. However, it is worth highlighting, as seen in Figs. 2 (log-returns of the market indexes) and 3 (aggregated indexes) that the reduction in variability was not immediate after the shock.

Fig. 3.

Historical evolution of the aggregated indexes for November 17, 2018, to October 25, 2021. The aggregated indexes were obtained from market index returns. The dotted grey line indicates November 17, 2019, and the dotted red line indicates March 9, 2020. Note: ${\Lambda }_N$, ${\Lambda }_C$ and ${\Lambda }_D$ are the aggregated indexes. ${\Lambda }_N$ is the naive aggregation (equally weighted); ${\Lambda }_C$ is based on the number of cases (weights returns by the percentage of COVID-19 cases); and ${\Lambda }_D$ is based on the number of deaths (weights returns by the percentage of COVID-19 deaths. Aggregate indexes are built using log-returns (in %) from market indexes of 35 countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

A portion of the market’s recovery after the shock can be explained by the expansionary policies carried by central banks of global economies. The countries have expanded the monetary base through different mechanisms and at different levels. In this respect, Cantú et al. (2021) provides a comprehensive dataset on the monetary measures adopted around the world. As a consequence of the inherent heterogeneity across countries and the monetary policies they adopted, the effectiveness of these measures also varied. Several works report a significant positive effect of the monetary expansions in softening the drop of economic activity and stock prices, as well as in decreasing the risk in the financial markets (Aguilar et al., 2020, Cortes et al., 2021, Feldkircher et al., 2021). However, other authors have pointed out that expansionary policies had very limited effects in some cases (Apergis, 2021, Pinshi et al., 2020, Rubbaniy et al., 2021, Wei and Han, 2021). In this regard, an agenda for future research is to quantify the influence of these policies on the recovery of the financial system as a whole, which can be measured, for instance, by the aggregated indexes we proposed. As argued in Khalfaoui, Nammouri, Labidi, and Jabeur (2021), sentiments also affect the performance of the markets. In particular, market optimism regarding the development and approval of vaccines – which would stimulate economic growth and the return to normality – might also have played a role in the market’s recovery. In this line, Khalfaoui et al. (2021) showed that the COVID-19 vaccination had a strong and significant positive influence on S&P 500 returns.16

As a consequence of this dynamic of abrupt shock and posterior recovery, the standard deviation of the aggregated indexes increased substantially between the sub-samples, which is illustrated in Fig. 3. The average standard deviation of all aggregated indexes increased more than 100% between the sub-samples. Fig. 3 suggests that this happened because of the shock in the week of March 9 and the fact that the variability did not immediately return to the levels before the shock. The greater variability during sub-sample 2 is also indicated by the fact that all aggregated indexes’ minimum and maximum values are registered in sub-sample 2. All aggregated indexes attained their minimum on March 12, 2020 (the day after WHO updated the classification of the coronavirus crisis as a pandemic (Zhang et al., 2020)) and their maximum on March 24, 2020.17 This consistency indicates that the methodology of aggregating indexes is robust to the weights used.

The descriptive statistics of the aggregated indexes also vary substantially between sub-samples 1 and 2. For instance, the minimum returns of ${\Lambda }_N,{\Lambda }_C$, and ${\Lambda }_D$ in sub-sample 1 range from approximately -2.36% to −1.7%, depending on the index considered, while in sub-sample 2 they range between −10.5% to −8.7%. The maximum returns of the aggregate indexes range from 1.54% to 1.80% in sub-sample 1 and from 4.79% to 6.45% in sub-sample 2. The skewness is negative for all aggregated indexes and samples and becomes even more negative in sub-sample 2. In sub-sample 1, the skewness ranges from −0.76 to −0.65, while in sub-sample 2, it goes from −3.14 to −2.63. The kurtosis of the indexes also increased considerably between the sub-samples. It ranges from 1.9 to 2.3 in sub-sample 1 and 26.3 to 29 in sub-sample 2. Since the aggregated indexes are weighted means, such an increase in the prevalence of extreme values indicates that the individual indexes’ returns moved in synchronicity during sub-sample 2. This is an indication that the aggregation functions we considered were able to reflect the strong dependence structure between the returns in sub-sample 2 (which can be deduced by Fig. 1).18

3.3. Models and risk estimation procedures

After the descriptive analysis of the data, we proceed to risk estimation. For both single-index and systemic risk, we consider VaR, EL, MSD, ES, EVaR, and ML as functional bases to quantify the risk estimates considering data from the in-sample period. We consider these functionals because they are common in risk forecasting literature and fit the general approach for measuring systemic risk used in this study. For risk estimation, we consider a semi-parametric approach known as Filtered Historical Simulation (FHS) (Barone-Adesi et al., 1998, Barone-Adesi et al., 1999). Our study considered the FHS because empirical evidence points to good results from using this approach in predicting risk measures (Christoffersen and Gonçalves, 2005, Giannopoulos and Tunaru, 2005). Besides that, this approach is quite flexible in the sense that it can handle individual stocks and portfolios (Giannopoulos & Tunaru, 2005). Consider that $Y$ has a fully parametric location-scale specification based on the expectation, dispersion, and random component, which is represented by $Y_t={\mu }_t+{\sigma }_t{z}_t$, where ${\mu }_t$ and ${\sigma }_t$ are the conditional mean and the conditional standard deviation, respectively, and $z_t$ is a white noise process, which can assume many probability distributions ($F$). The main idea of this method is to construct the returns series through the filtered residuals $Z_T≔{\left\{z_t\right\}}_{t=1}^T$ using the conditional mean and volatility predicted for the period $t$ for which risk measures are estimated.

In the first step, we extract from historical data the mean and conditional deviation using an Autoregressive (AR)-Generalized Autoregressive Conditional Heteroskedasticity (GARCH),19 which can be described as:

$$Y_t={\varphi }_0+\sum _{i=1}^p{\varphi }_i{Y}_{t-i}+{ϵ}_t={\mu }_t+{ϵ}_t,$$

$${ϵ}_t={\sigma }_t{z}_t,z_t\sim i.i.d.F\left(\mathit{\theta }\right),$$

$${\sigma }_t^2=a_0+\sum _{j=1}^q{a}_j{ϵ}_{t-j}^2+\sum _{k=1}^s{b}_k{\sigma }_{t-k}^2,$$ (5)

where $p$ is the order of the autoregressive component, ${\varphi }_i$ (for $i=0,1,\dots ,p$) are the parameters of the autoregressive model, ${ϵ}_t$ is the error term, $z_t$ is a white noise process with distribution $F\left(\mathit{\theta }\right)$, where $\mathit{\theta }$ is a vector of parameters of the distribution, including zero mean and unit variance in addition to additional parameters that vary as the distribution. ${\mu }_t$ and ${\sigma }_t^2$ are the mean and variance conditional on past information, $q$ and $s$ are the orders of the GARCH model, and $a_j$ and $b_k$, for $j=0,1,\dots ,q$ and $k=0,1,\dots ,s$ are the parameters of the GARCH model ($a_0>0$, $a_j\ge 0$, $b_k\ge 0$).

Additionally to the AR-GARCH model, we consider asymmetric GARCH specifications to account for the leverage effect, which is a common characteristic in financial time series (Rodríguez & Ruiz, 2012), such as AR-Exponential GARCH (AR-EGARCH) and AR-Glosten–Jagannathan–Runkle GARCH (GJR-GARCH) model. The AR($p$)-EGARCH($q$, $s$) model can be described in this manner:

$$Y_t={\varphi }_0+\sum _{i=1}^p{\varphi }_i{Y}_{t-i}+{ϵ}_t={\mu }_t+{ϵ}_t,$$

$${ϵ}_t={\sigma }_t{z}_t,z_t\sim i.i.d.F\left(\mathit{\theta }\right),ln\left({\sigma }_t^2\right)=a_0+\sum _{j=1}^q{a}_{j}g\left({ϵ}_{t-j}\right)+\sum _{k=1}^s{b}_{k}ln\left({\sigma }_{t-k}^2\right),$$ (6)

where $ln$ is the natural logarithm, and $g\left(\cdot \right)$ is the impact curve given by:

$$g\left({ϵ}_t\right)=\gamma {ϵ}_t+\lambda (\left|{ϵ}_t\right|-E\left[\left|{ϵ}_t\right|\right]),$$

where $\gamma$ and $\lambda$ are real constants, and ${ϵ}_t$ and $\left|{ϵ}_t\right|-E\left[\left|{ϵ}_t\right|\right]$ are zero-mean independent and identically distributed (i.i.d.) sequences with continuous distributions. The volatility specification in terms of logarithmic transformation implies that there are no restrictions on the values of the parameters to guarantee the positivity of the variance. For more details, see Nelson (1991).

Further, AR($p$)-GJR($q$, $s$) model can be written in the following way:

$$Y_t={\varphi }_0+\sum _{i=1}^p{\varphi }_i{Y}_{t-i}+{ϵ}_t={\mu }_t+{ϵ}_t,$$

$${ϵ}_t={\sigma }_t{z}_t,z_t\sim i.i.d.F\left(\mathit{\theta }\right),$$

$${\sigma }_t^2=a_0+\sum _{j=1}^q(a_j+{\lambda }_j{I}_{t-j}){ϵ}_{t-j}+\sum _{k=1}^s{b}_k{\sigma }_{t-k}^2,$$ (7)

where $I_{t-j}$ is an indicator function that assumes 1 if ${ϵ}_{t-j}<0$ and takes zero otherwise. We have that $a_j\ge 0,b_k\ge 0,{\lambda }_j\ge 0$ and $a_0>0$. More details can be seen at Glosten, Jagannathan, and Runkle (1993).

For $F$, we assume normal, skewed normal, Student-$t$, skewed Student-$t$, generalized error, skewed generalized error, normal inverse Gaussian, and Johnson SU distributions. Besides the normal distribution, we select distributions that can capture asymmetry and heavy tail, which are common stylized facts in financial series (Cont, 2001). The parameters of the models were estimated through Quasi-Maximum Likelihood (QML). We choose the best specifications based on the Akaike information criterion (AIC). The Appendix presents the specifications for the individual market and aggregated indexes. The AR-EGARCH had the best fit for 28 out of 35 countries for the individual market indexes, while the student-t distribution was selected for 31 countries. The AR-EGARCH presents lower AIC for all aggregated indexes, with the generalized error distribution providing the best fit. To estimate the conditional mean, we use an AR(1). As stated by Garcia-Jorcano and Novales (2021), this specification is sufficient to produce serially uncorrelated innovations. We extract the standardized residuals ($Z_T$) independently and identically distributed for each estimated model. This step is necessary to form the returns series. We perform usual diagnostics under standardized residuals to assess if the information is appropriately filtered. The estimates from the AR-GARCH fits and diagnostics tests are available under request.

After model estimation, we use a non-parametric method, known as Historical Simulation (HS),20 to represent the distribution of the market log-returns and aggregated index. Therefore, the risk measures are quantified as follows:

$${\text{VaR}}_t^{\alpha }=-{\mu }_t+{\sigma }_t{\text{VaR}}^{\alpha }\left(Z_T\right),$$

$${\text{EL}}_t=-{\mu }_t+{\sigma }_t\text{EL}\left(Z_T\right),$$

$${\text{MSD}}_t=-{\mu }_t+{\sigma }_t\text{MSD}\left(Z_T\right),$$

$${\text{ES}}_t^{\alpha }=-{\mu }_t+{\sigma }_t{\text{ES}}^{\alpha }\left(Z_T\right),$$

$${\text{EVaR}}_t^{\alpha }=-{\mu }_t+{\sigma }_t{\text{EVaR}}^{\alpha }\left(Z_T\right),$$

$${\text{ML}}_t=-{\mu }_t+{\sigma }_t\text{ML}\left(Z_T\right)$$ (8)

where ${\mu }_t$ and ${\sigma }_t$ are, respectively, the mean and conditional standard deviation for the in-sample period obtained by the GARCH models (see the models’ specification in Appendix). ${\text{VaR}}^{\alpha }$, $\text{EL}$, $\text{MSD}$, ${\text{ES}}^{\alpha }$, ${\text{EVaR}}^{\alpha }$, and $\text{ML}$ are risk measures, which are quantified using HS approach. For MSD, we use $\beta =1$ to incorporate all the deviation. The values of $\alpha$ are 0.01, 0.025, and 0.00145 for VaR, ES, and EVaR, respectively. For VaR and ES, these levels are recommended by Basel Committee on Banking Supervision (2013). Regarding EVaR, Bellini and Di Bernardino (2017) show that $\alpha =0.00145$ makes the EVaR measurements closely comparable to the levels suggested by the Basel Committee for ES and VaR. We conduct all computational implementations using R programming language (R. Core Team, 2020), and the package for estimating the model parameters is $\mathtt{rugarch}$ (Ghalanos, 2019).

We compute mean, minimum, maximum, standard deviation, skewness, and kurtosis for descriptive analysis of the single-index and systemic risk. These statistics are provided for the full sample and sub-samples. Additionally, for both single-index and systemic risk, we applied the bilateral and right one-tailed Mann–Whitney test to assess whether there is a significant difference between the results of sub-sample 1 and 2. The description and discussion of these results are presented in the next section.

4. Empirical results

In this section, we describe the single-index and systemic risk estimation results.

4.1. Single-index risk results

The descriptive statistics of single-index risks, as measured by the risk measures in Eq. (8), are presented in Table 4, Table 5, Table 6, Table 7, Table 8, Table 9. Each table presents the average, minimum, maximum, standard deviation, asymmetry, and kurtosis for the single-index risk computed by one of the following measures VaR, EL, MSD, ES, EVaR, and ML for the thirty-five countries analyzed.

Table 4.

Descriptive statistics of the Value at Risk (VaR) forecasting computed from log-returns of the market indexes (in %). The full sample period refers from November 17, 2018, to October 25, 2021. Sub-sample 1 comprehends data from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends data from November 17, 2019, to October 25, 2021.

Countries	Full sample						Sub-sample 1						Sub-sample 2
	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt
Argentina	6.509	4.867	15.699	1.788	2.331	5.946	6.887	4.867	15.699	2.670	1.584	1.174	6.316	5.175	10.062	1.040	1.060	0.266
Austria	3.297	1.265	14.003	1.839	2.837	9.982	2.878	1.666	5.770	0.768	1.289	1.689	3.511	1.265	14.003	2.162	2.350	6.239
Bangladesh	1.875	0.162	8.240	0.868	2.672	13.235	1.720	0.162	3.097	0.482	−0.214	0.498	1.954	0.457	8.240	1.001	2.463	9.928
Belgium	3.431	1.438	14.633	2.013	2.540	7.930	3.005	1.606	5.172	0.851	0.574	−0.523	3.649	1.438	14.633	2.370	2.101	4.748
Brazil	4.184	1.762	23.067	2.420	4.536	25.677	3.532	2.114	5.740	0.803	0.500	−0.452	4.517	1.762	23.067	2.864	3.816	17.241
Canada	2.171	0.570	19.958	2.298	4.735	26.098	1.648	0.669	4.395	0.771	1.397	1.373	2.438	0.570	19.958	2.733	3.971	17.352
Chile	3.507	1.243	15.867	1.832	2.525	10.102	2.216	1.243	5.058	0.709	2.146	5.143	4.167	1.473	15.867	1.878	2.702	10.129
China	2.813	1.612	4.832	0.555	1.122	0.812	2.852	1.612	4.388	0.518	0.797	0.248	2.794	2.024	4.832	0.572	1.262	1.052
Czechia	2.486	1.214	14.266	1.419	3.387	15.533	1.958	1.214	3.717	0.424	1.186	1.869	2.756	1.229	14.266	1.655	2.775	10.160
Egypt	3.240	1.226	13.997	1.409	3.248	16.257	3.049	1.226	7.770	1.024	1.203	1.710	3.337	1.649	13.997	1.562	3.326	15.052
France	3.851	0.763	20.894	2.767	2.911	10.819	3.166	0.957	6.251	1.259	0.466	−0.660	4.202	0.763	20.894	3.226	2.491	7.117
Germany	3.691	1.714	14.790	1.947	2.801	9.240	3.127	1.887	4.888	0.688	0.389	−0.636	3.979	1.714	14.790	2.291	2.258	5.407
India	2.932	0.978	14.245	1.656	3.536	15.405	2.598	1.393	3.646	0.506	−0.330	−0.724	3.102	0.978	14.245	1.982	2.878	9.494
Indonesia	2.653	1.311	11.522	1.260	3.413	14.638	2.183	1.311	4.275	0.502	1.219	2.083	2.894	1.531	11.522	1.450	2.938	10.057
Iraq	1.527	1.065	6.418	0.436	3.926	28.404	1.481	1.102	2.497	0.255	1.133	1.471	1.551	1.065	6.418	0.502	3.696	23.067
Israel	3.345	1.359	12.039	1.874	2.396	6.326	2.706	1.586	5.862	0.818	1.279	1.353	3.671	1.359	12.039	2.157	1.960	3.657
Italy	3.753	0.781	14.366	2.046	1.959	4.697	2.814	0.781	5.134	0.925	−0.257	−0.238	4.233	1.532	14.366	2.283	1.640	2.708
Mexico	2.731	1.714	8.514	1.069	3.101	11.162	2.347	1.721	4.519	0.495	1.780	4.078	2.928	1.714	8.514	1.220	2.700	7.638
Morocco	1.773	0.911	9.720	1.044	4.698	26.653	1.497	0.948	2.426	0.298	0.589	−0.215	1.914	0.911	9.720	1.242	3.891	17.479
Nepal	3.095	1.004	9.568	1.180	1.370	3.058	2.570	1.004	4.401	0.534	0.870	0.921	3.364	1.248	9.568	1.322	0.958	1.692
Netherlands	3.225	1.281	16.414	1.915	3.150	13.687	2.685	1.281	5.542	0.993	0.888	−0.053	3.501	1.311	16.414	2.195	2.826	10.039
Pakistan	2.761	1.740	9.374	1.014	3.109	12.684	2.736	1.928	4.689	0.541	1.202	1.453	2.773	1.740	9.374	1.185	2.858	9.476
Philippines	3.324	2.314	9.435	1.050	2.876	9.516	2.739	2.314	3.335	0.209	0.285	−0.552	3.624	2.515	9.435	1.175	2.412	6.171
Poland	2.890	1.520	12.578	1.350	3.687	17.594	2.443	1.640	3.555	0.438	0.388	−0.670	3.119	1.520	12.578	1.583	3.066	11.575
Portugal	2.556	1.145	10.245	1.159	3.455	16.592	2.184	1.283	3.544	0.507	0.355	−0.776	2.746	1.145	10.245	1.339	3.019	11.729
Romania	2.711	1.404	16.817	1.531	3.421	16.229	2.783	1.539	16.817	1.570	3.844	23.028	2.674	1.404	13.012	1.511	3.170	12.005
Russia	2.498	1.614	9.611	1.137	3.891	16.865	2.093	1.620	2.891	0.268	0.682	0.042	2.706	1.614	9.611	1.338	3.169	10.519
Saudi Arabia	2.295	0.744	13.579	1.323	3.925	22.913	2.355	1.250	4.852	0.748	0.698	−0.156	2.264	0.744	13.579	1.536	3.796	18.778
South Africa	3.112	1.694	10.255	1.183	3.213	13.011	2.690	1.694	3.816	0.480	0.096	−0.722	3.328	1.828	10.255	1.364	2.762	8.734
Spain	3.470	1.638	15.503	1.958	3.148	12.458	2.678	1.638	4.390	0.649	0.814	−0.202	3.876	1.694	15.503	2.258	2.617	8.112
Sweden	3.052	2.001	9.493	1.231	2.890	9.029	2.684	2.003	3.835	0.382	0.539	−0.272	3.241	2.001	9.493	1.454	2.294	5.052
Switzerland	2.557	1.122	21.354	1.713	4.487	29.299	2.220	1.327	6.695	0.835	2.058	5.340	2.730	1.122	21.354	1.999	3.983	21.845
Turkey	4.091	2.502	9.849	0.842	2.173	8.691	4.104	2.638	7.510	0.695	0.842	2.082	4.084	2.502	9.849	0.909	2.429	9.195
UK	2.670	0.843	14.637	1.788	3.353	12.940	2.070	1.140	3.933	0.579	1.060	0.920	2.976	0.843	14.637	2.094	2.746	8.045
USA	3.059	1.011	20.052	2.359	3.590	17.146	2.671	1.091	7.357	1.230	1.132	0.983	3.257	1.011	20.052	2.743	3.226	12.619
Average	3.061	1.415	13.309	1.522	3.155	14.018	2.668	1.527	5.356	0.726	0.928	1.446	3.262	1.510	13.040	1.720	2.732	9.839

Note: Min, Max, SD, Skew, and Kurt are minimum, maximum, standard deviation, skewness, and kurtosis of the single-index risk, respectively. We estimate the VaR from log-returns of the market indexes of countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020. We obtain VaR estimates using $\alpha =1\text{\%}$, i.e., VaR${}^{1\text{\%}}$ and for estimation, we consider Filtered Historical Simulation (FHS). Average refers to the average value of descriptive statistics of VaR risk estimates.

