Financial Systemic Risk and the COVID-19 Pandemic

Abstract

The COVID-19 pandemic has caused market turmoil and economic distress. To understand the effect of the pandemic on the U.S. financial systemic risk, we analyze the explanatory power of detailed COVID-19 data on three market-based systemic risk measures (SRMs): Conditional Value at Risk, Distress Insurance Premium, and SRISK. In the time-series dimension, we use the Dynamic OLS model and find that financial variables, such as credit default swap spreads, equity correlation, and firm size, significantly affect the SRMs, but the COVID-19 variables do not appear to drive the SRMs. However, if we focus on the first wave of the COVID-19 pandemic in March 2020, we find a positive and significant COVID-19 effect, especially before the government interventions. In the cross-sectional dimension, we run fixed-effect and event-study regressions with clustered variance-covariance matrices. We find that market capitalization helps to reduce a firm’s contribution to the SRMs, while firm size significantly predicts the surge in a firm’s SRM contribution when the pandemic first hits the system. The policy implications include that proper market interventions can help to mitigate the negative pandemic effect, and policymakers should continue the current regulation of required capital holding and consider size when designating systemically important financial institutions.

1. Introduction

The COVID-19 pandemic, starting in early 2020, caused market turmoil and economic recession. The stock market crashed, and volatility surged in March 2020. The National Bureau of Economic Research (NBER) identifies March and April 2020 as an economic contraction period.1 In view of the severe financial and economic consequences from the COVID-19 pandemic, we want to get a better understanding of how this pandemic affects the overall financial system. To reach this goal, we use the concept of financial systemic risk (FSR). FSR is the risk to the entire financial system with potential negative real economic effects, as the failure of the aggregate financial intermediation can severely impair the functioning of the broader economy (Adrian and Brunnermeier 2016; Acharya et al. 2012). If the pandemic affects the overall financial system, it will show up as a significant driver of FSR.

The importance of FSR became apparent from the 2007–2009 Global Financial Crisis (GFC), because focusing on the risk of individual financial institutions (FIs) was insufficient to ensure the safety of the entire financial system. Thus, in response to GFC, Basel Committee on Banking Supervision (BCBS) developed the Basel III regulatory framework in 2010 (BCBS 2010) from the 2004 Basel II framework (BCBS 2004).

Specific to our goal of understanding the effect of the pandemic on FSR, we follow the macroprudential approach in Basel III designed to address FSR, which consists of the time series and cross-sectional dimensions (Crockett 2000; Borio 2003). In the time series dimension, we study the FSR time series since the early 2000s, analyzing its dynamics through various crises in this period, identifying financial variables that significantly affect the FSR, and detecting the effects of the COVID-19 variables, if any. In the cross-sectional dimension, we compare the contributions to the FSR from major financial institutions (FIs) and identify firm characteristics that explain their contributions or predict the surge in their contributions to the FSR at the beginning of the pandemic. The empirical results will provide statistical evidence on the severity of the exogenous pandemic shock, the effectiveness of government interventions in mitigating the pandemic effect, and the FIs’ vulnerability from the system’s perspective. These observations will provide valuable empirical reference for improving financial regulations and emergency responses in the future.

To obtain concrete FSR time series, we need quantitative measures of FSR, called systemic risk measures (SRMs). Due to the importance of FSR, many SRMs have been proposed since the GFC. See, for example, Bisias et al. (2012) for a detailed survey of 31 SRMs proposed during the GFC. Among the SRMs proposed since the GFC, we choose three market-based SRMs that capture FSR from different perspectives, so that our results characterize FSR robustly and do not depend on a particular SRM.

The three SRMs in our paper are Conditional Value at Risk (CoVaR), Distress Insurance Premium (DIP), and SRISK (a capital-shortfall based SRM).2 Adrian and Brunnermeier (2016) propose $\Delta$CoVaR as “the change in the value at risk of the financial system conditional on an institution being under distress relative to its median state.” For brevity, we refer to $\Delta$CoVaR simply as CoVaR in the following text unless explicitly specified. Huang et al. (2009) propose DIP as the “price of insurance against financial distress,” where financial distress is represented by large losses of a portfolio of debt instruments issued by member firms. Acharya et al. (2012) propose SRISK as “the capital that a firm is expected to need if we have another financial crisis.” The SRISK for the system is the sum of all firms’ non-negative SRISKs.