Table 5.

Descriptive statistics of the Expected Loss (EL) forecasting computed from log-returns of the market indexes (in %). The full sample period refers from November 17, 2018, to October 25, 2021. Sub-sample 1 comprehends data from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends data from November 17, 2019, to October 25, 2021.

Countries	Full sample						Sub-sample 1						Sub-sample 2
	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt
Argentina	−0.094	−2.318	0.426	0.139	−4.558	71.681	−0.096	−2.318	0.426	0.173	−6.683	85.851	−0.093	−0.828	0.399	0.119	−0.564	6.403
Austria	−0.027	−0.044	0.059	0.013	2.951	11.432	−0.030	−0.040	−0.010	0.005	1.155	1.554	−0.026	−0.044	0.059	0.015	2.465	7.367
Bangladesh	−0.046	−0.201	−0.004	0.021	−2.672	13.235	−0.042	−0.076	−0.004	0.012	0.214	0.498	−0.048	−0.201	−0.011	0.024	−2.463	9.928
Belgium	−0.001	−0.052	0.245	0.038	2.604	9.116	−0.008	−0.051	0.051	0.017	0.523	0.228	0.003	−0.052	0.245	0.044	2.206	5.827
Brazil	−0.034	−1.186	1.213	0.140	−0.255	21.191	−0.038	−0.360	0.229	0.085	−0.255	1.614	−0.032	−1.186	1.213	0.161	−0.263	17.722
Canada	−0.028	−0.051	0.227	0.033	4.683	25.556	−0.036	−0.050	0.003	0.011	1.350	1.150	−0.024	−0.051	0.227	0.039	3.917	16.922
Chile	0.025	−0.392	0.839	0.077	2.177	25.097	0.024	−0.105	0.272	0.042	1.025	5.443	0.025	−0.392	0.839	0.090	2.002	19.581
China	−0.028	−0.245	0.126	0.028	−0.432	8.129	−0.028	−0.183	0.123	0.029	0.059	5.998	−0.028	−0.245	0.126	0.027	−0.723	9.380
Czechia	−0.026	−0.060	0.126	0.015	4.146	29.189	−0.030	−0.045	0.001	0.007	1.399	2.722	−0.024	−0.060	0.126	0.017	3.678	21.927
Egypt	0.017	−0.557	1.097	0.122	1.767	14.392	0.012	−0.318	0.607	0.105	0.851	5.387	0.020	−0.557	1.097	0.130	1.961	15.503
France	−0.007	−0.057	0.288	0.047	2.928	11.018	−0.019	−0.055	0.035	0.022	0.439	−0.705	−0.001	−0.057	0.288	0.055	2.505	7.264
Germany	−0.012	−0.549	0.332	0.050	−2.100	22.261	−0.008	−0.141	0.109	0.033	−0.516	2.669	−0.014	−0.549	0.332	0.056	−2.053	19.402
India	−0.063	−0.185	0.213	0.023	3.224	31.155	−0.064	−0.152	−0.026	0.014	−1.085	6.194	−0.062	−0.185	0.213	0.026	3.236	25.839
Indonesia	−0.014	−0.150	0.255	0.025	1.569	18.822	−0.017	−0.074	0.029	0.015	0.204	1.113	−0.013	−0.150	0.255	0.029	1.477	15.749
Iraq	−0.009	−0.358	0.318	0.049	0.517	10.646	−0.009	−0.139	0.165	0.039	0.880	3.151	−0.009	−0.358	0.318	0.053	0.436	10.604
Israel	−0.038	−0.135	−0.015	0.021	−2.396	6.326	−0.030	−0.066	−0.018	0.009	−1.279	1.353	−0.041	−0.135	−0.015	0.024	−1.960	3.657
Italy	−0.021	−0.274	0.206	0.032	0.927	11.608	−0.030	−0.097	0.040	0.019	0.114	0.862	−0.017	−0.274	0.206	0.036	0.707	10.143
Mexico	−0.017	−0.217	0.220	0.039	0.091	4.474	−0.015	−0.134	0.141	0.030	0.033	3.241	−0.018	−0.217	0.220	0.043	0.138	3.991
Morocco	−0.043	−0.257	0.203	0.024	−0.168	29.725	−0.040	−0.110	0.009	0.015	−0.703	3.684	−0.044	−0.257	0.203	0.028	−0.029	24.874
Nepal	−0.075	−0.231	−0.024	0.028	−1.370	3.058	−0.062	−0.106	−0.024	0.013	−0.870	0.921	−0.081	−0.231	−0.030	0.032	−0.958	1.692
Netherlands	−0.029	−0.235	0.344	0.040	2.164	14.409	−0.036	−0.124	0.055	0.024	0.223	1.663	−0.025	−0.235	0.344	0.045	2.019	11.708
Pakistan	−0.006	−0.101	0.192	0.027	1.695	10.362	−0.005	−0.082	0.077	0.024	0.158	1.176	−0.006	−0.101	0.192	0.028	2.178	12.629
Philippines	−0.001	−0.574	0.274	0.052	−2.115	23.820	0.001	−0.119	0.110	0.033	0.156	1.548	−0.002	−0.574	0.274	0.060	−2.111	20.306
Poland	−0.025	−0.623	0.204	0.051	−2.115	23.996	−0.025	−0.135	0.088	0.034	0.014	1.430	−0.025	−0.623	0.204	0.058	−2.168	21.078
Portugal	−0.017	−0.104	0.110	0.015	1.255	12.010	−0.019	−0.045	0.015	0.009	0.158	0.918	−0.016	−0.104	0.110	0.016	1.138	10.076
Romania	−0.049	−0.058	0.063	0.009	4.809	37.179	−0.048	−0.057	0.063	0.010	5.911	54.966	−0.049	−0.058	0.038	0.009	4.051	23.690
Russia	−0.064	−0.214	0.123	0.022	1.132	15.887	−0.067	−0.109	−0.021	0.013	0.215	0.847	−0.062	−0.214	0.123	0.025	0.997	13.236
Saudi Arabia	−0.062	−0.307	0.262	0.036	2.144	21.889	−0.061	−0.139	0.075	0.029	0.493	1.594	−0.063	−0.307	0.262	0.038	2.495	24.197
South Africa	−0.014	−0.419	0.447	0.056	0.728	14.523	−0.019	−0.147	0.125	0.037	−0.182	1.693	−0.011	−0.419	0.447	0.063	0.693	12.593
Spain	0.012	−0.330	0.377	0.046	1.649	14.475	0.002	−0.083	0.092	0.025	0.164	1.222	0.017	−0.330	0.377	0.053	1.391	11.203
Sweden	−0.038	−0.643	0.458	0.072	0.037	10.277	−0.043	−0.211	0.141	0.052	−0.269	1.205	−0.035	−0.643	0.458	0.080	0.020	9.646
Switzerland	−0.025	−0.067	0.272	0.032	3.735	23.531	−0.029	−0.065	0.063	0.020	1.369	3.065	−0.022	−0.067	0.272	0.036	3.591	19.815
Turkey	−0.059	−0.108	0.086	0.017	2.212	13.174	−0.059	−0.104	0.025	0.015	0.873	4.437	−0.059	−0.108	0.086	0.018	2.604	15.039
UK	−0.014	−0.042	0.086	0.015	3.330	13.639	−0.019	−0.039	−0.002	0.005	0.711	1.091	−0.012	−0.042	0.086	0.018	2.759	8.724
USA	−0.032	−0.525	0.713	0.082	2.740	23.579	−0.039	−0.210	0.313	0.052	1.158	7.500	−0.028	−0.525	0.713	0.093	2.620	19.974
Average	−0.027	−0.339	0.296	0.044	1.058	18.596	−0.029	−0.180	0.096	0.031	0.229	6.208	−0.026	−0.297	0.294	0.048	1.085	13.934

Note: Min, Max, SD, Skew, and Kurt are minimum, maximum, standard deviation, skewness, and kurtosis of the single-index risk, respectively. We estimate the EL from log-returns of the market indexes of countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020. For EL estimation, we consider Filtered Historical Simulation (FHS). Average refers to the average value of descriptive statistics of EL risk estimates.

Table 6.

Descriptive statistics of the Mean plus Semi-Deviation (MSD) forecasting computed from log-returns of the market indexes (in %). The full sample period refers from November 17, 2018, to October 25, 2021. Sub-sample 1 comprehends data from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends data from November 17, 2019, to October 25, 2021.

Countries	Full sample						Sub-sample 1						Sub-sample 2
	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt
Argentina	2.344	1.606	5.663	0.672	2.239	5.424	2.482	1.606	5.663	0.994	1.550	1.068	2.274	1.773	3.967	0.405	1.128	0.670
Austria	0.820	0.297	3.599	0.477	2.838	9.991	0.711	0.400	1.462	0.199	1.292	1.693	0.875	0.297	3.599	0.562	2.351	6.243
Bangladesh	0.470	0.041	2.065	0.217	2.672	13.235	0.431	0.041	0.776	0.121	−0.214	0.498	0.490	0.115	2.065	0.251	2.463	9.928
Belgium	0.841	0.325	3.733	0.519	2.536	7.887	0.731	0.369	1.276	0.219	0.569	−0.534	0.897	0.325	3.733	0.611	2.095	4.709
Brazil	0.989	0.393	5.952	0.606	4.580	26.880	0.828	0.408	1.544	0.208	0.544	−0.164	1.072	0.393	5.952	0.716	3.873	18.249
Canada	0.546	0.113	5.344	0.623	4.723	25.906	0.404	0.138	1.143	0.209	1.393	1.345	0.619	0.113	5.344	0.742	3.959	17.209
Chile	0.959	0.308	4.293	0.500	2.456	9.803	0.612	0.308	1.459	0.199	2.076	5.040	1.136	0.311	4.293	0.514	2.588	9.754
China	0.729	0.405	1.315	0.151	1.140	0.914	0.740	0.405	1.214	0.142	0.864	0.464	0.724	0.510	1.315	0.155	1.264	1.119
Czechia	0.577	0.262	3.519	0.350	3.414	15.951	0.447	0.265	0.892	0.106	1.231	1.996	0.643	0.262	3.519	0.408	2.804	10.496
Egypt	0.767	0.065	3.907	0.376	3.414	19.297	0.719	0.130	2.188	0.279	1.423	3.605	0.792	0.065	3.907	0.415	3.517	18.220
France	0.864	0.131	4.902	0.661	2.910	10.785	0.700	0.178	1.438	0.300	0.460	−0.672	0.948	0.131	4.902	0.770	2.489	7.085
Germany	0.823	0.389	3.296	0.429	2.793	9.169	0.699	0.420	1.067	0.152	0.378	−0.672	0.887	0.389	3.296	0.505	2.252	5.359
India	0.658	0.167	3.387	0.407	3.525	15.368	0.577	0.275	0.833	0.126	−0.342	−0.693	0.700	0.167	3.387	0.487	2.876	9.498
Indonesia	0.643	0.307	2.756	0.310	3.390	14.271	0.525	0.307	1.025	0.122	1.201	2.014	0.703	0.362	2.756	0.357	2.915	9.760
Iraq	0.431	0.288	1.614	0.130	2.930	14.778	0.418	0.298	0.812	0.084	1.289	2.206	0.437	0.288	1.614	0.147	2.814	12.422
Israel	0.696	0.283	2.504	0.390	2.396	6.326	0.563	0.330	1.219	0.170	1.279	1.353	0.764	0.283	2.504	0.449	1.960	3.657
Italy	0.858	0.150	3.149	0.490	1.940	4.538	0.632	0.150	1.190	0.222	−0.275	−0.236	0.974	0.328	3.149	0.547	1.621	2.571
Mexico	0.685	0.408	2.183	0.274	3.124	11.381	0.589	0.408	1.111	0.125	1.651	3.276	0.735	0.411	2.183	0.313	2.713	7.757
Morocco	0.362	0.175	2.322	0.230	4.777	27.753	0.302	0.183	0.506	0.065	0.596	−0.173	0.392	0.175	2.322	0.274	3.956	18.233
Nepal	0.681	0.221	2.105	0.260	1.370	3.058	0.565	0.221	0.969	0.117	0.870	0.921	0.740	0.275	2.105	0.291	0.958	1.692
Netherlands	0.728	0.260	3.721	0.458	3.125	13.287	0.596	0.260	1.236	0.236	0.852	−0.175	0.795	0.310	3.721	0.525	2.799	9.678
Pakistan	0.727	0.452	2.621	0.275	3.186	13.573	0.721	0.495	1.290	0.145	1.190	1.444	0.730	0.452	2.621	0.321	2.928	10.166
Philippines	0.837	0.576	2.467	0.264	2.886	9.858	0.691	0.576	0.896	0.058	0.454	−0.094	0.911	0.618	2.467	0.296	2.429	6.500
Poland	0.735	0.375	3.368	0.350	3.651	17.453	0.618	0.407	0.940	0.116	0.407	−0.575	0.794	0.375	3.368	0.409	3.044	11.543
Portugal	0.692	0.296	2.853	0.323	3.449	16.496	0.588	0.351	0.962	0.140	0.350	−0.794	0.745	0.296	2.853	0.373	3.010	11.638
Romania	0.682	0.331	4.502	0.412	3.438	16.452	0.702	0.368	4.502	0.423	3.875	23.466	0.673	0.331	3.475	0.406	3.177	12.078
Russia	0.594	0.355	2.482	0.299	3.908	17.122	0.488	0.355	0.707	0.072	0.652	0.096	0.649	0.361	2.482	0.352	3.187	10.722
Saudi Arabia	0.531	0.110	3.463	0.342	3.985	24.032	0.547	0.239	1.276	0.195	0.723	0.038	0.522	0.110	3.463	0.396	3.871	19.858
South Africa	0.796	0.412	2.855	0.318	3.259	13.575	0.683	0.412	1.041	0.129	0.132	−0.594	0.854	0.450	2.855	0.366	2.806	9.187
Spain	0.851	0.389	3.938	0.492	3.139	12.411	0.651	0.389	1.089	0.163	0.799	−0.246	0.954	0.403	3.938	0.566	2.611	8.086
Sweden	0.748	0.411	2.672	0.333	2.904	9.583	0.650	0.422	1.040	0.112	0.567	0.160	0.798	0.411	2.672	0.393	2.333	5.567
Switzerland	0.600	0.255	5.115	0.427	4.407	27.654	0.515	0.287	1.570	0.205	1.954	4.685	0.643	0.255	5.115	0.498	3.898	20.433
Turkey	0.866	0.481	2.249	0.198	2.207	9.115	0.869	0.521	1.694	0.164	0.868	2.286	0.864	0.481	2.249	0.214	2.469	9.666
UK	0.686	0.191	3.882	0.477	3.352	12.947	0.526	0.275	1.023	0.155	1.059	0.919	0.768	0.191	3.882	0.559	2.746	8.051
USA	0.813	0.227	5.609	0.667	3.564	16.823	0.702	0.253	2.040	0.347	1.125	1.033	0.870	0.227	5.609	0.775	3.198	12.342
Average	0.761	0.327	3.412	0.392	3.132	13.803	0.663	0.356	1.403	0.195	0.938	1.542	0.811	0.350	3.334	0.439	2.717	9.719

Note: Min, Max, SD, Skew, and Kurt are minimum, maximum, standard deviation, skewness, and kurtosis of the single-index risk, respectively. We estimate the MSD from log-returns of the market indexes of countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020. For MSD estimation, we consider Filtered Historical Simulation (FHS) and $\beta =1$. Average refers to the average value of descriptive statistics of MSD estimates.

Table 7.

Descriptive statistics of the Expected Shortfall (ES) forecasting computed from log-returns of the market indexes (in %). The full sample period refers from November 17, 2018, to October 25, 2021. Sub-sample 1 comprehends data from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends data from November 17, 2019, to October 25, 2021.

Countries	Full sample						Sub-sample 1						Sub-sample 2
	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt
Argentina	8.844	6.627	22.069	2.417	2.352	6.120	9.357	6.627	22.069	3.614	1.597	1.247	8.582	7.082	13.478	1.400	1.055	0.240
Austria	3.391	1.302	14.397	1.890	2.837	9.982	2.960	1.714	5.933	0.790	1.289	1.689	3.611	1.302	14.397	2.223	2.350	6.239
Bangladesh	1.960	0.170	8.615	0.907	2.672	13.235	1.798	0.170	3.238	0.504	−0.214	0.498	2.043	0.478	8.615	1.046	2.463	9.928
Belgium	3.538	1.484	15.082	2.074	2.540	7.931	3.099	1.657	5.333	0.877	0.574	−0.523	3.763	1.484	15.082	2.442	2.101	4.748
Brazil	4.217	1.776	23.248	2.440	4.536	25.676	3.560	2.131	5.784	0.810	0.500	−0.452	4.553	1.776	23.248	2.886	3.816	17.241
Canada	2.288	0.603	21.010	2.418	4.736	26.102	1.738	0.707	4.629	0.812	1.397	1.373	2.569	0.603	21.010	2.876	3.971	17.355
Chile	3.931	1.399	17.796	2.054	2.527	10.114	2.483	1.399	5.672	0.794	2.147	5.147	4.672	1.667	17.796	2.106	2.706	10.142
China	3.148	1.806	5.397	0.620	1.122	0.814	3.191	1.806	4.898	0.579	0.796	0.246	3.127	2.267	5.397	0.639	1.263	1.055
Czechia	2.517	1.230	14.440	1.436	3.387	15.531	1.982	1.230	3.763	0.429	1.186	1.869	2.790	1.245	14.440	1.675	2.775	10.159
Egypt	3.207	1.212	13.866	1.396	3.248	16.266	3.018	1.212	7.698	1.014	1.204	1.715	3.304	1.632	13.866	1.547	3.326	15.061
France	3.862	0.766	20.951	2.775	2.911	10.819	3.175	0.960	6.269	1.263	0.466	−0.660	4.214	0.766	20.951	3.235	2.491	7.117
Germany	3.583	1.664	14.349	1.890	2.801	9.238	3.036	1.834	4.744	0.668	0.389	−0.637	3.862	1.664	14.349	2.223	2.258	5.406
India	2.864	0.954	13.922	1.619	3.536	15.404	2.538	1.360	3.563	0.494	−0.330	−0.723	3.031	0.954	13.922	1.938	2.878	9.493
Indonesia	2.663	1.316	11.565	1.265	3.413	14.638	2.191	1.316	4.291	0.504	1.219	2.083	2.905	1.537	11.565	1.455	2.938	10.058
Iraq	1.808	1.264	7.647	0.515	4.003	29.467	1.753	1.307	2.967	0.300	1.140	1.495	1.836	1.264	7.647	0.594	3.764	23.884
Israel	3.198	1.300	11.512	1.792	2.396	6.326	2.588	1.517	5.606	0.782	1.279	1.353	3.511	1.300	11.512	2.063	1.960	3.657
Italy	3.737	0.777	14.304	2.037	1.959	4.697	2.802	0.777	5.112	0.921	−0.257	−0.238	4.215	1.525	14.304	2.273	1.640	2.708
Mexico	2.728	1.712	8.504	1.068	3.101	11.162	2.344	1.719	4.514	0.494	1.780	4.078	2.925	1.712	8.504	1.219	2.700	7.638
Morocco	1.711	0.879	9.400	1.008	4.699	26.658	1.445	0.915	2.340	0.288	0.588	−0.217	1.848	0.879	9.400	1.200	3.892	17.483
Nepal	3.174	1.029	9.811	1.210	1.370	3.058	2.635	1.029	4.513	0.547	0.870	0.921	3.450	1.279	9.811	1.356	0.958	1.692
Netherlands	3.155	1.253	16.057	1.875	3.150	13.683	2.626	1.253	5.422	0.972	0.887	−0.054	3.426	1.283	16.057	2.149	2.826	10.036
Pakistan	2.907	1.833	9.859	1.067	3.108	12.668	2.881	2.031	4.933	0.569	1.203	1.454	2.920	1.833	9.859	1.248	2.857	9.464
Philippines	3.555	2.474	10.081	1.123	2.876	9.517	2.929	2.474	3.561	0.223	0.283	−0.557	3.875	2.688	10.081	1.257	2.412	6.171
Poland	3.126	1.645	13.586	1.460	3.688	17.606	2.643	1.775	3.848	0.473	0.389	−0.667	3.373	1.645	13.586	1.711	3.067	11.583
Portugal	2.711	1.215	10.858	1.228	3.455	16.594	2.317	1.360	3.758	0.537	0.356	−0.775	2.912	1.215	10.858	1.419	3.019	11.731
Romania	3.094	1.606	19.142	1.742	3.421	16.219	3.176	1.760	19.142	1.787	3.842	23.008	3.052	1.606	14.812	1.719	3.170	12.002
Russia	2.611	1.688	10.032	1.186	3.891	16.861	2.188	1.695	3.020	0.280	0.682	0.042	2.827	1.688	10.032	1.396	3.169	10.517
Saudi Arabia	2.456	0.801	14.503	1.413	3.923	22.887	2.520	1.342	5.179	0.798	0.698	−0.160	2.423	0.801	14.503	1.640	3.795	18.754
South Africa	3.262	1.775	10.746	1.239	3.213	13.008	2.820	1.775	4.001	0.503	0.097	−0.722	3.488	1.915	10.746	1.429	2.761	8.733
Spain	3.507	1.655	15.667	1.979	3.148	12.459	2.706	1.655	4.436	0.656	0.814	−0.202	3.916	1.712	15.667	2.281	2.617	8.113
Sweden	3.241	2.127	10.052	1.305	2.890	9.021	2.850	2.132	4.063	0.405	0.539	−0.277	3.441	2.127	10.052	1.541	2.294	5.044
Switzerland	2.601	1.141	21.716	1.742	4.487	29.309	2.258	1.351	6.809	0.849	2.058	5.344	2.777	1.141	21.716	2.032	3.984	21.853
Turkey	4.068	2.488	9.794	0.838	2.173	8.691	4.081	2.623	7.469	0.691	0.842	2.082	4.061	2.488	9.794	0.904	2.429	9.196
UK	2.824	0.894	15.473	1.890	3.353	12.940	2.190	1.208	4.159	0.612	1.060	0.920	3.148	0.894	15.473	2.213	2.746	8.045
USA	3.513	1.170	23.081	2.702	3.592	17.181	3.070	1.260	8.459	1.410	1.133	0.988	3.740	1.170	23.081	3.142	3.228	12.648
Average	3.229	1.515	13.958	1.589	3.157	14.054	2.827	1.631	5.748	0.779	0.929	1.448	3.434	1.618	13.589	1.785	2.734	9.863

Note: Min, Max, SD, Skew, and Kurt are, respectively, minimum, maximum, standard deviation, skewness, and kurtosis of the single-index risk. We estimate the ES from log-returns of the market indexes of countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020. For ES estimation, we consider Filtered Historical Simulation (FHS) and $\alpha =2.5\text{\%}$, i.e., ES${}^{2.5\text{\%}}$. Average refers to the average value of descriptive statistics of ES estimates.

Table 8.

Descriptive statistics of the Expectile Value at Risk (EVaR) forecasting computed from log-returns of the market indexes (in %). The full sample period refers from November 17, 2018, to October 25, 2021. Sub-sample 1 comprehends data from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends data from November 17, 2019, to October 25, 2021.

Countries	Full sample						Sub-sample 1						Sub-sample 2
	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt
Argentina	23.056	17.345	60.844	6.252	2.395	6.514	24.387	17.345	60.844	9.364	1.626	1.428	22.375	18.615	34.580	3.600	1.050	0.229
Austria	3.658	1.406	15.519	2.037	2.837	9.982	3.194	1.850	6.397	0.851	1.289	1.689	3.895	1.406	15.519	2.396	2.350	6.239
Bangladesh	2.305	0.199	10.130	1.067	2.672	13.235	2.114	0.199	3.807	0.592	−0.214	0.498	2.402	0.562	10.130	1.230	2.463	9.928
Belgium	4.063	1.710	17.297	2.377	2.540	7.934	3.559	1.908	6.121	1.005	0.574	−0.522	4.320	1.710	17.297	2.799	2.101	4.751
Brazil	4.790	2.011	26.331	2.766	4.535	25.669	4.045	2.417	6.536	0.918	0.496	−0.458	5.170	2.011	26.331	3.273	3.816	17.235
Canada	2.690	0.717	24.627	2.833	4.736	26.112	2.046	0.839	5.433	0.951	1.397	1.375	3.020	0.717	24.627	3.369	3.971	17.363
Chile	5.119	1.834	23.191	2.677	2.532	10.137	3.230	1.834	7.395	1.033	2.149	5.153	6.085	2.208	23.191	2.744	2.713	10.166
China	4.815	2.770	8.210	0.944	1.124	0.823	4.880	2.770	7.435	0.881	0.792	0.241	4.782	3.477	8.210	0.974	1.266	1.068
Czechia	2.705	1.323	15.498	1.542	3.386	15.522	2.131	1.323	4.041	0.460	1.185	1.866	2.998	1.340	15.498	1.798	2.774	10.152
Egypt	4.103	1.593	17.556	1.774	3.237	16.083	3.862	1.593	9.719	1.288	1.194	1.629	4.226	2.102	17.556	1.966	3.314	14.879
France	4.403	0.880	23.845	3.156	2.912	10.820	3.621	1.100	7.140	1.436	0.466	−0.660	4.803	0.880	23.845	3.679	2.491	7.118
Germany	3.846	1.785	15.420	2.029	2.801	9.242	3.258	1.963	5.094	0.717	0.390	−0.635	4.146	1.785	15.420	2.387	2.258	5.409
India	3.299	1.108	15.997	1.857	3.536	15.407	2.924	1.573	4.100	0.567	−0.330	−0.724	3.490	1.108	15.997	2.224	2.878	9.494
Indonesia	3.216	1.591	13.974	1.526	3.415	14.664	2.647	1.591	5.183	0.609	1.221	2.088	3.507	1.858	13.974	1.756	2.940	10.079
Iraq	2.562	1.799	10.951	0.730	4.128	31.190	2.484	1.859	4.232	0.422	1.157	1.557	2.602	1.799	10.951	0.843	3.873	25.207
Israel	3.544	1.440	12.755	1.985	2.396	6.326	2.867	1.681	6.211	0.866	1.279	1.353	3.890	1.440	12.755	2.285	1.960	3.657
Italy	4.201	0.877	16.102	2.286	1.959	4.704	3.152	0.877	5.743	1.033	−0.256	−0.238	4.737	1.717	16.102	2.551	1.640	2.714
Mexico	2.842	1.784	8.860	1.112	3.101	11.159	2.442	1.792	4.704	0.515	1.782	4.089	3.047	1.784	8.860	1.270	2.699	7.637
Morocco	2.064	1.064	11.260	1.212	4.696	26.630	1.744	1.106	2.833	0.346	0.591	−0.205	2.228	1.064	11.260	1.442	3.890	17.465
Nepal	3.906	1.267	12.075	1.490	1.370	3.058	3.243	1.267	5.555	0.674	0.870	0.921	4.246	1.575	12.075	1.668	0.958	1.692
Netherlands	3.451	1.374	17.569	2.047	3.150	13.697	2.873	1.374	5.931	1.061	0.888	−0.050	3.746	1.401	17.569	2.346	2.827	10.048
Pakistan	3.077	1.940	10.421	1.129	3.106	12.652	3.049	2.150	5.216	0.602	1.203	1.456	3.091	1.940	10.421	1.320	2.855	9.452
Philippines	4.394	3.057	12.430	1.389	2.877	9.522	3.619	3.057	4.383	0.276	0.277	−0.568	4.790	3.317	12.430	1.554	2.412	6.176
Poland	3.669	1.933	15.905	1.713	3.690	17.628	3.102	2.085	4.520	0.555	0.391	−0.663	3.959	1.933	15.905	2.007	3.068	11.598
Portugal	3.048	1.368	12.194	1.379	3.455	16.598	2.605	1.528	4.224	0.603	0.356	−0.775	3.274	1.368	12.194	1.594	3.019	11.735
Romania	4.971	2.599	30.541	2.778	3.419	16.192	5.103	2.844	30.541	2.849	3.838	22.956	4.904	2.599	23.639	2.741	3.169	11.993
Russia	2.978	1.928	11.406	1.348	3.890	16.851	2.497	1.939	3.441	0.317	0.683	0.040	3.224	1.928	11.406	1.586	3.168	10.509
Saudi Arabia	3.093	1.026	18.154	1.768	3.919	22.812	3.173	1.707	6.487	0.998	0.697	−0.169	3.052	1.026	18.154	2.052	3.789	18.684
South Africa	3.683	2.004	12.126	1.397	3.212	13.002	3.185	2.004	4.524	0.568	0.098	−0.721	3.938	2.160	12.126	1.611	2.760	8.730
Spain	3.956	1.870	17.691	2.230	3.148	12.465	3.053	1.870	5.004	0.739	0.814	−0.199	4.417	1.933	17.691	2.571	2.618	8.118
Sweden	3.677	2.417	11.347	1.476	2.889	9.005	3.235	2.432	4.592	0.457	0.540	−0.286	3.903	2.417	11.347	1.742	2.293	5.031
Switzerland	2.891	1.269	24.118	1.933	4.490	29.364	2.510	1.505	7.567	0.943	2.062	5.365	3.085	1.269	24.118	2.254	3.987	21.901
Turkey	4.535	2.781	10.895	0.931	2.172	8.678	4.549	2.930	8.311	0.768	0.841	2.076	4.527	2.781	10.895	1.005	2.428	9.182
UK	3.113	0.989	17.038	2.081	3.353	12.940	2.415	1.334	4.583	0.673	1.060	0.920	3.469	0.989	17.038	2.437	2.746	8.045
USA	5.648	1.916	37.290	4.313	3.599	17.279	4.942	2.056	13.629	2.252	1.138	1.002	6.009	1.916	37.290	5.016	3.236	12.732
Average	4.210	2.085	17.702	1.988	3.162	14.111	3.764	2.220	8.042	1.091	0.930	1.452	4.439	2.232	16.754	2.174	2.737	9.898

Note: Min, Max, SD, Skew, and Kurt are, respectively, minimum, maximum, standard deviation, skewness, and kurtosis of the single-index risk. We estimate the EVaR from log-returns of the market indexes of countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020. For EVaR estimation, we consider Filtered Historical Simulation (FHS) and $\alpha =0.145\text{\%}$, i.e., EVaR${}^{0.145\text{\%}}$. Average refers to the average value of descriptive statistics of EVaR estimates.

Table 9.

Descriptive statistics of the Maximum Loss (ML) forecasting computed from log-returns of the market indexes (in %). The full sample period refers from November 17, 2018, to October 25, 2021. Sub-sample 1 comprehends data from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends data from November 17, 2019, to October 25, 2021.

Countries	Full sample						Sub-sample 1						Sub-sample 2
	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt
Argentina	54.095	40.752	145.530	14.633	2.413	6.688	57.215	40.752	145.530	21.926	1.638	1.512	52.499	43.716	82.056	8.411	1.050	0.238
Austria	5.669	2.192	23.966	3.142	2.836	9.981	4.954	2.878	9.894	1.313	1.289	1.688	6.034	2.192	23.966	3.695	2.350	6.239
Bangladesh	3.677	0.318	16.163	1.702	2.672	13.235	3.373	0.318	6.075	0.945	−0.214	0.498	3.833	0.897	16.163	1.963	2.463	9.928
Belgium	5.814	2.462	24.710	3.387	2.541	7.939	5.097	2.744	8.755	1.432	0.575	−0.521	6.181	2.462	24.710	3.988	2.101	4.755
Brazil	7.325	3.052	39.987	4.215	4.534	25.665	6.192	3.686	9.868	1.400	0.486	−0.470	7.905	3.052	39.987	4.988	3.816	17.234
Canada	4.765	1.301	43.288	4.971	4.738	26.138	3.635	1.517	9.585	1.669	1.398	1.378	5.343	1.301	43.288	5.912	3.973	17.382
Chile	8.383	3.032	38.019	4.388	2.538	10.166	5.285	3.032	12.130	1.690	2.150	5.161	9.968	3.697	38.019	4.498	2.722	10.194
China	10.133	5.849	17.184	1.980	1.126	0.835	10.269	5.849	15.534	1.846	0.790	0.240	10.063	7.333	17.184	2.043	1.270	1.084
Czechia	3.889	1.912	22.162	2.205	3.384	15.485	3.068	1.912	5.793	0.657	1.181	1.854	4.309	1.939	22.162	2.570	2.771	10.122
Egypt	6.607	2.659	27.951	2.832	3.222	15.849	6.222	2.659	15.372	2.056	1.183	1.531	6.803	3.418	27.951	3.140	3.298	14.648
France	8.362	1.718	45.041	5.948	2.912	10.825	6.889	2.132	13.519	2.707	0.467	−0.658	9.115	1.718	45.041	6.934	2.491	7.123
Germany	5.624	2.605	22.662	2.972	2.802	9.259	4.765	2.838	7.464	1.051	0.391	−0.627	6.064	2.605	22.662	3.496	2.260	5.423
India	5.348	1.839	25.782	2.983	3.537	15.416	4.745	2.581	6.635	0.909	−0.329	−0.726	5.656	1.839	25.782	3.572	2.879	9.497
Indonesia	4.608	2.286	20.043	2.185	3.417	14.702	3.795	2.286	7.433	0.872	1.223	2.097	5.024	2.668	20.043	2.514	2.942	10.110
Iraq	4.676	3.297	20.210	1.332	4.264	33.072	4.533	3.405	7.774	0.762	1.183	1.660	4.749	3.297	20.210	1.539	3.993	26.649
Israel	4.785	1.945	17.223	2.681	2.396	6.326	3.872	2.269	8.387	1.170	1.279	1.353	5.252	1.945	17.223	3.086	1.960	3.657
Italy	6.240	1.316	24.014	3.382	1.962	4.725	4.689	1.316	8.522	1.529	−0.254	−0.238	7.034	2.560	24.014	3.774	1.643	2.732
Mexico	4.740	2.993	14.765	1.852	3.096	11.133	4.073	2.998	7.879	0.860	1.797	4.201	5.081	2.993	14.765	2.113	2.696	7.628
Morocco	3.229	1.672	17.600	1.884	4.691	26.585	2.730	1.737	4.461	0.539	0.598	−0.179	3.485	1.672	17.600	2.242	3.886	17.439
Nepal	6.303	2.044	19.484	2.404	1.370	3.058	5.233	2.044	8.963	1.087	0.870	0.921	6.851	2.541	19.484	2.692	0.958	1.692
Netherlands	5.128	2.060	26.151	3.026	3.153	13.744	4.275	2.060	8.823	1.570	0.892	−0.036	5.564	2.073	26.151	3.468	2.830	10.091
Pakistan	4.746	2.997	15.961	1.736	3.098	12.557	4.703	3.326	8.004	0.927	1.207	1.468	4.767	2.997	15.961	2.029	2.848	9.382
Philippines	6.757	4.702	19.051	2.139	2.878	9.537	5.565	4.702	6.701	0.426	0.271	−0.577	7.367	5.092	19.051	2.393	2.414	6.188
Poland	5.510	2.908	24.012	2.569	3.694	17.675	4.660	3.135	6.802	0.833	0.396	−0.652	5.945	2.908	24.012	3.012	3.072	11.631
Portugal	5.335	2.409	21.263	2.405	3.456	16.614	4.564	2.671	7.392	1.053	0.357	−0.771	5.729	2.409	21.263	2.779	3.021	11.750
Romania	11.703	6.157	71.405	6.492	3.417	16.167	12.009	6.729	71.405	6.657	3.835	22.906	11.546	6.157	55.284	6.406	3.169	11.985
Russia	4.692	3.044	17.825	2.102	3.888	16.824	3.942	3.078	5.408	0.495	0.685	0.035	5.076	3.044	17.825	2.474	3.166	10.489
Saudi Arabia	4.576	1.550	26.660	2.594	3.913	22.717	4.693	2.557	9.537	1.464	0.696	−0.181	4.516	1.550	26.660	3.012	3.783	18.596
South Africa	5.602	3.048	18.416	2.117	3.209	12.993	4.847	3.048	6.905	0.861	0.102	−0.717	5.987	3.277	18.416	2.440	2.759	8.727
Spain	6.121	2.902	27.455	3.444	3.150	12.485	4.728	2.902	7.747	1.142	0.817	−0.189	6.833	3.000	27.455	3.971	2.619	8.133
Sweden	6.231	4.118	18.930	2.477	2.886	8.960	5.490	4.161	7.690	0.766	0.542	−0.308	6.611	4.118	18.930	2.924	2.289	4.995
Switzerland	4.534	1.994	37.752	3.014	4.499	29.547	3.942	2.378	11.869	1.472	2.072	5.433	4.837	1.994	37.752	3.515	3.996	22.060
Turkey	9.693	6.014	23.051	1.961	2.167	8.618	9.724	6.316	17.615	1.617	0.837	2.048	9.678	6.014	23.051	2.117	2.422	9.115
UK	4.264	1.367	23.279	2.841	3.353	12.939	3.311	1.836	6.271	0.919	1.060	0.920	4.751	1.367	23.279	3.328	2.746	8.044
USA	10.417	3.576	69.042	7.914	3.605	17.362	9.124	3.834	25.183	4.135	1.142	1.015	11.078	3.576	69.042	9.203	3.242	12.802
Average	7.417	3.831	30.458	3.369	3.166	14.166	6.749	4.048	15.055	2.022	0.932	1.459	7.758	4.098	28.184	3.607	2.740	9.936

Note: Min, Max, SD, Skew, and Kurt are minimum, maximum, standard deviation, skewness, and kurtosis of the single-index risk, respectively. We estimate the ML from log-returns of the market indexes of countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020. For ML estimation, we consider Filtered Historical Simulation (FHS). Average refers to the average value of descriptive statistics of ML estimates.