We pick these measures for three reasons. First, these are among the first SRMs proposed during the GFC and have been applied to address various practical topics. See, for example, Black et al. (2016), Bevilacqua et al. (2023), and Acharya et al. (2025). Second, in comparison to the traditional risk measures based on balance sheet or accounting information, these market-based SRMs are forward-looking and can be updated from daily data, thus reflecting the risk more timely and at a much higher frequency. Third, these three measures complement each other, thus providing a complete picture of the overall FSR.

In view of the severe consequences of the COVID-19 pandemic, many papers have studied its effects since its outbreak in 2020. The strand of literature that is directly related to our paper is the analysis of the pandemic effect on FSR. However, most of these papers use the pandemic as an indicator type of variable. For example, Borri and di Giorgio (2022) study large European banks’ CoVaR during the initial period of the pandemic from January to September 2020. Chavleishvili and Kremer (2023) classify March and April 2020 as the COVID-19 stress period and illustrate how the systemic stress, measured by their systemic financial stress index, contributes to the GDP drop during the Great Recession but not during the COVID-19 pandemic. Bevilacqua et al. (2023) may be an exception, as they use detailed COVID-19 data, such as cases and deaths, to study the effects of the pandemic and policy interventions on cross-country CoVaR. But their sample is restricted to the year of 2020, and the FSR measure is limited to CoVaR in their main analysis.3

To obtain a comprehensive understanding of the effect of the pandemic on FSR, we need to conduct a formal study of detailed COVID-19 data over the complete pandemic period and apply them to multiple SRMs to ensure robustness of the results. This paper contributes to the literature by filling such a gap in the existing papers. Specifically, we use detailed COVID-19 data, such as confirmed cases and deaths, over the complete pandemic period from 2020 to 2023, and measure FSR using three different SRMs. In addition, we extend the empirical sample beyond the pandemic period, starting from the early 2000s, when all three market-based SRMs are computable, to August 2024, about one year after the pandemic data end. This extended full sample allows us to put the dynamics of the SRMs during the pandemic in the context of a longer history, to better assess the severity and persistence of the pandemic effect relative to other crises. It also allows us to discover other financial driving factors in addition to the COVID-19 variables.

The main findings of this paper include the following. Financial variables, such as CDS spreads, equity correlation, and firm size, significantly affect the SRMs, but the COVID-19 variables do not appear to drive the SRMs over the full pandemic period. However, if we focus on the first wave of the COVID-19 pandemic in March 2020, we find positive and significant COVID-19 effects on two of the three SRMs. This is because the three SRMs initially increased with the daily COVID-19 confirmed cases and deaths but started to level off or decrease after the Federal Reserve introduced policy measures to stabilize the financial system. Thus, the market interventions help to mitigate the COVID-19 effect on the FSR. In the cross-sectional dimension, we find that market capitalization serves as a cushion to a negative shock and helps to reduce a firm’s contribution to the SRMs, while firm size significantly predicts the surge in a firm’s contribution to the SRMs when the pandemic first hits the system.

As the COVID-19 pandemic has caused major disruption to our daily life, by studying its effect on FSR, we hope to contribute to our broader understanding of the pandemic, and to be better prepared for similar events in the future. Accordingly, there are two directions for future research. First, our sample of the U.S. financial system can be extended to the financial systems in other countries and regions. By observing the country- or region-specific effect, regulators in these areas can design policies that best suit their needs. Second, if good market data are available before the early 2000s, the SRM time series can be extended further back in history. By comparing the effects of more historical crises, we may be able to uncover robust patterns and design measures that can help mitigating the effects of future crises.

The rest of this paper is organized as follows. Section 2 reviews the relevant literature and reports the findings of the three SRMs in previous crises. Section 3 reviews the concepts and computations of the three market-based SRMs. Section 4 describes the empirical data. Section 5 analyzes the time series dynamics of the SRMs before and during the COVID-19 pandemic. Section 6 studies their cross-sectional characteristics at the firm level. Section 7 discusses the empirical results and compare them to those in the literature. Section 8 concludes the paper.

2. Literature Review

As we study the effect of the COVID-19 pandemic on FSR, our paper is related to the intersection of two strands of literature: SRMs to quantify FSR and the effect of the pandemic.

For the first strand of literature on SRMs, as the GFC highlights the importance of FSR, many SRMs have been proposed to quantify FSR. Bisias et al. (2012) provide a detailed survey of 31 SRMs that were proposed during the GFC. Since then, new SRMs have continued to emerge. For example, the systemic financial stress index proposed by Chavleishvili and Kremer (2023) and the Australian stress index proposed by Gomis-Porqueras et al. (2023).

Among the SRMs proposed by the existing literature, we pick three SRMs—CoVaR, DIP, and SRISK—for three reasons. First, these are among the first SRMs proposed during the GFC and have been applied to address various practical issues. For example, Huang et al. (2012) and Black et al. (2016) apply DIP to assess the FSR of the Asian-Pacific and European regions. Bevilacqua et al. (2023) use CoVaR to study the effects of the COVID-19 pandemic and policy interventions in the top 10 countries with confirmed cases. Acharya et al. (2025) use both CoVaR and SRISK to predict FIs’ performance across various crises or stress episodes from 1907 to 2023.4

Second, unlike the traditional risk measures based on balance sheet or accounting information, which is only available on a quarterly or longer time frequency with a significant lag, these market-based SRMs can be updated from daily data, thus reflecting the risk more timely and at a much higher frequency. Moreover, balance sheet data summarize historical information and are thus backward-looking, while market data reflect market participants’ expectations about the future and are thus forward-looking, which is particularly useful in the risk modeling process.

Third, these three measures capture FSR from different angles, complementing each other, thus providing a complete picture of the overall FSR. CoVaR and SRISK are physical measures, while DIP is risk-neutral, including both the physical risk and the risk premium components. Meanwhile, CoVaR and SRISK are conditional concepts, measuring the losses when losses do occur, while DIP is a joint concept, considering both the losses and the probability of loss occurring. Consequently, the magnitude of DIP tends to be smaller than CoVaR or SRISK. The two conditional measures also switch their direction of conditional and main events. CoVaR measures the system’s distress conditional on the distress of each firm, while SRISK is the opposite. Relatively speaking, CoVaR and SRISK mainly rely on stock prices to extract risk information, while DIP mainly relies on credit default swap (CDS) spreads. Thus, the former two lean on the equity side, while the latter one leans on the liability side. As a result, the three SRMs show both similarities and differences, complementing each other in measuring the FSR.

The empirical findings of these three SRMs in the literature suggest that they are typically low during economic booms and high during stress periods. For example, Adrian and Brunnermeier (2016) use the data of the 50 largest U.S. FIs from 1971 to 2013 and find that the contemporaneous CoVaR is small during the 2003–2006 credit boom and high during the GFC. Based on a sample of 58 large European banks from 2001 to 2013, Black et al. (2016) observe that DIP peaked in November 2011 during the height of the European sovereign debt crisis. Acharya et al. (2025) study a longer history of the SRISK of U.S FIs from 1965 to 2023 and find that SRISK reached the highest level during the GFC. These patterns provide a context in which we can compare the dynamics of the SRMs during the COVID-19 pandemic with those in the previous crises.

For the second strand of literature on the pandemic effect, due to the severe consequences of the COVID-19 pandemic, many papers have studied its effects since its outbreak in 2020. See, for example, the special issue of the Journal of Banking and Finance, titled “The Impact of Global Pandemic on Financial Markets and Institutions,” for a collection of papers on this topic. The papers in this special issue study the pandemic effect on specific aspects of the financial system, such as the corporate bond dealers and market (Anderson et al. 2023), algorithmic traders (Chakrabarty and Pascual 2023), and corporate CDS spreads (Hasan et al. 2023).