The mean risk in sub-sample 2 is higher than in sub-sample 1 for almost all countries and risk measures. For example, the mean VaR for Brazil and the USA are 3.532% and 2.671% for sub-sample 1, while for sub-sample 2, the mean values are equal to 4.517% and 3.257%, respectively. It is valid to mention that both countries were, at some point, at the epicenter of COVID-19’s dissemination. Also, the expansionary fiscal and monetary policies adopted in both countries might have contributed to the recovery of the markets and, consequently, ameliorated the rise of tail risk during sub-sample 2 (Feldkircher et al., 2021). Cantú et al. (2021) mentioned that in previous crisis episodes, emerging markets have reacted by raising interest rates, not by cutting them. The rationale was that low-interest policies could lead to massive capital outflows and generate a balance of payments deficits and currency depreciation. In the recession of 2020–2021, on the other hand, the international scenario, particularly regarding advanced economies like the USA, was that of lower interest rate policies, which would decrease the risk of capital outflows from emerging economies that chose to cut interest rates.

The Mann–Whitney test described in Appendix confirms the risk increase between the sub-samples. The test indicates that the risk in sub-sample 2 is significantly higher than in sub-sample 1 for almost all countries and risk measures considered except for EL. The exception of the EL is expected. EL evaluates the risk in terms of the central trend of the losses, which are close to zero. Besides, it ignores the variability and less likely losses, known as tail risk. The increase of single-index risk during the pandemic period is in line with the findings of investigations of Baek et al., 2020, Baker et al., 2020, Breugem et al., 2020, and Zhang et al. (2020).

We realize that there is a positive association between average risk in sub-sample 2 and death and case rates caused by COVID-19.21 This result indicates that countries with higher death and case rates tend to have a higher single-index risk. On the other hand, in countries with lower death and case rates, the risk tends to be lower.22 That are, however, exceptions to this pattern. The United States, for instance, has the highest percentage of cases and deaths in our sample. However, it has the seventeenth and eleventh highest average values for VaR and ES in sub-sample 2, respectively. The increase in average risk in the USA – which is the median of the increases among the countries – did not closely follow its high exposure to COVID. Plausible explanations for this exception are the high capitalization of the USA’s financial market and the expansionary policies adopted by its government, which might have contributed to softening the risk increase.

We emphasize that the risk measures considered present conceptual differences and, for this reason, they vary in absolute value. However, when analyzing the relative variation in single-index risk between sub-sample 1 and 2, we find that the values are similar regardless of the measure. This variation is not valid for EL for the reasons previously mentioned. We also realized, as well as verified by Rout et al. (2020), that the pandemic shocks affected the countries differently. We observe that only Argentina, China, Romania, Saudi Arabia, and Turkey have the highest mean risk registered in sub-sample 1 (for all risk measures considered). For example, China, for sub-samples 1 and 2, has a mean value of ES equal to 3.191% and 3.127%, respectively.23 Despite the lower average risk in sub-sample 2, China presents the maximum risk estimate in this sub-sample. (Rout et al., 2020) studied the tail risk of the G20 countries and also found that China was less affected by the pandemic compared to other countries. This finding explains that China has managed to contain the virus quickly and restarted its economic activities. The country injected trillions of RMB into the banking sector through open market operations, reduced interest rates, and decreased the 1-year medium-term lending facility rate (Rizwan et al., 2020). Although Turkey suffered losses and high volatility around March 9, 2020, we found that its risk was similar in both sub-samples. Considering the countries of Asia and Europe, Turkey presented the highest average risk in sub-sample 1. This finding reflects Turkey’s financial and economic crisis in 2018, which has unleashed excessive current account deficit and foreign currency debt (Arbaa & Varon, 2019). With the arrival of the pandemic, Turkish companies that were already facing difficulties in accessing financing had their situation aggravated. The challenges facing Turkey’s economy have led the World Bank, in 2021, to support the country in limiting the damage of COVID-19 and also to advance the country’s long-term needs (Celasin, 2021). Romania’s market underwent a volatility clustering at the beginning of the log-returns series, which may have contributed to the average risk of sub-sample 1 being higher than that of sub-sample 2. Romania’s greatest risk may be associated with the perceived level of corruption in the country’s public and private sector (Transparency International, 2021). For Europe, Turkey and Romania have the highest average risk values. Regarding Saudi Arabia, we also noticed a small cluster of volatility before the peak in March 2020 (see Fig. 2). This increase in volatility was accompanied by a drop in prices in mid-2019 (see Fig. 1).

As far as Argentina is concerned, the country experienced a high risk period in the full sample. In sub-sample 1, we see that the average ES for the country is 9.357%, whereas the overall average single-index risk for all countries is 2.827%. During the pandemic period, we noticed that the country’s ES reduced to 8.582%. However, it remains high compared to the overall average ES in the same sub-sample, 3.434%. This happened because, during the period analyzed, the financial market in Argentina reacted to several adverse macroeconomic and political shocks, thereby presenting remarkably high volatility compared to the other countries (see Fig. 2, for instance). The high risk presented by Argentina contributed to the higher average risk of countries that belong to America compared to countries that belong to other continents.24 For instance, the average ES in sub-sample 2 of the countries that belong to America (Argentina, Brazil, Canada, Chile, Mexico, and the USA) is equal to 4.823%. If we exclude Argentina, this figure drops to 3.883%. As a similar exercise, we noted that if we exclude Argentina from the group of G20 countries,25 the average ES of these countries in sub-sample 2 drops from 3.677% to 3.370%. For the sake of comparison, the average ES during sub-sample 2 for European countries equals 3.462%, and for countries that do not belong to G20, we have an average ES of 3.204% during sub-sample 2.

Chile and Italy, followed by Canada, Spain, and the UK, were the countries with the most percentage increase in their risks. The increase in Chilean risk may be explained by the severity and extension of the containment measures applied by the Chilean government. Also, the fall of copper prices exacerbated the impact of COVID-19 on the Chilean economy and, presumably, on its financial markets (Osterhuber, 2020). For Canada, this is a presumable consequence of a relatively stable financial performance during sub-sample 1 and the record decline of the FSX index during the week of March 9, 2020 (Smith, 2020). Regarding Italy, in March 2020, the country surpassed China as the country with the highest death toll, becoming the epicenter of the pandemic during that period. In a short period, the country closed its factories and all non-essential production to contain what the prime minister called the country’s most difficult crisis since World War II (Horowitz, Bubola, & Povoledo, 2020). In addition to these measures, the authorities carried out a nationwide lockdown, closed parks, and banned outdoor activities. We can highlight that these restrictive measures are not exclusive to Italy and were present in many countries to reduce the spread of SARS-CoV-2, the virus that causes COVID-19. While measures of mandatory social distancing and business closures were imposed for public health reasons, some authors, such as Baker et al. (2020), present evidence indicating that they had a severe adverse effect on the stock markets. The lockdown drastically affected the real economy, decreasing companies’ cash flow and, as a consequence, their trading price. The extreme character of the lockdown measures and uncertainty regarding the duration and effects of the measures may have also led investors to desperately flee from risky assets towards “safe-heavens” like gold and Treasury securities (Akhtaruzzaman, Boubaker, Lucey, & Sensoy, 2021).

In addition to the mechanisms mentioned above, evidence shows that the number of cases and deaths caused by COVID-19 have a direct partial effect on the market’s risk and volatility (Al-Awadhi et al., 2020, Andrieś et al., 2021, Li et al., 2021, Xu, 2021). A major mechanism linking cases and deaths to market volatility and risk, as indicated in Baek et al. (2020), might be the negative news about pandemics (a surge of cases and deaths, for instance). This case is strengthened by Baker et al. (2020), which showed that the media’s coverage of the pandemic developments (cases and deaths) was gigantic. Chundakkadan and Nedumparambil (2021) indicate that the media’s focus on the pandemic has generated a pessimistic attitude among investors and weakened stock exchanges around the world. In periods of the outbreak, social media alter market sentiment, which then stimulates trading activities and can cause extreme price movements (Broadstock & Zhang, 2019). Besides that, the uncertainty about the future of the economic and financial environment might have influenced stock valuation negatively. In light of this evidence, we infer that, as investors received a continuous flow of (mainly) bad news regarding the COVID-19 cases and death tolls, as well as regarding the collapse of the health system of developed economies like Italy, Spain, and the United Kingdom, for example, the market sentiment changed, which contributed to the movements observed in the financial markets (see, for instance, Huynh, Foglia, Nasir, & Angelini, 2021, and Lehrer, Xie, & Zhang, 2021).

In Fig. 4 we present the graphical evolution of VaR results for the group of countries investigated.26 For the sake of brevity, we do not provide illustrations of the other risk measures; however, they are available upon request. For most countries, the Value at Risk was stable at low levels during sub-sample 1 and at the beginning of sub-sample 2 (November 17, 2019). The VaR of most countries peaked near the red-dotted line, which indicates March 9, 2020. This characteristic is also valid for the single-index risk obtained by the other risk measures. Thus, similar to Breugem et al. (2020) and Jackwerth (2020), we identify that the single-index risk did not react timely to the burst of the pandemic. As we mentioned for the descriptive statistics of the returns, essential explanations for the synchronicity of the peak of the risks are the Saudi-Russian oil price war,27 which escalated on March 8, 2020, and the WHO’s classification, on March 11, 2020, of the COVID-19 surge as a pandemic. Corroborating, Chundakkadan and Nedumparambil (2021) find that the negative effect of the pandemic on daily returns was strong in the week that the World Health Organization declared it a pandemic.

Fig. 4.

Historical evolution of the VaR estimates for market indexes from November 17, 2018, to October 25, 2021. The dotted grey line indicates November 17, 2019, and the dotted red line indicates March 9, 2020. We estimate the VaR from log-returns of the market indexes of countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020. For VaR estimation, we consider Filtered Historical Simulation (FHS) and $\alpha =1\text{\%}$. The VaR estimates are with its signal converted. We make this transformation to compare VaR estimates with the indexes’ negative returns (losses).(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

As we can see in Fig. 4 in the second half to the end of 2020, there is a reduction in single-index risk in most countries. Among the reasons for the recovery of the financial markets, it is possible to point out the help of central banks offered around the world to mitigate the impacts on the capital markets. Rouatbi, Demir, Kizys, and Zaremba (2021) also show that COVID-19 vaccination helped to stabilize global equity markets. Furthermore, the authors point out that the impact of vaccination was greater in developed markets than in emerging ones. Corroborating, Yu, Xiao, and Liu (2021) find that the correlations between pandemic anxiety indexes and stock market returns are smaller and vary less after the COVID-19 vaccine results were announced. For these reasons, the emergence of new variants in 2021, such as the delta variant, did not imply an increase in individual market risk.

In general, we verified that, as for losses, there is a synchronism in the increase and reduction of the single-index risk of the different analyzed markets. Although we observe that all countries felt the impacts of the pandemic, it is worth noting that it affected all economies differently, and not all reacted in the same way. This is clear from the individual analysis of each market. To corroborate this, we performed a correlation matrix28 between the VaR estimates for the 35 countries that make up our sample. See Appendix. Higher positive values indicate a greater similarity in the evolution of risk in these countries. For example, for Argentina and Brazil, the correlation is 0.998 (in sub-sample 2). The relationship between the risk of the two countries can be explained by both being neighbors in Latin America and by the commercial relationship performed by both countries. Although several countries with high positive correlations were found, there are situations such as Germany, in which we observed negative values in most cases, showing that the dynamics of single-index risk in this country did not evolve in a similar way to the others. The analysis of the correlation between country risk can also be used as a way to assess the contagion29 of market risk between countries. It is noted that there is an increase in the relationship during the pandemic period. The increase in correlation indicates a possible risk contagion among the countries. However, a more in-depth analysis of the contagion between markets during the pandemic is beyond the scope of our work. For excellent references on contagion, we refer (Kenourgios, Dimitriou, & Samitas, 2018) and Samitas et al. (2020). Akhtaruzzaman, Boubaker, and Sensoy (2021) and Baumöhl et al. (2020) are good examples regarding investigations about financial contagion during COVID-19 crisis.

We also note that the standard deviation of the risk increased from sub-sample 1 to sub-sample 2 for all risk measures considered and in almost all countries. The standard deviation of the VaR of the United States and Germany, for instance, rose from 1.230 to 2.743 and 0.688 to 2.291, respectively, between sub-samples 1 and 2. The variation of the standard deviation of the risk between the sub-samples, in absolute values, depends on the risk measure being used. However, we note that the percentage variation in the standard deviation of each country’s risk, from sub-sample 1 to 2, is similar across the different risk measures, except for EL. The increase in the dispersion of the risk estimates during the pandemic is also confirmed when we verify the amplitude between the maximum and minimum values. For instance, the gap between the minimum and maximum VaR for Germany is approximately 3% for sub-sample 1 and 13% for sub-sample 2.

Following the losses, around thirty countries registered their maximum risk in March 2020, considering all risk measures.30 The notable exceptions are Argentina and Romania, for which the maximum risks were registered in sub-sample 1 for all risk measures considered. This result may be associated with the internal problems of both countries, which were previously discussed. Moreover, these countries are the only ones for which the maximum VaR in sub-sample 1 was above 15%. Remarkably, all risk measures peaked on the same day for most countries, except the EL (and the MSD in a few cases). Also, four countries had their maximum risk during the week of March 9, 2020, and all of these countries registered their minimum returns during this same week. Interestingly, the week of March 9, 2020, concentrated more on maximum losses than maximum risks, the former occurring before. This time ordering of the maximum loss and the maximum risk was also observed for the countries that did not attain their maximum risks during the week of March 9, 2020. This time delay was also observed in Breugem et al. (2020) and Jackwerth (2020). According to Ramelli and Wagner (2020), in March 2020, COVID-19 began to attract the attention of financial market participants because it was during this period that the Federal Reserve Board announced major interventions in the corporate bond market. The authors also comment that the virus also spread to Europe and the United States31 during this period, leading to the lockdown of many economies. As a result of the lockdowns, investors were concerned about the high corporate indebtedness and the chances of survival of companies with little cash flow. The dates of the minimum risk of most countries were also invariant concerning the risk measure being used, except for the EL (see Table 17).

The skewness and kurtosis are also systematically higher in sub-sample 2 than in sub-sample 1. This is illustrated by the increase of the average skewness and the average kurtosis of the market risks between sub-sample 1 and 2. These figures are presented in the last line of Table 4, Table 5, Table 6, Table 7, Table 8, Table 9. The higher (positive) skewness of the risk in sub-sample 2 is compatible with the more negative skewness of the returns in sub-sample 2. Also, it reflects the more prominent right-sided asymmetry of the risk. The higher kurtosis in sub-sample 2 is explained by more extreme realizations of the risks in sub-sample 2. Exceptions to these patterns are, for instance: Argentina, for which the standard deviation, skewness, and kurtosis of the risk, as measured by all risk measures considered, except the EL, are higher in sub-sample 1 than in the sub-sample 2, and Romania, for which the kurtosis of the risk, as measured by all risk measures considered, is higher in sub-sample 1 than in sub-sample 2. A remarkable fact is that these averages for both sub-samples are very similar across the different risk measures (except EL). Similarities of this sort (across different risk measures) were described throughout this sub-section, and most of them will be confirmed for systemic risk. In particular, for VaR, ES and EVaR, these observations are positive evidence that the levels of significance provided in Basel Committee on Banking Supervision (2013) for VaR and ES and in Bellini and Di Bernardino (2017) for the EVaR do make the historical evolution of the measures very similar.

Table 10.

Descriptive statistics of systemic risk. The full sample period refers from November 17, 2018, to October 25, 2021. Sub-sample 1 comprehends data from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends data from November 17, 2019, to October 25, 2021.

Indexes	VaR						ES
	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt
	Full Sample
${\Lambda }_C$	2.191	0.867	14.728	1.702	4.283	21.676	2.305	0.912	15.483	1.789	4.283	21.669
${\Lambda }_D$	2.351	0.710	18.251	1.866	4.509	26.614	2.377	0.718	18.450	1.887	4.509	26.613
${\Lambda }_N$	1.754	0.695	11.933	1.332	4.366	23.176	1.868	0.743	12.662	1.415	4.364	23.137
Average	2.099	0.757	14.971	1.633	4.386	23.822	2.183	0.791	15.532	1.697	4.385	23.806
	Sub-Sample 1
${\Lambda }_C$	1.843	0.982	3.477	0.591	0.840	−0.296	1.939	1.034	3.656	0.621	0.839	−0.298
${\Lambda }_D$	1.934	0.879	4.190	0.701	0.772	0.059	1.955	0.889	4.236	0.708	0.772	0.059
${\Lambda }_N$	1.463	0.779	2.841	0.494	0.863	−0.358	1.559	0.832	3.018	0.525	0.861	−0.365
Average	1.747	0.880	3.503	0.595	0.825	−0.198	1.818	0.918	3.637	0.618	0.824	−0.201
	Sub-Sample 2
${\Lambda }_C$	2.394	0.871	14.803	2.051	3.554	13.970	2.500	0.909	15.450	2.141	3.554	13.967
${\Lambda }_D$	2.585	0.711	18.285	2.225	3.806	17.903	2.596	0.714	18.360	2.234	3.806	17.903
${\Lambda }_N$	1.913	0.689	11.911	1.599	3.618	14.895	2.044	0.739	12.689	1.705	3.616	14.865
Average	2.278	0.757	14.971	1.939	3.705	16.010	2.370	0.791	15.532	2.014	3.705	15.998
Indexes	EL						EVaR
	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt
	Full Sample
${\Lambda }_C$	−0.049	−0.349	−0.002	0.033	−4.418	27.091	2.551	1.010	17.118	1.979	4.282	21.655
${\Lambda }_D$	−0.046	−0.333	−0.003	0.033	−4.659	29.663	2.583	0.780	20.035	2.050	4.509	26.611
${\Lambda }_N$	−0.031	−0.312	0.673	0.058	4.468	43.859	2.075	0.831	13.989	1.567	4.360	23.077
Average	−0.042	−0.331	0.223	0.041	−1.536	33.538	2.403	0.874	17.047	1.865	4.384	23.781
	Sub-Sample 1
${\Lambda }_C$	−0.043	−0.090	−0.010	0.014	−0.754	0.376	2.146	1.146	4.043	0.687	0.839	−0.301
${\Lambda }_D$	−0.039	−0.076	−0.003	0.013	−0.608	0.034	2.125	0.967	4.603	0.770	0.772	0.059
${\Lambda }_N$	−0.032	−0.139	0.100	0.032	0.875	2.573	1.733	0.927	3.342	0.581	0.857	−0.378
Average	−0.038	−0.102	0.029	0.020	−0.162	0.994	2.001	1.013	3.996	0.679	0.823	−0.207
	Sub-Sample 2
${\Lambda }_C$	−0.052	−0.349	−0.002	0.038	−3.827	19.081	2.758	1.010	17.118	2.357	3.582	14.209
${\Lambda }_D$	−0.050	−0.333	−0.009	0.039	−4.021	20.835	2.818	0.780	20.035	2.427	3.837	18.225
${\Lambda }_N$	−0.030	−0.312	0.673	0.067	4.202	35.203	2.251	0.831	13.989	1.858	3.690	15.502
Average	−0.044	−0.331	0.221	0.048	−1.215	25.040	2.609	0.874	17.047	2.214	3.703	15.979
Indexes	MSD						ML
	Mean	Min	Max	SD	Skew	Kurt	Mean	Min	Max	SD	Skew	Kurt
	Full Sample
${\Lambda }_C$	0.504	0.195	3.528	0.401	4.320	22.262	3.411	1.353	22.828	2.643	4.280	21.623
${\Lambda }_D$	0.527	0.156	4.228	0.424	4.513	26.739	4.211	1.275	32.554	3.338	4.509	26.601
${\Lambda }_N$	0.419	0.121	3.395	0.357	4.510	25.644	2.805	1.139	18.673	2.102	4.351	22.942
Average	0.483	0.157	3.717	0.394	4.448	24.882	3.476	1.256	24.685	2.694	4.380	23.722
	Sub-Sample 1
${\Lambda }_C$	0.423	0.213	0.821	0.140	0.872	−0.176	2.870	1.538	5.398	0.918	0.837	−0.308
${\Lambda }_D$	0.433	0.190	0.945	0.159	0.779	0.066	3.464	1.582	7.500	1.253	0.772	0.059
${\Lambda }_N$	0.344	0.149	0.760	0.136	0.975	0.117	2.344	1.264	4.479	0.778	0.850	−0.405
Average	0.400	0.184	0.842	0.145	0.875	0.002	2.893	1.461	5.792	0.983	0.820	−0.218
	Sub-Sample 2
${\Lambda }_C$	0.545	0.195	3.528	0.477	3.619	14.666	3.688	1.353	22.828	3.147	3.580	14.185
${\Lambda }_D$	0.575	0.156	4.228	0.501	3.841	18.328	4.593	1.275	32.554	3.952	3.837	18.217
${\Lambda }_N$	0.457	0.121	3.395	0.423	3.838	17.499	3.040	1.139	18.673	2.491	3.682	15.398
Average	0.526	0.157	3.717	0.467	3.766	16.831	3.774	1.256	24.685	3.197	3.700	15.933

Note: Min refers to the minimum, Max is the maximum, StD is the standard deviation, Skew is the Skewness, and Kurt is the kurtosis. VaR, EL, MSD, ES, EVaR, and ML, are, respectively, Value at Risk, Expected Loss, Mean plus Semi-Deviation, Expected Shortfall, Expectile Value at Risk, and Maximum Loss. ${\Lambda }_N$, ${\Lambda }_C$ and ${\Lambda }_D$ are the aggregated indexes. ${\Lambda }_N$ is the naive aggregation (equally weighted); ${\Lambda }_C$ is based on the number of cases (weights returns by the percentage of COVID-19 cases); and ${\Lambda }_D$ is based on the number of deaths (weights returns by the percentage of COVID-19 deaths). Aggregate indexes are built using log-returns (in %) from market indexes of 35 countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020.

4.2. Systemic risk results

In this subsection, we present the systemic risk estimates obtained by applying single component risk measures to the aggregate indexes. In comparison to the results, we described in Section 3.2 – where the focus was the aggregated indexes’ returns – the figures we provide in the present section reflect the tails of the aggregate indexes’ distribution. The descriptive statistics of the systemic risk estimates are introduced in Table 10.

Our results show that, regardless of the aggregate index, the mean systemic risk increases from sub-sample 1 to 2, except when EL is used. For an illustration, see ${\Lambda }_D$ and ES; the mean value is equal to 1.955% in sub-sample 1 and increases to 2.596% in sub-sample 2. The estimates are similar for VaR, and those for EVaR are slightly higher. Notice that, as most risk measures we use are not linear (but convex), results of this sort could not be inferred from the risk estimates of the individual indexes.

Moreover, except for EL, the risk estimates in both sub-samples are smaller when ${\Lambda }_N$ is used. For instance, when ES is combined with ${\Lambda }_N$, the average systemic risk is 1.559% in sub-sample 1 and 2.044% in sub-sample 2, which are smaller figures than when ${\Lambda }_D$ is used. The fact that the systemic risk increased less when ${\Lambda }_N$ was used (in comparison to that of ${\Lambda }_C$ and ${\Lambda }_D$) is explained by the findings of Al-Awadhi et al., 2020, Andrieś et al., 2021, Ashraf, 2020 and Xu (2021), that show that the market’s performance was affected by the number of cases and deaths by COVID-19. Also, these results suit the observation of Li et al. (2021) that investors take the number of cases and deaths by COVID-19 as concerning factors of risk. As previously mentioned, we also observed a positive correlation between the death and confirmed coronavirus case rates and the mean risk of the individual countries. In a similar spirit, Andrieś et al. (2021) found that, for European countries, the number of cases and deaths by COVID-19 is directly related to the countries’ sovereign CDS spreads, which is an indication of high uncertainty. Therefore, it was expected that the risk would increase when the countries with more cases and deaths by COVID-19 receive higher weights. Furthermore, we see that ${\Lambda }_D$ generates the highest systemic risks among all other aggregation functions. This result can be justified because we observed a greater correlation between the death rates and the average single-index risk.32

We applied the right one-tailed (bilateral, respectively) Mann–Whitney test to analyze whether the median of the systemic risk in sub-sample 2 is higher (different, respectively) than in sub-sample 1. The tests are reported in Appendix. For both tests, the null hypothesis that the medians of the systemic risk are equal was rejected at a significance level of 1% for all aggregated index and risk measures except the EL. This result was expected, given the increased single-index risk observed. According to Fang, Chen, Yu, and Qian (2018), when individual markets are in distress, the risk to the entire system increases significantly at the start of the crisis. The significant median tests that we report sustain this argument, keeping in mind that we are adopting the “portfolio like” view on the financial system, as explained in Section 2. Our findings corroborate previous studies indicating a significant increase in systemic risk due to the COVID-19 outbreak. Abuzayed et al., 2021, Baumöhl et al., 2020, and Rizwan et al. (2020) reached conclusions similar to ours, although they employed a view on systemic risk more focused on the dissemination of financial shocks. For the banking system, the systemic risk vulnerabilities are mainly due to: (i) liquidity risk associated with economic downturns and reduced access to financing sources; (ii) loss of intermediation income that is a reflection of policy and regulatory responses, which suspended loan payments and made more loans available,33 for example; and (iii) reduction in intermediation business, which may affect the ability to finance operations and financing costs of financial institutions (Rizwan et al., 2020). Given these risks, the interconnection among financial institutions can spread individual issues to the network of institutions, resulting in a general heating-up of the financial system. In addition to adverse events generating chain reactions, they also facilitate the spread of pessimistic expectations, which contributes to an increase in systemic risk (Abuzayed et al., 2021).

Furthermore, it is important to highlight that the dynamics of the systemic risk were not V-shaped, even if abnormal positive returns dominated the period following the shock of March 2020. As illustrated in Fig. 5, the systemic risk remained above pre-pandemic levels until the end 2020. A possible reason for this is that several issues related to the pandemic – the availability of vaccines, for instance – were not settled right after March 2020. Yet, several novel sources of uncertainty have appeared since then. These considerations and our estimates indicate that the financial system was not as stable after March 2020 as before. The reduction in systemic risk observed at the end of 2020, in the first place, attests to the positive systemic risk response to expansionary fiscal and monetary policies. For a description of policy responses, see section 2 of Aguilar et al. (2020) and Rizwan et al. (2020). Furthermore, as the positive results of the vaccines were released, agents and investors are pricing in the recovery of economies, which contributes to the stock’s valuation and reduction of systemic and single-index risks.

Fig. 5.

Historical evolution of systemic risk estimates that we computed from aggregated indexes from November 17, 2018, to October 25, 2021. The dotted grey line indicates November 17, 2019, and the dotted red line indicates March 9, 2020. Note: ${\Lambda }_N$, ${\Lambda }_C$ and ${\Lambda }_D$ are the aggregated indexes. ${\Lambda }_N$ is the naive aggregation (equally weighted); ${\Lambda }_C$ is based on the number of cases (weights returns by the percentage of COVID-19 cases); and ${\Lambda }_D$ is based on the number of deaths (weights returns by the percentage of COVID-19 deaths). Aggregate indexes are built using log-returns (in %) from market indexes of 35 countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020.. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 5 shows that, for a given aggregation function, the historical evolution of the systemic risk follows remarkably similar patterns whenever we consider the VaR, ES, or EVAR as a single component risk measure. On the other hand, the plot changes abruptly when the EL is used as the single component risk measure. This follows, as mentioned earlier because the EL is a measure of the central tendency of the losses, not tail risk. This also explains why MSD also generates low systemic risk estimates. The ML, by its definition, generates the highest systemic risk among all other risk measures. Also, although the absolute values of ML and MSD differ from those of VaR, ES and EVaR, notice that they all generate the same pattern for the historical evolution of the systemic risk. This can be seen by looking at the red dotted line in Fig. 5, where these five measures indicate a sharp increase in systemic risk. As reported in Appendix (Table 19), for all risk measures, the systemic risk peaked in March 2020. For this period, Hanif, Mensi, and Vo (2021), in a study that investigates the spillover between the US and Chinese equity sectors also find significant abrupt changes in risk spillovers for all sectors analyzed. For Hanif et al. (2021), this change is explained by the investors’ sentiment, which affects investment decisions and, consequently, stock pricing. Baumöhl et al. (2020) points out that the systemic risk and the density of the spillover network were not so high even during the Subprime crisis. In 2008, the global financial crisis started in the United States and progressively spread to other nations. On the contrary, the coronavirus disease quickly brought the world economy to a standstill by instantly shutting down demand and supply lines around the globe due to extensive lockdowns (Ozkan, 2021).

Similarly to the single-index risks, we verify that the standard deviation of the systemic risk was higher during sub-sample 2 than in sub-sample 1 for all indexes and risk measures considered. The increase of the variability and the average value of systemic risk was also observed by Borri and Di Giorgio (2021), which investigated the systemic risk contribution of large European banks during the Great Financial Crisis, the European sovereign debt crisis, and the COVID-19 pandemic. The increase in systemic risk variability reflects the risk’s movement of abrupt increase near March 9, 2020, and the posterior retraction, as seen in Fig. 5. These downward and upward dynamics are the most distinctive characteristic of the historical evolution of the risks during sub-sample 2. Therefore, these are natural candidates for the leading causes of the increase in the standard deviation of the risk between sub-samples. Nonetheless, it is valid to stress that the systemic risk after March 2020 did not return to the pre-pandemic levels until almost the end of 2020. For ${\Lambda }_C$, ${\Lambda }_D$, and ${\Lambda }_N$, we note an increase in the variability of systemic risk by approximately 245%, 215%, and 225%, respectively, from sub-sample 1 to sub-sample 2 (except when EL is used). By illustration, the standard deviation for systemic risk estimates of ${\Lambda }_C$ using ES is equal to 0.621 in sub-sample 1 and equal to 2.141 in sub-sample 2. The increased variability in systemic risk estimates is also noticed when the maximum and minimum systemic risks are compared. For instance, for both sub-samples, the minimum systemic VaR varies between 0.69% and 0.98% (depending on the aggregation function considered). On the other hand, the maximum VaR ranges from 2.85% to 4.19% in sub-sample 1, while in sub-sample 2 it ranges from 12% to 18.3%. This means that the maximum systemic risk during sub-sample 2 was far above the minimum and that this gap is approximately 3 to 4 times wider in sub-sample 2 than in sub-sample 1. Similar figures hold for ES and EVaR. This also shows that the maximum systemic risk increased substantially between the sub-samples. This increase was even more remarkable for ML. The maximum systemic ML was similar to the others during sub-sample 1. However, the ML detaches from the general trend during March 2020, which caused the systemic ML to present the largest gap between the maximum systemic risk sub-sample 1 (near 4.5% to 7.5%) and in sub-sample 2 (18.7% to 32.5%). As expected, the maximum systemic risk is the lowest for the EL, ranging from -0.009% to 0.673% during sub-sample 2. It is valid to mention that although the variation of the maximum systemic EL is small in absolute terms, it is remarkably large in percentage terms. For instance, when ${\Lambda }_N$ is used with EL, the maximum risk in sub-sample 2 is more than six times the maximum risk in sub-sample 1. This happens mainly due to the low values of the systemic EL in sub-sample 1. For all risk measures, we found that the maximum systemic risk occurred in March 2020, corroborating with single-index risk findings.

The skewness and kurtosis were also higher in sub-sample 2. The higher skewness indicates a strong right-sided asymmetry of the distribution of the systemic risk, while the higher kurtosis indicates more realizations of extreme values. In addition, we found that these descriptive statistics of the systemic risk are similar for MSD, VaR, ES, EVaR, or ML. As mentioned for the single-index risks, this observation is explained by the similarity of these risk measures’ historical evolution over the period considered. The similarity between the descriptive statistics is greater for ES, EVaR, ML, and VaR. These are tail risk measures, and the significance levels were chosen to make them similar. We have also considered other weighted averages as aggregation functions as a robustness check. In particular, we observed that the systemic risk behavior remains qualitatively equal when the weights are given by the number of deaths and cases per 1 million inhabitants. Because of this similarity, these results are omitted from the study.

Furthermore, to confirm whether the evolution of systemic and single-index risks from different markets moved in similar directions during the sample period, we describe in Table 16 a correlation of the VaR risks of each market with the systemic risk computed by VaR.34 We note that during sub-sample 1, the correlation tends to be negative. Thus, each market’s risk does not follow the behavior of systemic risk. This result indicates no spread of financial disturbances from one market to another in the period before the pandemic. However, we observed that this correlation was positive for most markets during the pandemic. Corroborating with our descriptive statistics, we can conclude that as the single-index risk of the markets increased, the risk of the system followed the same direction. It is also noted that the correlations between single-index risk from countries and systemic risk differ. This finding indicates that the contribution of each market to the risk of the system tends to be different. Future analysis can investigate the markets that most contributed to political uncertainty and panic in the economy of each of the markets analyzed during the pandemic. Investigations along these lines, for the spread of the Subprime Crisis and the European Sovereign Debt Crisis, are found in Samitas et al. (2020). However, this point deserves future investigations into the current crisis.

5. Conclusions

In this paper, we describe how COVID-19 affected the risk of individual market indexes and the risk of the system composed of these indexes. We considered market indexes from the thirty-five countries with the higher number of cases and deaths by COVID-19. Our results confirm that the impact of the COVID-19 pandemic was felt beyond the health sector and led to severe consequences in stock markets and the financial system composed of these markets.

We assessed the single-index risk with VaR, ES, EL, EVaR, MSD, and ML using a semi-parametric approach known as Filtered Historical Simulation. Our single-index risk estimates corroborate known facts and unveil new ones. For instance, we observed that the initial financial shock of March 2020, which was already documented in the literature, occurred with a remarkable simultaneity across a large sample of countries. Moreover, this synchronicity involved a time delay between the maximum loss and the peak of their risks. Also, we could identify that some European and American countries, particularly those which were, at some point, epicenters of the COVID-19 pandemic, had their financial markets among the most affected in our sample.

We quantified the systemic risk using the approach developed by Chen et al. (2013). This approach considers a single component risk measure and an aggregation function. As single component risk measures, we used those employed for the single-index risk analysis. We considered three aggregation functions, which are averages with different weights. As the benchmark, we used the naive average, and we further considered aggregation functions based on the number of confirmed cases and deaths due to COVID-19 in each country. Regardless of the combination of risk measure and aggregation functions being employed, the systemic risk followed the single-index risks, in that both spiked during March 2020. The systemic risk remained above pre-pandemic levels until the end of 2020.

The estimates we obtained for the systemic risk were consistent across several “robustness checks”. Our estimates are similar for the various aggregation functions and most single component risk measures considered. This result indicates that the systemic risk measures we employed are reliable tools for measuring systemic risk. We present a detailed description of the dynamics of systemic risk, illustrating Chen’s approach’s potential to serve as a tool for regulatory authorities and policymakers to assess, monitor, and manage systemic risk.

CRediT authorship contribution statement

Fernanda Maria Müller: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Software, Supervision, Validation, Visualization, Roles/Writing – original draft, Writing – review & editing. Samuel Solgon Santos: Formal analysis, Funding acquisition, Investigation, Resources, Software, Validation, Visualization, Roles/Writing – original draft, Writing – review & editing. Marcelo Brutti Righi: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Roles/Writing – original draft, Writing – review & editing.

Declaration of Competing Interest

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.

Appendix. Appendix - results of empirical analysis

See Table 11, Table 12, Table 13, Table 14, Table 15, Table 16, Table 17, Table 18, Table 19, Table 20.

Table 16.