The intersection of the first strand of literature on SRMs and the second strand on the pandemic effect is the study of the pandemic effect on SRMs and directly related to our paper. However, most of the existing papers mainly use the pandemic as an indicator type of variable. For example, Borri and di Giorgio (2022) study large European banks’ CoVaR during the initial period of the pandemic from January to September 2020. Chavleishvili and Kremer (2023) classify March and April 2020 as the COVID-19 stress period and illustrate how the systemic stress, measured by their systemic financial stress index, contributes to the GDP drop during the Great Recession but not during the COVID-19 pandemic. Gomis-Porqueras et al. (2023) plot their Australian stress index and the daily new confirmed COVID-19 cases together to illustrate the coincidence of an increase in the financial stress and the first wave of the COVID-19 pandemic. From a slightly different angle, Acharya et al. (2023) divide their sample by 23 March 2022 into the COVID periods before and after government interventions and show that the balance-sheet liquidity risk of banks through their credit lines significantly affects their stock decline and SRISK increase during the initial COVID-19 shock in 2020. From an opposite direction, Acharya et al. (2025) analyze how CoVaR and SRISK predict FIs’ performance across various stress episodes over a long history from 1907 to 2023. Bevilacqua et al. (2023) may be an exception, as they use detailed COVID-19 data, such as cases and deaths, to study the effects of the pandemic and policy interventions on cross-country CoVaR. But their sample is restricted to the year of 2020, and the FSR measure is limited to CoVaR in their main analysis.

Given the limited usage of the COVID-19 data, the incomplete pandemic period, and the application of a single SRM in the existing literature, we lack a complete picture of the pandemic effect on FSR. Our paper strives to fill this gap in the literature by using the detailed COVID-19 data, such as confirmed cases and deaths, over the complete pandemic period from 2020 to 2023, and measure FSR using three different SRMs. We investigate the significance or non-significance of the pandemic effect, the time period for its significance, the potential mitigating factors, such as government interventions, as well as firm characteristics that contribute to FIs’ vulnerability during this exogenous shock. Our results will provide valuable empirical reference for improving financial regulations and emergency responses in the future.

3. Review of CoVaR, DIP, and SRISK

To lay the foundation of the empirical analysis in the following sections, we review the concepts and computations of the three market-based SRMs in this section.

3.1. CoVaR

CoVaR measures the FSR from the persecutive of value at risk. Let $X_i$ denote the return of institution i. The value at risk of institution i at the $q\%$ quantile is

$$Pr(X^i\le Va{R}_q^i)=q\%.$$

(1)

Adrian and Brunnermeier (2016) define $CoVa{R}_q^{j\left|C\right(X^i)}$ as “the VaR of the institution j (or the financial system) conditional on some event $C\left(X^i\right)$ of institution i”:

$$Pr\left(X^j\right|C\left(X^i\right)\le CoVa{R}_q^{j\left|C\right(X^i)})=q\%.$$

(2)

To measure the change in the system’s VaR as institution i moves from its median state ($Va{R}_{50}^i$) to the distress state ($Va{R}_q^i$, where q typically set at 5), Adrian and Brunnermeier (2016) propose

$$\Delta CoVa{R}_q^{j|i}=CoVa{R}_q^{j|X^i=Va{R}_q^i}-CoVa{R}_q^{j|X^i=Va{R}_{50}^i}.$$

(3)

To calculate time-varying $\Delta CoVa{R}_{q,t}^{j|i}$, they first predict $Va{R}_{q,t}^i$ and $CoVa{R}_{q,t}^{j\left|C\right(X^i)}$ by running the following quantile regressions:

$$\begin{array}{ccc}\hfill X_t^i& =& {\alpha }_q^i+{\gamma }_q^i{\mathbf{M}}_{\mathbf{t}-\mathbf{1}}+{ϵ}_{q,t}^i,\hfill \end{array}$$

(4)

$$\begin{array}{ccc}\hfill X_t^{system|i}& =& {\alpha }_q^{system|i}+{\gamma }_q^{system|i}{\mathbf{M}}_{\mathbf{t}-\mathbf{1}}+{\beta }_q^{system|i}X{i}_t+{ϵ}_{q,t}^i,\hfill \end{array}$$

(5)

where ${\mathbf{M}}_{\mathbf{t}-\mathbf{1}}$ contains the lagged state variables. The resulting predicted values:

$$\begin{array}{ccc}\hfill Va{R}_{q,t}^i& =& {\widehat{\alpha }}_q^i+{\widehat{\gamma }}_q^i{\mathbf{M}}_{\mathbf{t}-\mathbf{1}},\hfill \end{array}$$

(6)

$$\begin{array}{ccc}\hfill CoVa{R}_{q,t}^i& =& {\widehat{\alpha }}_q^{system|i}+{\widehat{\gamma }}_q^{system|i}{\mathbf{M}}_{\mathbf{t}-\mathbf{1}}+{\widehat{\beta }}_q^{system|i}Va{R}_{q,t}^i,\hfill \end{array}$$

(7)

are used to compute $\Delta CoVa{R}_{q,t}^i$:

$$\begin{array}{ccc}\hfill \Delta CoVa{R}_{q,t}^i& =& CoVa{R}_{q,t}^i-CoVa{R}_{50,t}^i\hfill \end{array}$$

(8)

$$\begin{array}{ccc}& =& {\widehat{\beta }}_q^{system|i}(Va{R}_{q,t}^i-Va{R}_{50,t}^i).\hfill \end{array}$$

(9)

Adrian and Brunnermeier (2016) select seven state variables: VIX (Chicago Board Options Exchange (CBOE) Volatility Index), three-month (3 m) Treasury yield change, 3 m SOFR (Secured Overnight Financing Rate) and Treasury yield spreads, the change in the spread between the BAA-rated corporate bonds and ten-year (10 y) Treasury yield, the change in the 10 y and 3 m Treasury yield spread, the return of the DJUSRE index (the Dow Jones U.S. real estate industry group index), and the equity market return (that is, the S&P 500 index return). They capture different aspects of the financial system that condition the CoVaR measure. For example, the S&P 500 index return and VIX capture the return and volatility of the aggregate equity market, the DJUSRE index represents the housing market, and the spread between the BAA-rated corporate bonds and 10 y Treasury yields proxies corporate credit risk. Adrian and Brunnermeier (2016) originally use the difference between 3 m London Interbank Offered Rate (LIBOR) and the 3 m Treasury bill rate to measure “short-term funding liquidity risk.” As LIBOR is phased out towards the end of our sample period, we replace it with its current counterpart, SOFR, published daily by the Federal Reserve Bank of New York.5

Notice that we convert the estimated negative $\Delta CoVaR$ values to positive to facilitate the comparison to other SRMs, and convert the percentage values to dollar values (${\Delta }^{\$}CoVaR$) by multiplying each institution’s $\Delta CoVaR$ percentage value by its book equity. The ${\Delta }^{\$}CoVaR$ for the financial system is the sum of each institution’s ${\Delta }^{\$}CoVaR$. For brevity, we drop $\Delta$ in front of $CoVaR$ in the following text unless explicitly specified.

3.2. DIP

DIP measures the FSR from the perspective of expected credit losses. Huang et al. (2009) propose DIP as an insurance premium that protects against large losses of a portfolio of debt instruments issued by member firms.

To calculate DIP, they first back out the risk-neutral probability of default ($P{D}_{i,t}$) from each firm’s CDS spreads ($s_{i,t}$):

$$P{D}_{i,t}={\displaystyle \frac{a_t{s}_{i,t}}{a_{t}LG{D}_{i,t}+b_t{s}_{i,t}}},$$

(10)

where $a_t\equiv {\int }_t^{t+T}{e}^{-r\tau }d\tau$, $b_t\equiv {\int }_t^{t+T}\tau e^{-r\tau }d\tau$, $LGD$ is the loss-given-default and r is the risk-free rate. $LGD$ can be simulated from the expected recovery rate available with the CDS spreads data ($LGD$ = 1 − recovery rate). Then they calculate the correlations between firms from their stock returns. Based on the PD and correlations, they simulate the joint default scenarios for a portfolio of debt instruments issued by member firms. By the no-arbitrage condition, DIP is equal to the expected portfolio losses that equal to or exceed a minimum share of this portfolio:

$$DIP=E\left[L\times 1(L\ge L_{min})\right],$$

(11)

where L is the portfolio loss and $L_{min}$ is the minimum share, say 10%.