Correlation (Kendall correlation) matrix between VaR estimates for market indexes from November 17, 2018, to October 25, 2021. Correlations were performed only for the sub-samples. Sub-sample 1 comprehends risk forecasting from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends risk forecasting from November 17, 2019, to October 25, 2021.

Countries	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35
	Sub-sample 1
Argentina	1.000	0.999	0.151	1.000	0.999	0.821	1.000	−0.002	0.999	0.053	0.596	0.031	0.588	0.037	−0.265	−0.517	0.673	1.000	0.215	−0.126	0.261	0.410	0.291	0.729	0.338	−0.278	1.000	0.455	0.099	1.000	0.894	0.830	0.389	0.439	1.000
Austria	0.999	1.000	0.150	0.999	0.998	0.820	0.999	−0.003	0.999	0.052	0.595	0.031	0.587	0.037	−0.264	−0.517	0.672	0.999	0.215	−0.127	0.261	0.409	0.290	0.728	0.337	−0.278	0.999	0.454	0.098	0.999	0.893	0.830	0.388	0.438	0.999
Bangladesh	0.151	0.150	1.000	0.151	0.151	0.103	0.151	0.063	0.151	0.036	0.026	0.106	0.121	0.083	−0.007	−0.196	0.051	0.151	0.001	0.176	0.038	0.132	−0.046	0.095	−0.080	−0.085	0.151	0.101	−0.019	0.151	0.128	0.121	0.187	−0.008	0.151
Belgium	1.000	0.999	0.151	1.000	0.999	0.821	1.000	−0.002	0.999	0.053	0.596	0.031	0.588	0.037	−0.265	−0.517	0.673	1.000	0.215	−0.127	0.261	0.410	0.291	0.729	0.338	−0.278	1.000	0.455	0.099	1.000	0.894	0.830	0.389	0.439	1.000
Brazil	0.999	0.998	0.151	0.999	1.000	0.820	0.999	−0.002	0.998	0.052	0.595	0.031	0.587	0.037	−0.265	−0.516	0.672	0.999	0.215	−0.126	0.262	0.409	0.290	0.729	0.338	−0.278	0.999	0.455	0.098	0.999	0.893	0.830	0.388	0.439	0.999
Canada	0.821	0.820	0.103	0.821	0.820	1.000	0.821	0.109	0.820	0.127	0.710	−0.002	0.632	0.014	−0.234	−0.374	0.782	0.821	0.269	−0.118	0.327	0.456	0.353	0.839	0.454	−0.222	0.821	0.473	0.131	0.821	0.892	0.860	0.380	0.506	0.821
Chile	1.000	0.999	0.151	1.000	0.999	0.821	1.000	−0.002	0.999	0.053	0.596	0.031	0.588	0.037	−0.265	−0.517	0.673	1.000	0.215	−0.126	0.261	0.410	0.291	0.729	0.338	−0.278	1.000	0.455	0.099	1.000	0.894	0.830	0.389	0.439	1.000
China	−0.002	−0.003	0.063	−0.002	−0.002	0.109	−0.002	1.000	−0.003	−0.064	0.202	0.067	0.215	0.008	0.241	−0.170	0.204	−0.002	0.078	0.205	0.088	0.450	0.333	0.179	0.240	0.050	−0.002	0.173	−0.294	−0.002	0.044	0.082	0.438	0.294	−0.002
Czechia	0.999	0.999	0.151	0.999	0.998	0.820	0.999	−0.003	1.000	0.053	0.595	0.031	0.587	0.037	−0.264	−0.517	0.672	0.999	0.215	−0.127	0.261	0.409	0.290	0.729	0.337	−0.278	0.999	0.454	0.099	0.999	0.893	0.830	0.388	0.438	0.999
Egypt	0.053	0.052	0.036	0.053	0.052	0.127	0.053	−0.064	0.053	1.000	0.242	−0.112	0.023	0.003	−0.141	0.161	0.137	0.053	0.275	0.169	0.314	−0.022	0.197	0.214	0.277	0.152	0.053	0.215	0.414	0.053	0.108	0.144	0.035	0.221	0.053
France	0.596	0.595	0.026	0.596	0.595	0.710	0.596	0.202	0.595	0.242	1.000	−0.085	0.617	0.015	−0.102	−0.225	0.814	0.596	0.319	−0.146	0.441	0.494	0.486	0.763	0.598	−0.077	0.596	0.541	0.255	0.596	0.690	0.740	0.478	0.725	0.596
Germany	0.031	0.031	0.106	0.031	0.031	−0.002	0.031	0.067	0.031	−0.112	−0.085	1.000	0.000	−0.022	−0.021	−0.157	−0.029	0.031	−0.094	0.163	−0.090	0.037	−0.142	−0.048	−0.188	0.048	0.031	−0.036	−0.140	0.031	−0.010	−0.039	0.006	−0.040	0.031
India	0.588	0.587	0.121	0.588	0.587	0.632	0.588	0.215	0.587	0.023	0.617	0.000	1.000	0.061	−0.066	−0.322	0.695	0.588	0.233	−0.034	0.219	0.622	0.348	0.646	0.432	−0.101	0.588	0.447	0.097	0.588	0.662	0.616	0.397	0.478	0.588
Indonesia	0.037	0.037	0.083	0.037	0.037	0.014	0.037	0.008	0.037	0.003	0.015	−0.022	0.061	1.000	0.031	−0.013	0.034	0.037	−0.017	−0.002	−0.055	0.025	0.002	0.052	0.018	−0.038	0.037	0.066	0.037	0.037	0.034	0.029	0.031	0.048	0.037
Iraq	−0.265	−0.264	−0.007	−0.265	−0.265	−0.234	−0.265	0.241	−0.264	−0.141	−0.102	−0.021	−0.066	0.031	1.000	0.046	−0.098	−0.265	−0.178	0.039	−0.022	0.052	0.127	−0.191	−0.096	0.114	−0.265	−0.073	−0.156	−0.265	−0.232	−0.204	0.090	0.058	−0.265
Israel	−0.517	−0.517	−0.196	−0.517	−0.516	−0.374	−0.517	−0.170	−0.517	0.161	−0.225	−0.157	−0.322	−0.013	0.046	1.000	−0.282	−0.517	−0.011	−0.001	−0.022	−0.225	−0.055	−0.300	−0.056	0.144	−0.517	−0.199	0.110	−0.517	−0.431	−0.383	−0.362	−0.239	−0.517
Italy	0.673	0.672	0.051	0.673	0.672	0.782	0.673	0.204	0.672	0.137	0.814	−0.029	0.695	0.034	−0.098	−0.282	1.000	0.673	0.273	−0.077	0.323	0.591	0.429	0.799	0.519	−0.121	0.673	0.505	0.173	0.673	0.768	0.749	0.474	0.638	0.673
Morocco	1.000	0.999	0.151	1.000	0.999	0.821	1.000	−0.002	0.999	0.053	0.596	0.031	0.588	0.037	−0.265	−0.517	0.673	1.000	0.215	−0.126	0.261	0.410	0.291	0.729	0.338	−0.278	1.000	0.455	0.099	1.000	0.894	0.830	0.389	0.439	1.000
Mexico	0.215	0.215	0.001	0.215	0.215	0.269	0.215	0.078	0.215	0.275	0.319	−0.094	0.233	−0.017	−0.178	−0.011	0.273	0.215	1.000	0.042	0.278	0.191	0.376	0.268	0.326	0.131	0.215	0.182	0.222	0.215	0.279	0.306	0.152	0.267	0.215
Nepal	−0.126	−0.127	0.176	−0.127	−0.126	−0.118	−0.126	0.205	−0.127	0.169	−0.146	0.163	−0.034	−0.002	0.039	−0.001	−0.077	−0.126	0.042	1.000	−0.148	0.058	−0.032	−0.062	−0.128	0.030	−0.126	−0.030	−0.024	−0.127	−0.130	−0.125	0.047	−0.084	−0.127
Netherlands	0.261	0.261	0.038	0.261	0.262	0.327	0.261	0.088	0.261	0.314	0.441	−0.090	0.219	−0.055	−0.022	−0.022	0.323	0.261	0.278	−0.148	1.000	0.147	0.421	0.349	0.460	0.157	0.261	0.303	0.285	0.261	0.307	0.349	0.172	0.363	0.261
Pakistan	0.410	0.409	0.132	0.410	0.409	0.456	0.410	0.450	0.409	−0.022	0.494	0.037	0.622	0.025	0.052	−0.225	0.591	0.410	0.191	0.058	0.147	1.000	0.337	0.505	0.371	−0.091	0.410	0.341	−0.134	0.410	0.481	0.442	0.538	0.460	0.410
Philippines	0.291	0.290	−0.046	0.291	0.290	0.353	0.291	0.333	0.290	0.197	0.486	−0.142	0.348	0.002	0.127	−0.055	0.429	0.291	0.376	−0.032	0.421	0.337	1.000	0.419	0.440	0.086	0.291	0.316	0.163	0.291	0.352	0.410	0.288	0.462	0.291
Poland	0.729	0.728	0.095	0.729	0.729	0.839	0.729	0.179	0.729	0.214	0.763	−0.048	0.646	0.052	−0.191	−0.300	0.799	0.729	0.268	−0.062	0.349	0.505	0.419	1.000	0.504	−0.232	0.729	0.542	0.194	0.729	0.808	0.807	0.449	0.583	0.729
Portugal	0.338	0.337	−0.080	0.338	0.338	0.454	0.338	0.240	0.337	0.277	0.598	−0.188	0.432	0.018	−0.096	−0.056	0.519	0.338	0.326	−0.128	0.460	0.371	0.440	0.504	1.000	0.132	0.338	0.346	0.255	0.338	0.419	0.443	0.263	0.536	0.338
Romania	−0.278	−0.278	−0.085	−0.278	−0.278	−0.222	−0.278	0.050	−0.278	0.152	−0.077	0.048	−0.101	−0.038	0.114	0.144	−0.121	−0.278	0.131	0.030	0.157	−0.091	0.086	−0.232	0.132	1.000	−0.278	0.015	0.193	−0.278	−0.235	−0.215	−0.135	0.038	−0.278
Russia	1.000	0.999	0.151	1.000	0.999	0.821	1.000	−0.002	0.999	0.053	0.596	0.031	0.588	0.037	−0.265	−0.517	0.673	1.000	0.215	−0.126	0.261	0.410	0.291	0.729	0.338	−0.278	1.000	0.455	0.099	1.000	0.894	0.830	0.389	0.439	1.000
Saudi Arabia	0.455	0.454	0.101	0.455	0.455	0.473	0.455	0.173	0.454	0.215	0.541	−0.036	0.447	0.066	−0.073	−0.199	0.505	0.455	0.182	−0.030	0.303	0.341	0.316	0.542	0.346	0.015	0.455	1.000	0.166	0.455	0.455	0.491	0.350	0.416	0.455
South Africa	0.099	0.098	−0.019	0.099	0.098	0.131	0.099	−0.294	0.099	0.414	0.255	−0.140	0.097	0.037	−0.156	0.110	0.173	0.099	0.222	−0.024	0.285	−0.134	0.163	0.194	0.255	0.193	0.099	0.166	1.000	0.099	0.141	0.193	−0.085	0.189	0.099
Spain	1.000	0.999	0.151	1.000	0.999	0.821	1.000	−0.002	0.999	0.053	0.596	0.031	0.588	0.037	−0.265	−0.517	0.673	1.000	0.215	−0.127	0.261	0.410	0.291	0.729	0.338	−0.278	1.000	0.455	0.099	1.000	0.894	0.830	0.389	0.439	1.000
Sweden	0.894	0.893	0.128	0.894	0.893	0.892	0.894	0.044	0.893	0.108	0.690	−0.010	0.662	0.034	−0.232	−0.431	0.768	0.894	0.279	−0.130	0.307	0.481	0.352	0.808	0.419	−0.235	0.894	0.455	0.141	0.894	1.000	0.892	0.389	0.505	0.894
Switzerland	0.830	0.830	0.121	0.830	0.830	0.860	0.830	0.082	0.830	0.144	0.740	−0.039	0.616	0.029	−0.204	−0.383	0.749	0.830	0.306	−0.125	0.349	0.442	0.410	0.807	0.443	−0.215	0.830	0.491	0.193	0.830	0.892	1.000	0.437	0.541	0.830
Turkey	0.389	0.388	0.187	0.389	0.388	0.380	0.389	0.438	0.388	0.035	0.478	0.006	0.397	0.031	0.090	−0.362	0.474	0.389	0.152	0.047	0.172	0.538	0.288	0.449	0.263	−0.135	0.389	0.350	−0.085	0.389	0.389	0.437	1.000	0.514	0.389
UK	0.439	0.438	−0.008	0.439	0.439	0.506	0.439	0.294	0.438	0.221	0.725	−0.040	0.478	0.048	0.058	−0.239	0.638	0.439	0.267	−0.084	0.363	0.460	0.462	0.583	0.536	0.038	0.439	0.416	0.189	0.439	0.505	0.541	0.514	1.000	0.439
USA	1.000	0.999	0.151	1.000	0.999	0.821	1.000	−0.002	0.999	0.053	0.596	0.031	0.588	0.037	−0.265	−0.517	0.673	1.000	0.215	−0.127	0.261	0.410	0.291	0.729	0.338	−0.278	1.000	0.455	0.099	1.000	0.894	0.830	0.389	0.439	1.000
	Sub-sample 2
Argentina	1.000	1.000	−0.108	0.983	0.998	0.068	1.000	0.180	1.000	−0.107	0.066	−0.099	−0.082	0.001	0.193	0.027	0.135	1.000	0.095	−0.051	0.094	−0.043	−0.041	0.127	0.182	0.098	1.000	−0.239	0.080	1.000	0.029	0.024	0.065	0.034	1.000
Austria	1.000	1.000	−0.108	0.983	0.998	0.068	1.000	0.180	1.000	−0.107	0.066	−0.099	−0.082	0.001	0.193	0.027	0.135	1.000	0.095	−0.051	0.094	−0.043	−0.041	0.127	0.182	0.098	1.000	−0.239	0.080	1.000	0.029	0.024	0.065	0.034	1.000
Bangladesh	−0.108	−0.108	1.000	−0.114	−0.107	−0.363	−0.108	0.025	−0.108	−0.096	−0.275	0.138	−0.037	0.022	0.043	−0.264	−0.200	−0.108	−0.147	0.426	−0.228	0.002	−0.189	−0.269	−0.228	−0.191	−0.108	0.006	−0.302	−0.108	−0.382	−0.353	0.035	−0.173	−0.108
Belgium	0.983	0.983	−0.114	1.000	0.983	0.052	0.983	0.171	0.983	−0.122	0.050	−0.084	−0.098	−0.001	0.192	0.013	0.120	0.983	0.080	−0.048	0.079	−0.058	−0.057	0.111	0.166	0.083	0.983	−0.248	0.064	0.983	0.013	0.008	0.048	0.017	0.983
Brazil	0.998	0.998	−0.107	0.983	1.000	0.067	0.998	0.181	0.998	−0.108	0.065	−0.098	−0.083	0.002	0.195	0.027	0.136	0.998	0.095	−0.051	0.094	−0.044	−0.042	0.127	0.182	0.098	0.998	−0.238	0.079	0.998	0.028	0.023	0.064	0.034	0.998
Canada	0.068	0.068	−0.363	0.052	0.067	1.000	0.068	0.349	0.068	0.450	0.780	−0.406	0.350	0.085	0.156	0.773	0.590	0.068	0.477	−0.150	0.671	0.276	0.610	0.730	0.680	0.632	0.068	0.122	0.763	0.068	0.840	0.876	0.354	0.579	0.068
Chile	1.000	1.000	−0.108	0.983	0.998	0.068	1.000	0.180	1.000	−0.107	0.066	−0.099	−0.082	0.001	0.193	0.027	0.135	1.000	0.095	−0.051	0.094	−0.043	−0.041	0.127	0.182	0.098	1.000	−0.239	0.080	1.000	0.029	0.024	0.065	0.034	1.000
China	0.180	0.180	0.025	0.171	0.181	0.349	0.180	1.000	0.180	0.266	0.352	−0.197	0.177	0.110	0.327	0.377	0.331	0.180	0.142	0.300	0.325	0.109	0.372	0.281	0.264	0.305	0.180	−0.051	0.291	0.180	0.368	0.387	0.430	0.348	0.180
Czechia	1.000	1.000	−0.108	0.983	0.998	0.068	1.000	0.180	1.000	−0.107	0.066	−0.099	−0.082	0.001	0.193	0.027	0.135	1.000	0.095	−0.051	0.094	−0.043	−0.041	0.127	0.182	0.098	1.000	−0.239	0.080	1.000	0.029	0.024	0.065	0.034	1.000
Egypt	−0.107	−0.107	−0.096	−0.122	−0.108	0.450	−0.107	0.266	−0.107	1.000	0.482	−0.318	0.238	0.086	0.027	0.502	0.331	−0.107	0.382	0.001	0.451	0.310	0.561	0.424	0.405	0.409	−0.107	0.273	0.455	−0.107	0.434	0.484	0.241	0.424	−0.107
France	0.066	0.066	−0.275	0.050	0.065	0.780	0.066	0.352	0.066	0.482	1.000	−0.408	0.481	0.101	0.119	0.769	0.747	0.066	0.550	−0.087	0.705	0.386	0.669	0.798	0.761	0.731	0.066	0.215	0.816	0.066	0.736	0.798	0.417	0.732	0.066
Germany	−0.099	−0.099	0.138	−0.084	−0.098	−0.406	−0.099	−0.197	−0.099	−0.318	−0.408	1.000	−0.291	−0.169	−0.042	−0.440	−0.342	−0.099	−0.423	0.084	−0.389	−0.258	−0.402	−0.454	−0.465	−0.421	−0.099	−0.242	−0.462	−0.099	−0.406	−0.437	−0.266	−0.349	−0.099
India	−0.082	−0.082	−0.037	−0.098	−0.083	0.350	−0.082	0.177	−0.082	0.238	0.481	−0.291	1.000	0.109	0.033	0.466	0.595	−0.082	0.442	−0.070	0.406	0.492	0.397	0.451	0.424	0.497	−0.082	0.379	0.463	−0.082	0.325	0.352	0.355	0.578	−0.082
Indonesia	0.001	0.001	0.022	−0.001	0.002	0.085	0.001	0.110	0.001	0.086	0.101	−0.169	0.109	1.000	−0.037	0.137	0.123	0.001	0.138	0.026	0.100	0.101	0.114	0.137	0.138	0.159	0.001	0.104	0.130	0.001	0.083	0.090	0.115	0.129	0.001
Iraq	0.193	0.193	0.043	0.192	0.195	0.156	0.193	0.327	0.193	0.027	0.119	−0.042	0.033	−0.037	1.000	0.167	0.140	0.193	−0.011	0.253	0.122	−0.134	0.155	0.053	0.004	0.036	0.193	−0.171	0.069	0.193	0.202	0.155	0.162	0.140	0.193
Israel	0.027	0.027	−0.264	0.013	0.027	0.773	0.027	0.377	0.027	0.502	0.769	−0.440	0.466	0.137	0.167	1.000	0.632	0.027	0.562	−0.022	0.685	0.382	0.667	0.733	0.695	0.678	0.027	0.243	0.783	0.027	0.698	0.746	0.373	0.643	0.027
Italy	0.135	0.135	−0.200	0.120	0.136	0.590	0.135	0.331	0.135	0.331	0.747	−0.342	0.595	0.123	0.140	0.632	1.000	0.135	0.504	−0.061	0.581	0.381	0.521	0.721	0.669	0.659	0.135	0.211	0.690	0.135	0.584	0.618	0.479	0.750	0.135
Morocco	1.000	1.000	−0.108	0.983	0.998	0.068	1.000	0.180	1.000	−0.107	0.066	−0.099	−0.082	0.001	0.193	0.027	0.135	1.000	0.095	−0.051	0.094	−0.043	−0.041	0.127	0.182	0.098	1.000	−0.239	0.080	1.000	0.029	0.024	0.065	0.034	1.000
Mexico	0.095	0.095	−0.147	0.080	0.095	0.477	0.095	0.142	0.095	0.382	0.550	−0.423	0.442	0.138	−0.011	0.562	0.504	0.095	1.000	−0.187	0.537	0.432	0.484	0.573	0.620	0.624	0.095	0.287	0.611	0.095	0.428	0.477	0.250	0.473	0.095
Nepal	−0.051	−0.051	0.426	−0.048	−0.051	−0.150	−0.051	0.300	−0.051	0.001	−0.087	0.084	−0.070	0.026	0.253	−0.022	−0.061	−0.051	−0.187	1.000	−0.132	−0.088	−0.007	−0.135	−0.146	−0.108	−0.051	−0.035	−0.140	−0.051	−0.140	−0.113	0.111	0.021	−0.051
Netherlands	0.094	0.094	−0.228	0.079	0.094	0.671	0.094	0.325	0.094	0.451	0.705	−0.389	0.406	0.100	0.122	0.685	0.581	0.094	0.537	−0.132	1.000	0.355	0.612	0.657	0.648	0.638	0.094	0.166	0.709	0.094	0.633	0.687	0.369	0.557	0.094
Pakistan	−0.043	−0.043	0.002	−0.058	−0.044	0.276	−0.043	0.109	−0.043	0.310	0.386	−0.258	0.492	0.101	−0.134	0.382	0.381	−0.043	0.432	−0.088	0.355	1.000	0.324	0.421	0.447	0.459	−0.043	0.506	0.402	−0.043	0.184	0.244	0.210	0.386	−0.043
Philippines	−0.041	−0.041	−0.189	−0.057	−0.042	0.610	−0.041	0.372	−0.041	0.561	0.669	−0.402	0.397	0.114	0.155	0.667	0.521	−0.041	0.484	−0.007	0.612	0.324	1.000	0.582	0.544	0.592	−0.041	0.221	0.630	−0.041	0.597	0.667	0.352	0.567	−0.041
Poland	0.127	0.127	−0.269	0.111	0.127	0.730	0.127	0.281	0.127	0.424	0.798	−0.454	0.451	0.137	0.053	0.733	0.721	0.127	0.573	−0.135	0.657	0.421	0.582	1.000	0.835	0.755	0.127	0.276	0.819	0.127	0.670	0.732	0.447	0.649	0.127
Portugal	0.182	0.182	−0.228	0.166	0.182	0.680	0.182	0.264	0.182	0.405	0.761	−0.465	0.424	0.138	0.004	0.695	0.669	0.182	0.620	−0.146	0.648	0.447	0.544	0.835	1.000	0.730	0.182	0.262	0.773	0.182	0.609	0.676	0.415	0.607	0.182
Romania	0.098	0.098	−0.191	0.083	0.098	0.632	0.098	0.305	0.098	0.409	0.731	−0.421	0.497	0.159	0.036	0.678	0.659	0.098	0.624	−0.108	0.638	0.459	0.592	0.755	0.730	1.000	0.098	0.283	0.718	0.098	0.555	0.622	0.390	0.653	0.098
Russia	1.000	1.000	−0.108	0.983	0.998	0.068	1.000	0.180	1.000	−0.107	0.066	−0.099	−0.082	0.001	0.193	0.027	0.135	1.000	0.095	−0.051	0.094	−0.043	−0.041	0.127	0.182	0.098	1.000	−0.239	0.080	1.000	0.029	0.024	0.065	0.034	1.000
SaudiArabia	−0.239	−0.239	0.006	−0.248	−0.238	0.122	−0.239	−0.051	−0.239	0.273	0.215	−0.242	0.379	0.104	−0.171	0.243	0.211	−0.239	0.287	−0.035	0.166	0.506	0.221	0.276	0.262	0.283	−0.239	1.000	0.251	−0.239	0.052	0.111	0.213	0.271	−0.239
SouthAfrica	0.080	0.080	−0.302	0.064	0.079	0.763	0.080	0.291	0.080	0.455	0.816	−0.462	0.463	0.130	0.069	0.783	0.690	0.080	0.611	−0.140	0.709	0.402	0.630	0.819	0.773	0.718	0.080	0.251	1.000	0.080	0.706	0.769	0.415	0.654	0.080
Spain	1.000	1.000	−0.108	0.983	0.998	0.068	1.000	0.180	1.000	−0.107	0.066	−0.099	−0.082	0.001	0.193	0.027	0.135	1.000	0.095	−0.051	0.094	−0.043	−0.041	0.127	0.182	0.098	1.000	−0.239	0.080	1.000	0.029	0.024	0.065	0.034	1.000
Sweden	0.029	0.029	−0.382	0.013	0.028	0.840	0.029	0.368	0.029	0.434	0.736	−0.406	0.325	0.083	0.202	0.698	0.584	0.029	0.428	−0.140	0.633	0.184	0.597	0.670	0.609	0.555	0.029	0.052	0.706	0.029	1.000	0.875	0.381	0.570	0.029
Switzerland	0.024	0.024	−0.353	0.008	0.023	0.876	0.024	0.387	0.024	0.484	0.798	−0.437	0.352	0.090	0.155	0.746	0.618	0.024	0.477	−0.113	0.687	0.244	0.667	0.732	0.676	0.622	0.024	0.111	0.769	0.024	0.875	1.000	0.409	0.596	0.024
Turkey	0.065	0.065	0.035	0.048	0.064	0.354	0.065	0.430	0.065	0.241	0.417	−0.266	0.355	0.115	0.162	0.373	0.479	0.065	0.250	0.111	0.369	0.210	0.352	0.447	0.415	0.390	0.065	0.213	0.415	0.065	0.381	0.409	1.000	0.408	0.065
UK	0.034	0.034	−0.173	0.017	0.034	0.579	0.034	0.348	0.034	0.424	0.732	−0.349	0.578	0.129	0.140	0.643	0.750	0.034	0.473	0.021	0.557	0.386	0.567	0.649	0.607	0.653	0.034	0.271	0.654	0.034	0.570	0.596	0.408	1.000	0.034
USA	1.000	1.000	−0.108	0.983	0.998	0.068	1.000	0.180	1.000	−0.107	0.066	−0.099	−0.082	0.001	0.193	0.027	0.135	1.000	0.095	−0.051	0.094	−0.043	−0.041	0.127	0.182	0.098	1.000	−0.239	0.080	1.000	0.029	0.024	0.065	0.034	1.000