Each firm’s FSR contribution is the portion of the expected portfolio loss due to its default. The percentage DIP value is converted to dollar value by multiplying it with the corresponding book liability.

3.3. SRISK

SRISK measures the FSR from the perspective of expected capital shortfall. Acharya et al. (2012) define SRISK as “the capital that a firm is expected to need if we have another financial crisis”.

$$\begin{array}{ccc}\hfill SRIS{K}_{i,t}& =& E_{t-1}\left(CaptialShorfal{l}_i\right|Crisis)\hfill \end{array}$$

(12)

$$\begin{array}{ccc}& =& E\left(\right(K(Debt+Equity)-Equity\left)\right|Crisis)\hfill \end{array}$$

(13)

$$\begin{array}{ccc}& =& KDeb{t}_{i,t}-(1-k)(1-LRME{S}_{i,t}),\times Equit{y}_{i,t},\hfill \end{array}$$

(14)

where K is the prudential capital ratio, set at 8% for U.S. FIs. They specify $Crisis$ as the scenarios when the aggregate equity market (represented by the S&P 500 index) falls by 40% over the next six months. $Equit{y}_{i,t}$ is firm i’s market capitalization on day t. The debt value is recognized to be relatively unchanged over the six-month period, so $Debt$ remains the same when moving outside the expectation operator. $LRME{S}_{i,t}$ is the Long Run Marginal Expected Shortfall for firm i on day t and represents the expected loss of firm i’s equity in the crisis scenarios.

To calculate $LRME{S}_{i,t}$, a bivariate model of the returns of firm i’s equity and the S&P 500 index is estimated.

$$\begin{array}{ccc}\hfill R_{m,t}& =& {\sigma }_{m,t}{ϵ}_{m,t}\hfill \end{array}$$

(15)

$$\begin{array}{ccc}\hfill R_{i,t}& =& {\sigma }_{i,t}({\rho }_{i,m,t}{ϵ}_{i,t}+\sqrt{1-{\rho }_{i,m,t}^2}{\xi }_{i,t})\hfill \end{array}$$

(16)

$$\begin{array}{ccc}\hfill ({ϵ}_{m,t},{\xi }_{i,t})& \sim & F,\hfill \end{array}$$

(17)

where $R_{m,t}$ is the S&P 500 index return on day t and $R_{i,t}$ is firm i’s equity return on day t. The volatilities, ${\sigma }_{m,t}$ and ${\sigma }_{i,t}$ are estimated by the GJR model (Glosten et al. 1993) and the correlation, ${\rho }_{i,m,t}$, is estimated by the Dynamic Conditional Correlation model (Engle 2002). With the estimated bivariate distribution, we can estimate firm i’s equity returns in the crisis scenarios, and $LRME{S}_{i,t}$ is the average of these returns.

A firm can have either a capital shortfall (SRISK ≥ 0) or a capital surplus (SRISK < 0) during a crisis. We focus on the risk posted by a capital shortfall, so we zero out negative SRISK for the firms. The SRISK for the system is the sum of all firms’ non-negative SRISKs.

4. Data

As we study the relationship between the FSR and the COVID-19 pandemic, we have two corresponding sources of data: the financial data for calculating the SRMs and the COVID-19 data. We discuss them separately in the following subsections.

4.1. Financial Data

There are three types of financial data used in the SRM computation: the aggregate financial time series, the firm-level market data, and the firm-level balance sheet data. They come from different sources.

First, the aggregate financial time series include the seven state variables used in the CoVaR calculation, the S&P 500 financial sector index (S&P 500.40) representing the financial system in CoVaR, and the five-year U.S. Treasury yield serving as the risk-free rate in the DIP calculation.6 As the severe-risk scenarios measured by the SRMs are rare events, we need as much historical information as possible to estimate the statistical risk models used in calculating CoVaR and SRISK, so long as the market structure is similar to the current one. DIP is the exception, because CDS spreads directly reveal the market assessment of the default risk of the reference entity. Accordingly, we estimate VIX before 1990 by the VXO index (CBOE S&P 100 Volatility Index) by regressing VIX on VXO in their overlapping period. Similarly, we extend the 3 m SOFR rate before 2019 by the 3 m LIBOR and repo (repurchase agreement) rates. We also extend the DJUSRE index return before 1992 by the daily housing returns from the Fama–French (FF) 48-industry portfolios.7

The aggregate financial time series are available at the daily frequency. We pull most of them from Bloomberg Finance LP, Bloomberg Per Security Data License, except the U.S. Treasury yields, which we obtain from the Board of Governors of the Federal Reserve System, Selected Interest Rates—Business Daily.8

Second, the firm-level market data include the stock prices and the CDS data. The daily stock prices include the adjusted version for computing the stock returns and the unadjusted version for computing the market capitalization when multiplied by the common shares outstanding. The stock price data are from CRSP (Center for Research in Security Prices)/Compustat Merged Database.

The CDS data include the daily quotes on CDS spreads and the expected recovery rate, both of which are from IHS Markit Ltd. Notice that for each firm, there are multiple CDS contracts traded at the same time. We pick the following specifications to get the most actively traded ones: five-year maturity, senior unsecured tier, and U.S. dollar denomination. For the document clauses, we use all four of them but give the highest weight to the most liquid one: the no-restructuring document clause.

Third, the firm-level balance sheet data include book asset, equity and liability, and common shares outstanding. The balance sheet data are from CRSP/Compustat Merged Database. We convert the quarterly balance sheet data to daily by setting the daily value equal to the latest quarterly value before that day, mimicking the real-world risk monitoring situation.

Based on the above data availability, the inputs for CoVaR and SRISK start in the mid-1980s, while the inputs for DIP start in 2002. A feature specific to CoVaR is that to avoid excessive noise, we compute the weekly moving averages of daily raw data before inputting them into the CoVaR formulae. After calculating and merging the SRMs, the final financial sample spans the period from 2 January 2004 to 30 August 2024.

As this paper studies the U.S. FSR, we select the sample firms that are directly relevant for this purpose. We start with the list of Global Systemically Important Financial Institutions (G-SIFIs) identified by the Financial Stability Board (FSB) (FSB 2024a), which includes banks (also known as G-SIBs: global systemically important banks) and, historically, insurers. We then keep the eight U.S. G-SIBs: Bank of America Corp. (BAC), Bank of New York Mellon (BK), Citigroup (C), Goldman Sachs (GS), JPMorgan Chase (JPM), Morgan Stanley (MS), State Street Corp. (SST), and Wells Fargo Corp. (WFC). For the foreign G-SIBs, we keep the three that have a major presence in the U.S.: Barclays PLC (BCS), Deutsche Bank (DB), and Union Bank of Switzerland AG (UBS) (Federal Reserve 2024). For the U.S. insurers, we keep American International Group (AIG) and Prudential Financial (PRU), because they were once designated as G-SIFIs and are in the 2024 FSB list of insurers subject to resolution standards (FSB 2024b).9 The choice of these FIs also bring data benefits, because they are the reference entities of the first traded single-name CDS contracts since the launch of CDS trading in the early 2000s. This feature ensures that we have as long a history of CDS data as possible for the DIP computation, to cover various economic peaks, troughs, and crises. In addition, these FIs are among the few financial reference entities that have liquid single-name CDS contracts, thus allowing for timely response to shocks.10

4.2. COVID-19 Data

The daily data on U.S. COVID-19 confirmed cases and deaths are from Dong et al. (2020). The data are available at the Data Repository hosted in GitHub and maintained by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (JHU).11 The raw numbers are cumulative and at the county level. In the empirical study, we mainly use the daily new confirmed cases and new deaths, which are the first differences of the raw cumulative numbers. In addition, we aggregate the county-level panel data into the country-level time series. The final COVID-19 data are daily from 22 January 2020, the first date of the JHU data, to 9 March 2023, the last date that JHU updated the data.

5. Time Series Analysis of the SRMs and the COVID-19 Pandemic

In the time series dimension, we study how the aggregate SRMs evolve over time before and during the pandemic, and how the financial and COVID-19 variables affect the SRMs. We start with the basic time series properties of the SRMs and the COVID-19 data.

5.1. Time Series Properties

Figure 1 plots the full sample of the SRMs, and Panel 1 in

Table 1. Descriptive statistics.