Note: In the line that labels each column, i.e., the country names, we use numbers to represent each country. We did this to organize the table on the same page. 1 is Argentina, 2 is Austria, 3 is Bangladesh, 4 is Belgium, 5 is Brazil, 6 is Canada, 7 is Chile, 8 is China, 9 is Czechia, 10 is Egypt, 11 is France, 12 is Germany, 13 is India, 14 is Indonesia, 15 is Iraq, 16 is Israel, 17 is Italy, 18 is Morocco, 19 is Mexico, 20 is Nepal, 21 is Netherlands, 22 is Pakistan, 23 is Philippines, 24 is Poland, 25 is Portugal, 26 is Romania, 27 is Russia, 28 is Saudi Arabia, 29 is South Africa, 30 is Spain, 31 is Sweden, 32 is Switzerland, 33 is Turkey, 34 is UK, and 35 is USA. Results for the full sample are omitted for brevity but are available on request.

Table 17.

Dates of maximum risk values and minimum values for the countries and risk measures considered. The date at the top is for the maximum, and the bottom is the minimum.

Countries	VaR	EL	MSD	ES	EVaR	ML
Argentina	08/13/2019	08/14/2019	08/15/2019	08/13/2019	08/13/2019	08/13/2019
	11/20/2018	08/13/2019	11/21/2018	11/20/2018	11/20/2018	11/20/2018
Austria	03/18/2020	03/22/2020	03/18/2020	03/18/2020	03/18/2020	03/18/2020
	01/08/2021	04/21/2021	01/08/2021	01/08/2021	01/08/2021	01/08/2021
Bangladesh	03/20/2020	11/18/2018	03/20/2020	03/20/2020	03/20/2020	03/20/2020
	11/19/2018	03/20/2020	11/19/2018	11/19/2018	11/19/2018	11/19/2018
Belgium	03/18/2020	03/25/2020	03/18/2020	03/18/2020	03/17/2020	03/17/2020
	12/30/2019	02/25/2020	12/30/2019	12/30/2019	12/30/2019	12/30/2019
Brazil	03/20/2020	03/15/2020	03/18/2020	03/20/2020	03/20/2020	03/20/2020
	12/27/2019	03/13/2020	12/29/2019	12/27/2019	12/27/2019	12/27/2019
Canada	03/19/2020	03/15/2020	03/19/2020	03/19/2020	03/19/2020	03/19/2020
	01/19/2020	01/22/2020	01/19/2020	01/19/2020	01/19/2020	01/19/2020
Chile	03/22/2020	03/17/2020	03/22/2020	03/22/2020	03/22/2020	03/22/2020
	01/13/2019	11/17/2019	01/13/2019	01/13/2019	01/13/2019	01/13/2019
China	03/26/2020	07/07/2020	03/26/2020	03/26/2020	03/26/2020	03/26/2020
	11/19/2018	02/04/2020	11/19/2018	11/19/2018	11/19/2018	11/19/2018
Czechia	03/17/2020	03/17/2020	03/17/2020	03/17/2020	03/17/2020	03/17/2020
	11/18/2018	07/16/2021	01/23/2020	11/18/2018	11/18/2018	11/18/2018
Egypt	03/17/2020	03/16/2020	03/17/2020	03/17/2020	03/19/2020	03/19/2020
	02/18/2019	03/23/2020	06/08/2020	02/18/2019	02/18/2019	02/18/2019
France	03/19/2020	03/20/2020	03/19/2020	03/19/2020	03/19/2020	03/19/2020
	04/18/2021	04/21/2021	04/18/2021	04/18/2021	04/18/2021	04/18/2021
Germany	03/19/2020	03/25/2020	03/20/2020	03/19/2020	03/19/2020	03/19/2020
	08/15/2021	03/13/2020	08/16/2021	08/15/2021	08/15/2021	08/15/2021
India	03/25/2020	03/24/2020	03/25/2020	03/25/2020	03/25/2020	03/25/2020
	09/01/2021	04/08/2020	09/01/2021	09/01/2021	09/01/2021	09/01/2021
Indonesia	03/20/2020	03/27/2020	03/20/2020	03/20/2020	03/20/2020	03/20/2020
	01/28/2019	03/10/2020	01/28/2019	01/28/2019	01/28/2019	01/28/2019
Iraq	08/26/2021	08/19/2021	08/26/2021	08/26/2021	08/26/2021	08/26/2021
	04/26/2020	05/07/2020	04/26/2020	04/26/2020	04/26/2020	04/26/2020
Israel	03/26/2020	01/15/2020	03/26/2020	03/26/2020	03/26/2020	03/26/2020
	01/15/2020	03/26/2020	01/15/2020	01/15/2020	01/15/2020	01/15/2020
Italy	03/13/2020	03/25/2020	03/19/2020	03/13/2020	03/13/2020	03/13/2020
	04/04/2019	03/13/2020	04/07/2019	04/04/2019	04/04/2019	04/04/2019
Morocco	03/30/2020	03/10/2020	03/29/2020	03/30/2020	03/30/2020	03/30/2020
	07/06/2021	03/25/2020	02/01/2019	07/06/2021	07/06/2021	07/06/2021
Mexico	03/17/2020	03/17/2020	03/17/2020	03/17/2020	03/20/2020	03/20/2020
	05/03/2021	03/11/2020	05/03/2021	05/03/2021	05/03/2021	05/03/2021
Nepal	07/03/2020	11/18/2018	07/03/2020	07/03/2020	07/03/2020	07/03/2020
	11/18/2018	07/03/2020	11/18/2018	11/18/2018	11/18/2018	11/18/2018
Netherlands	03/13/2020	03/25/2020	03/19/2020	03/13/2020	03/13/2020	03/13/2020
	04/24/2019	03/13/2020	04/24/2019	04/24/2019	04/24/2019	04/24/2019
Pakistan	03/18/2020	03/24/2020	03/18/2020	03/18/2020	03/18/2020	03/18/2020
	07/27/2021	04/17/2020	07/27/2021	07/27/2021	07/27/2021	07/27/2021
Philippines	03/22/2020	03/27/2020	03/22/2020	03/22/2020	03/22/2020	03/22/2020
	07/15/2019	03/20/2020	07/17/2019	07/15/2019	07/15/2019	07/15/2019
Poland	03/15/2020	03/18/2020	03/15/2020	03/15/2020	03/15/2020	03/13/2020
	06/07/2021	03/13/2020	06/08/2021	06/07/2021	06/07/2021	06/07/2021
Portugal	03/15/2020	03/25/2020	03/15/2020	03/15/2020	03/15/2020	03/15/2020
	01/21/2020	03/13/2020	01/21/2020	01/21/2020	01/21/2020	01/21/2020
Romania	12/20/2018	12/20/2018	12/20/2018	12/20/2018	12/20/2018	12/20/2018
	01/27/2020	01/10/2021	01/27/2020	01/27/2020	01/27/2020	01/27/2020
Russia	03/26/2020	03/20/2020	03/26/2020	03/26/2020	03/26/2020	03/26/2020
	01/03/2020	03/11/2020	05/08/2019	01/03/2020	01/05/2020	01/05/2020
Saudi Arabia	03/12/2020	03/09/2020	03/12/2020	03/12/2020	03/12/2020	03/12/2020
	08/24/2020	03/11/2020	08/19/2020	08/24/2020	08/24/2020	08/24/2020
South Africa	03/20/2020	03/27/2020	03/25/2020	03/20/2020	03/20/2020	03/20/2020
	04/24/2019	03/13/2020	04/25/2019	04/24/2019	04/24/2019	04/24/2019
Spain	03/17/2020	03/25/2020	03/18/2020	03/17/2020	03/17/2020	03/17/2020
	04/23/2019	03/13/2020	04/23/2019	04/23/2019	04/23/2019	04/23/2019
Sweden	03/26/2020	03/25/2020	03/25/2020	03/26/2020	03/26/2020	03/26/2020
	12/30/2019	03/13/2020	12/31/2019	12/30/2019	12/30/2019	12/30/2019
Switzerland	03/13/2020	03/25/2020	03/13/2020	03/13/2020	03/13/2020	03/13/2020
	12/23/2020	03/13/2020	02/01/2021	12/23/2020	12/23/2020	12/23/2020
Turkey	03/17/2020	03/23/2021	03/17/2020	03/17/2020	03/17/2020	03/17/2020
	11/12/2020	01/10/2020	11/12/2020	11/12/2020	11/12/2020	11/12/2020
UK	03/20/2020	03/20/2020	03/20/2020	03/20/2020	03/20/2020	03/20/2020
	12/15/2019	11/10/2020	12/15/2019	12/15/2019	12/15/2019	12/15/2019
USA	03/17/2020	03/15/2020	03/18/2020	03/17/2020	03/17/2020	03/17/2020
	12/29/2019	03/17/2020	12/30/2019	12/29/2019	12/29/2019	09/03/2020

Table 18.

Bilateral and right one-tailed Mann–Whitney test applied on systemic risk estimates from Sub-sample 1 and Sub-sample 2. This table presents the $p$-value of the test. Sub-sample 1 comprehends data from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends data from November 17, 2019, to October 25, 2021.

Bilateral
Aggregated indexes	VaR	EL	MSD	ES	EVaR	ML
${\Lambda }_C$	0.031${}^{\ast \ast }$	0.015${}^{\ast }$	0.039${}^{\ast \ast }$	0.031${}^{\ast \ast }$	0.031${}^{\ast \ast }$	0.030${}^{\ast \ast }$
${\Lambda }_D$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$
${\Lambda }_N$	$<0.001^{\ast \ast \ast }$	0.334	0.001${}^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Right-tailed
Aggregated indexes	VaR	EL	MSD	ES	EVaR	ML
${\Lambda }_C$	0.016${}^{\ast }$	0.993	0.020${}^{\ast \ast }$	0.015${}^{\ast \ast }$	0.015${}^{\ast \ast }$	0.015${}^{\ast \ast }$
${\Lambda }_D$	$<0.001^{\ast \ast \ast }$	1.000	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
${\Lambda }_N$	$<0.001^{\ast \ast \ast }$	0.833	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$

Note: This table presents the $p$-value of the bilateral and one-tailed Mann–Whitney test. The bilateral test has the null hypothesis that the location parameter of sub-sample 2 is equal to sub-sample 1, and the alternative hypothesis that the location parameter of sub-sample 2 is different from sub-sample 1. The right one-tailed Mann–Whitney test has the null hypothesis that the location parameter of sub-sample 2 is equal to sub-sample 1. The alternative hypothesis is that the location parameter of sub-sample 2 is higher than sub-sample 1. ${}^{\ast \ast \ast }$, ${}^{\ast \ast }$, and ${}^{\ast }$ indicate that the test is significant at 0.01, 0.05, and 0.10, respectively. VaR, EL, MSD, ES, EVaR, and ML, are, respectively, Value at Risk, Expected Loss, Mean plus Semi-Deviation, Expected Shortfall, Expectile Value at Risk, and Maximum Loss. ${\Lambda }_N$, ${\Lambda }_C$ and ${\Lambda }_D$ are the aggregated indexes. ${\Lambda }_N$ is the naive aggregation (equally weighted); ${\Lambda }_C$ is based on the number of cases (weights returns by the percentage of COVID-19 cases); and ${\Lambda }_D$ is based on the number of deaths (weights returns by the percentage of COVID-19 deaths). Aggregate indexes are built using log-returns (in %) from market indexes of 35 countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020.

Table 19.

Dates of maximum systemic risk values and minimum values for aggregated indexes and risk measures considered. The date at the top is for the maximum, and the bottom is the minimum.

Aggregated indexes	VaR	EL	MSD	ES	EVaR	ML
${\Lambda }_C$	03/19/2020	03/10/2020	03/19/2020	03/19/2020	03/19/2020	03/19/2020
	12/30/2019	03/25/2020	12/30/2019	12/30/2019	12/30/2019	12/30/2019
${\Lambda }_D$	03/13/2020	03/24/2019	03/13/2020	03/13/2020	03/13/2020	03/13/2020
	12/29/2019	03/18/2020	12/29/2019	12/29/2019	12/29/2019	12/29/2019
${\Lambda }_N$	03/17/2020	03/13/2020	03/17/2020	03/17/2020	03/17/2020	03/19/2020
	06/15/2021	03/25/2020	01/03/2020	06/15/2021	06/15/2021	06/15/2021

Note: ${\Lambda }_N$, ${\Lambda }_C$ and ${\Lambda }_D$ are the aggregated indexes. ${\Lambda }_N$ is the naive aggregation (equally weighted); ${\Lambda }_C$ is based on the number of cases (weights returns by the percentage of COVID-19 cases); and ${\Lambda }_D$ is based on the number of deaths (weights returns by the percentage of COVID-19 deaths). Aggregate indexes are built using log-returns (in %) from market indexes of 35 countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020.

Table 20.

Kendall’s correlation between VaR estimates for individual countries and the systemic risk of aggregate indexes. Systemic risk is computed using VaR and the three aggregation functions. Risk estimates comprise November 17, 2018, to October 25, 2021. Sub-sample 1 comprehends risk estimates from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends risk forecasting from November 17, 2019, to October 25, 2021.

Countries	Full sample			Sub-sample 1			Sub-sample 2
	${\Lambda }_C$	${\Lambda }_D$	${\Lambda }_N$	${\Lambda }_C$	${\Lambda }_D$	${\Lambda }_N$	${\Lambda }_C$	${\Lambda }_D$	${\Lambda }_N$
Argentina	0.149	0.155	0.188	−0.169	−0.174	−0.125	0.101	0.095	0.059
Austria	0.149	0.155	0.188	−0.170	−0.175	−0.126	0.101	0.095	0.059
Bangladesh	−0.205	−0.210	−0.226	−0.181	−0.188	−0.208	−0.183	−0.188	−0.222
Belgium	0.145	0.151	0.184	−0.169	−0.174	−0.125	0.085	0.079	0.044
Brazil	0.149	0.155	0.188	−0.169	−0.174	−0.125	0.101	0.095	0.059
Canada	0.340	0.340	0.385	−0.065	−0.072	−0.031	0.562	0.567	0.608
Chile	0.149	0.155	0.188	−0.169	−0.174	−0.125	0.101	0.095	0.059
China	0.022	0.038	0.047	−0.306	−0.275	−0.259	0.261	0.267	0.270
Czechia	0.149	0.155	0.188	−0.170	−0.175	−0.125	0.101	0.095	0.059
Egypt	0.335	0.339	0.312	0.283	0.285	0.240	0.394	0.397	0.399
France	0.466	0.468	0.519	0.119	0.109	0.157	0.695	0.697	0.748
Germany	−0.297	−0.298	−0.260	−0.175	−0.177	−0.125	−0.343	−0.339	−0.308
India	0.295	0.275	0.298	−0.049	−0.078	−0.017	0.552	0.536	0.526
Indonesia	0.053	0.054	0.037	−0.037	−0.036	−0.035	0.115	0.116	0.086
Iraq	−0.043	−0.027	0.001	−0.135	−0.112	−0.103	0.000	0.010	0.052
Israel	0.585	0.578	0.568	0.451	0.443	0.384	0.643	0.646	0.657
Italy	0.413	0.415	0.460	0.018	0.007	0.057	0.659	0.658	0.681
Morocco	0.149	0.155	0.188	−0.169	−0.174	−0.125	0.101	0.095	0.059
Mexico	0.420	0.422	0.386	0.163	0.170	0.111	0.555	0.549	0.527
Nepal	−0.039	−0.028	−0.025	−0.067	−0.065	−0.057	−0.066	−0.053	−0.066
Netherlands	0.458	0.469	0.477	0.152	0.172	0.118	0.624	0.626	0.660
Pakistan	0.183	0.173	0.161	−0.131	−0.130	−0.111	0.522	0.502	0.465
Philippines	0.350	0.369	0.396	0.055	0.080	0.072	0.539	0.547	0.574
Poland	0.407	0.411	0.452	0.014	0.011	0.051	0.686	0.684	0.693
Portugal	0.455	0.451	0.441	0.109	0.105	0.074	0.671	0.666	0.666
Romania	0.348	0.336	0.294	−0.041	−0.056	−0.094	0.729	0.728	0.714
Russia	0.149	0.155	0.188	−0.169	−0.174	−0.125	0.101	0.095	0.059
Saudi Arabia	0.173	0.167	0.167	0.024	0.022	0.080	0.344	0.337	0.309
South Africa	0.516	0.512	0.535	0.292	0.263	0.281	0.693	0.691	0.704
Spain	0.149	0.155	0.188	−0.169	−0.174	−0.125	0.101	0.095	0.059
Sweden	0.305	0.312	0.362	−0.087	−0.094	−0.049	0.486	0.494	0.540
Switzerland	0.339	0.343	0.392	−0.044	−0.052	−0.014	0.550	0.556	0.599
Turkey	0.110	0.123	0.130	−0.192	−0.166	−0.170	0.368	0.373	0.377
UK	0.428	0.443	0.480	0.046	0.059	0.092	0.685	0.694	0.717
USA	0.149	0.155	0.188	−0.169	−0.174	−0.125	0.101	0.095	0.059

Note: ${\Lambda }_N$, ${\Lambda }_C$ and ${\Lambda }_D$ are the aggregated indexes. ${\Lambda }_N$ is the naive aggregation (equally weighted); ${\Lambda }_C$ is based on the number of cases (weights returns by the percentage of COVID-19 cases); and ${\Lambda }_D$ is based on the number of deaths (weights returns by the percentage of COVID-19 deaths). Aggregate indexes are built using log-returns (in %) from market indexes of 35 countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020.

Table 11.

Bilateral and right one-tailed Mann–Whitney test applied under log-returns of the market indexes from Sub-sample 1 and Sub-sample 2. This table presents the $p$-value of the test. Sub-sample 1 comprehends data from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends data from November 17, 2019, to October 25, 2021.

Countries	Bilateral	Right tailed
Argentina	0.888	0.444
Austria	0.306	0.153
Bangladesh	0.008${}^{\ast \ast \ast }$	0.004${}^{\ast \ast \ast }$
Belgium	0.992	0.496
Brazil	0.998	0.501
Canada	0.365	0.183
Chile	0.556	0.278
China	0.542	0.271
Czechia	0.461	0.231
Egypt	0.668	0.666
France	0.702	0.649
Germany	0.657	0.672
India	0.112	0.056${}^{\ast }$
Indonesia	0.766	0.383
Iraq	0.991	0.495
Israel	0.966	0.483
Italy	0.966	0.517
Mexico	0.321	0.160
Morocco	0.418	0.209
Nepal	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$
Netherlands	0.931	0.465
Pakistan	0.119	0.060${}^{\ast }$
Philippines	0.689	0.656
Poland	0.602	0.301
Portugal	0.783	0.391
Romania	0.597	0.299
Russia	0.440	0.220
Saudi Arabia	0.141	0.070${}^{\ast }$
South Africa	0.686	0.343
Spain	0.776	0.388
Sweden	0.962	0.519
Switzerland	0.998	0.501
Turkey	0.292	0.146
UK	0.793	0.396
USA	0.579	0.289

Note: This table presents the $p$-value of the bilateral and one-tailed Mann–Whitney test. The bilateral test has the null hypothesis that the location parameter of sub-sample 2 is equal to sub-sample 1, and the alternative hypothesis that the location parameter of sub-sample 2 is different from sub-sample 1. The right one-tailed Mann–Whitney test has the null hypothesis that the location parameter of sub-sample 2 is equal to sub-sample 1. The alternative hypothesis is that the location parameter of sub-sample 2 is higher than sub-sample 1. ${}^{\ast \ast \ast }$, ${}^{\ast \ast }$, and ${}^{\ast }$ indicate that the test is significant at 0.01, 0.05, and 0.10, respectively.

Table 12.

Bilateral and right one-tailed Mann–Whitney test applied under aggregated indexes from Sub-sample 1 and Sub-sample 2. This table presents the $p$-value of the test. Sub-sample 1 comprehends data from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends data from November 17, 2019, to October 25, 2021.

Aggregated indexes	Bilateral	Right tailed
${\Lambda }_C$	0.246	0.123
${\Lambda }_D$	0.367	0.184
${\Lambda }_N$	0.139	0.069${}^{\ast }$

Note: This table presents the $p$-value of the bilateral and one-tailed Mann–Whitney test. The bilateral test has the null hypothesis that the location parameter of sub-sample 2 is equal to sub-sample 1, and the alternative hypothesis that the location parameter of sub-sample 2 is different from sub-sample 1. The right one-tailed Mann–Whitney test has the null hypothesis that the location parameter of sub-sample 2 is equal to sub-sample 1. The alternative hypothesis is that the location parameter of sub-sample 2 is higher than sub-sample 1. ${\Lambda }_N$, ${\Lambda }_C$ and ${\Lambda }_D$ are the aggregated indexes. ${\Lambda }_N$ is the naive aggregation (equally weighted); ${\Lambda }_C$ is based on the number of cases (weights returns by the percentage of COVID-19 cases); and ${\Lambda }_D$ is based on the number of deaths (weights returns by the percentage of COVID-19 deaths). Aggregate indexes are built using log-returns (in %) from market indexes of 35 countries with the highest total confirmed cases and/or deaths caused by COVID-19 until November 2020.

Table 13.

Specification of the parametric models used to filter the log-returns of the market indexes, i.e., to compute the mean and the conditional standard deviation of log-returns. The sample period comprehends data from November 17, 2018, to October 25, 2021.

Countries	Specification	Distribution
Argentina	AR(1)-GARCH(2, 2)	Student-$t$
Austria	AR(1)-EGARCH(2, 1)	Student-$t$
Bangladesh	AR(1)-EGARCH(2, 2)	Generalized error
Belgium	AR(1)-EGARCH(2, 1)	Student-$t$
Brazil	AR(1)-EGARCH(2, 1)	Student-$t$
Canada	AR(1)-EGARCH(2, 1)	Student-$t$
Chile	AR(1)-EGARCH(2, 2)	Student-$t$
China	AR(1)-EGARCH(1, 2)	Student-$t$
Czechia	AR(1)-EGARCH(2, 1)	Student-$t$
Egypt	AR(1)-EGARCH(2, 1)	Student-$t$
France	AR(1)-EGARCH(2, 1)	Student-$t$
Germany	AR(1)-EGARCH(1, 2)	Student-$t$
India	AR(1)-EGARCH(2, 1)	Student-$t$
Indonesia	AR(1)-EGARCH(1, 2)	Student-$t$
Iraq	AR(1)-EGARCH(2, 2)	Skewed Student-$t$
Israel	AR(1)-GJR(1, 1)	Generalized error
Italy	AR(1)-EGARCH(2, 1)	Student-$t$
Morocco	AR(1)-EGARCH(2, 1)	Student-$t$
Mexico	AR(1)-GJR(2, 1)	Student-$t$
Nepal	AR(1)-EGARCH(1, 1)	Generalized error
Netherlands	AR(1)-EGARCH(2, 2)	Student-$t$
Pakistan	AR(1)-GARCH(1,2)	Student-$t$
Philippines	AR(1)-EGARCH(1, 1)	Student-$t$
Poland	AR(1)-EGARCH(2, 2)	Student-$t$
Portugal	AR(1)-EGARCH(2, 1)	Student-$t$
Romania	AR(1)-EGARCH(2, 2)	Student-$t$
Russia	AR(1)-GARCH(2, 1)	Student-$t$
Saudi Arabia	AR(1)-EGARCH(2, 2)	Student-$t$
South Africa	AR(1)-EGARCH(1, 1)	Student-$t$
Spain	AR(1)-EGARCH(1, 1)	Student-$t$
Sweden	AR(1)-GARCH(2, 2)	Student-$t$
Switzerland	AR(1)-GJR(2, 2)	Student-$t$
Turkey	AR(1)-EGARCH(1, 2)	Student-$t$
UK	AR(1)-EGARCH(2, 2)	Student-$t$
USA	AR(1)-EGARCH(1, 1)	Student-$t$

Note: We choose the best specifications and the model based on the Akaike information criterion (AIC).

Table 14.

Specification of the parametric models used to filter aggregated indexes, i.e., compute the mean and the conditional standard deviation of indexes. The sample period comprehends data from November 17, 2018, to October 25, 2021.

Aggregated indexes	Specification	Distribution
${\Lambda }_C$	AR(1)-EGARCH(1,1)	generalized error
${\Lambda }_D$	AR(1)-EGARCH(2,2)	generalized error
${\Lambda }_N$	AR(1)-EGARCH(1,1)	generalized error

Note: ${\Lambda }_N$ is the naive aggregation; ${\Lambda }_C$ is based on the number of cases; and ${\Lambda }_D$ is based on the number of deaths. We choose the best specifications based on the Akaike information criterion (AIC).

Table 15.

Bilateral and right one-tailed Mann–Whitney test applied under risk forecasting from Sub-sample 1 and Sub-sample 2. This table presents the $p$-value of the test. Sub-sample 1 comprehends risk forecasting from November 17, 2018, to November 16, 2019; Sub-sample 2 comprehends risk forecasting from November 17, 2019, to October 25, 2021.

Countries	Bilateral						Right-tailed
	VaR	EL	MSD	ES	EVaR	ML	VaR	EL	MSD	ES	EVaR	ML
Argentina	$<0.001^{\ast \ast \ast }$	0.805	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.403	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Austria	0.624	0.240	0.618	0.624	0.624	0.628	0.312	0.120	0.309	0.312	0.312	0.314
Bangladesh	0.041${}^{\ast \ast }$	0.041${}^{\ast \ast }$	0.041${}^{\ast \ast }$	0.041${}^{\ast \ast }$	0.041${}^{\ast \ast }$	0.041${}^{\ast \ast }$	0.021${}^{\ast \ast }$	0.979	0.021${}^{\ast \ast }$	0.021${}^{\ast \ast }$	0.021${}^{\ast \ast }$	0.021${}^{\ast \ast }$
Belgium	0.727	0.849	0.716	0.726	0.727	0.724	0.363	0.424	0.358	0.363	0.364	0.362
Brazil	$<0.001^{\ast \ast \ast }$	0.375	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.187	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Canada	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Chile	$<0.001^{\ast \ast \ast }$	0.294	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.147	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
China	0.002${}^{\ast \ast \ast }$	0.820	0.003${}^{\ast \ast \ast }$	0.002${}^{\ast \ast \ast }$	0.002${}^{\ast \ast \ast }$	0.002${}^{\ast \ast \ast }$	0.999	0.410	0.998	0.999	0.999	0.999
Czechia	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Egypt	0.013${}^{\ast \ast }$	0.443	0.026${}^{\ast \ast }$	0.013${}^{\ast \ast }$	0.013${}^{\ast \ast }$	0.012${}^{\ast \ast }$	0.007${}^{\ast \ast \ast }$	0.222	0.013${}^{\ast \ast }$	0.007${}^{\ast \ast \ast }$	0.006${}^{\ast \ast \ast }$	0.006${}^{\ast \ast \ast }$
France	0.002${}^{\ast \ast \ast }$	0.002${}^{\ast \ast \ast }$	0.002${}^{\ast \ast \ast }$	0.002${}^{\ast \ast \ast }$	0.002${}^{\ast \ast \ast }$	0.002${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$
Germany	$<0.001^{\ast \ast \ast }$	0.148	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.926	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
India	0.829	0.285	0.881	0.828	0.827	0.824	0.415	0.857	0.440	0.414	0.413	0.412
Indonesia	$<0.001^{\ast \ast \ast }$	0.013${}^{\ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.006${}^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Iraq	0.869	0.753	0.867	0.872	0.871	0.868	0.566	0.624	0.566	0.564	0.564	0.566
Israel	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	1.000	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Italy	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Mexico	$<0.001^{\ast \ast \ast }$	0.036${}^{\ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.982	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Morocco	$<0.001^{\ast \ast \ast }$	0.011${}^{\ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.994	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Nepal	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	1.000	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Netherlands	$<0.001^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Pakistan	$<0.001^{\ast \ast \ast }$	0.039${}^{\ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	1.000	0.980	1.000	1.000	1.000	1.000
Philippines	$<0.001^{\ast \ast \ast }$	0.074${}^{\ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.963	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Poland	$<0.001^{\ast \ast \ast }$	0.915	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.458	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Portugal	$<0.001^{\ast \ast \ast }$	0.003${}^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Romania	0.030${}^{\ast \ast }$	0.052${}^{\ast }$	0.029${}^{\ast \ast }$	0.030${}^{\ast \ast }$	0.031${}^{\ast \ast }$	0.031${}^{\ast \ast }$	0.985	0.974	0.986	0.985	0.985	0.985
Russia	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Saudi Arabia	$<0.001^{\ast \ast \ast }$	0.070${}^{\ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	1.000	0.965	1.000	1.000	1.000	1.000
South Africa	$<0.001^{\ast \ast \ast }$	0.019${}^{\ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.009${}^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Spain	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Sweden	0.001${}^{\ast \ast \ast }$	0.243	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	0.121	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
Switzerland	0.001${}^{\ast \ast \ast }$	0.073${}^{\ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.037${}^{\ast \ast }$	$<0.001^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$	0.001${}^{\ast \ast \ast }$
Turkey	0.015${}^{\ast \ast }$	0.093${}^{\ast }$	0.015${}^{\ast \ast }$	0.015${}^{\ast \ast }$	0.015${}^{\ast \ast }$	0.015${}^{\ast \ast }$	0.992	0.954	0.992	0.993	0.993	0.993
UK	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$	$<0.001^{\ast \ast \ast }$
USA	0.143	0.285	0.133	0.142	0.142	0.145	0.071${}^{\ast }$	0.142	0.066${}^{\ast }$	0.071${}^{\ast }$	0.071${}^{\ast }$	0.072${}^{\ast }$

Note: This table presents the $p$-value of the bilateral and one-tailed Mann–Whitney test. The bilateral test has the null hypothesis that the location parameter of sub-sample 2 is equal to sub-sample 1, and the alternative hypothesis that the location parameter of sub-sample 2 is different from sub-sample 1. The right one-tailed Mann–Whitney test has the null hypothesis that the location parameter of sub-sample 2 is equal to sub-sample 1. The alternative hypothesis is that the location parameter of sub-sample 2 is higher than sub-sample 1. ${}^{\ast \ast }$, and ${}^{\ast }$ indicate that the test is significant at 0.01, 0.05, and 0.10, respectively. VaR, EL, MSD, ES, EVaR, and ML, are, respectively, Value at Risk, Expected Loss, Mean plus Semi-Deviation, Expected Shortfall, Expectile Value at Risk, and Maximum Loss.

Data availability

Data will be made available on request.