1. SRMs
	Mean	Median	Std.dev.	Skewness	Kurtosis	Min	Max	Obs.
(1) CoVaR (USD BN)
Level	136.78	124.98	72.00	1.67	9.23	26.63	692.62	4974
Log	4.78	4.83	0.54	−0.43	3.16	3.28	6.54	4974
Diff	0.02	0.28	11.32	−0.50	13.05	−125.87	74.84	4973
Diff(Log)	0.00	0.00	0.07	−0.23	4.33	−0.36	0.32	4973
(2) DIP (USD BN)
Level	86.25	68.97	69.07	1.39	5.29	1.94	409.76	4974
Log	4.00	4.23	1.16	−1.09	3.37	0.67	6.02	4974
Diff	0.01	−0.07	6.17	−3.46	143.84	−170.77	80.22	4973
Diff(Log)	0.00	0.00	0.07	−0.16	73.77	−1.23	1.20	4973
(3) SRISK (USD BN)
Level	639.39	615.66	265.04	0.30	2.47	139.18	1333.03	4974
Log	6.36	6.42	0.47	−0.65	2.90	4.94	7.20	4974
Diff	0.07	0.77	19.80	−1.22	19.41	−247.68	153.30	4973
Diff(Log)	0.00	0.00	0.03	−1.08	19.38	−0.37	0.29	4973
2. COVID-19
	Mean	Median	Std.dev.	Skewness	Kurtosis	Min	Max	Obs.
(1) Cases (1000 k)
Cumulative	47.08	36.85	36.48	0.21	1.54	0.00	103.80	1143
Daily	0.09	0.06	0.13	4.53	30.83	0.00	1.35	1142
7DMA	0.09	0.06	0.11	4.01	22.08	0.00	0.81	1139
Change in 7DMA	0.00	0.00	0.01	−1.17	51.43	−0.10	0.08	1138
(2) Deaths (1000)
Cumulative	624.56	618.03	376.42	−0.25	1.64	0.00	1123.84	1143
Daily	0.98	0.71	0.93	1.33	4.37	0.00	4.38	1142
7DMA	0.99	0.72	0.77	1.09	3.41	0.00	3.38	1139
Change in 7DMA	0.00	0.00	0.05	0.53	16.65	−0.34	0.49	1138

Note: CoVaR: Cconditional Value at Risk, DIP: Distress Insurance Premium, BN: billion, Diff: first difference, 7DMA: seven-day moving average.

provides their descriptive statistics. The major financial crises in the past two decades are clear from the joint peaks of the three SRMs: the 2007–2009 GFC, the 2011–2012 European sovereign debt crises, and the early 2020 COVID-19 initial shock.

To better understand the SRM dynamics, Figure 2 plots the SRMs followed by their main input variables. Note that some input variables, such as CDS spreads, correlation, and book asset, are originally at the firm level. To get the aggregate time series, we sum the variables that are measured in dollars, such as book asset, and average the rest of the variables across the sample firms. The subplots all look as expected, except the big spike for quasi leverage.12 That is due to the stock price crash during the GFC, when the book liability stayed almost unchanged. Among the seven state variables, VIX turns out to match the CoVaR dynamics best. For DIP, the average CDS spreads appear to be the first-order driving factor. For SRISK, there is no clear winner among its input variables.

To show the appropriate way of using the COVID-19 data, Figure 3 plots different forms of the case and death time series. The top-left subplot shows the daily cumulative data from the JHU website. It is obviously nonstationary and may not match the SRMs’ dynamics. The top-right subplot is the first difference of the cumulative numbers, meaning the daily new cases and new deaths. The lines contain obvious weekly seasonality. Thus, we take the seven-day moving average (7DMA) to remove the weekly pattern and show the results in the lower-left subplot. The lines are no longer noisy and show clear peaks and troughs throughout the pandemic. The lower-right subplot is the first difference of the 7DMA numbers, meaning the daily change in new cases and deaths after we smooth the raw daily numbers. Panel 2 in Table 1 provides the description statistics of these data to summarize their unconditional distributions.

To compare the SRMs dynamics with that of the COVID-19 data, Figure 4 adds the time series of the 7DMA COVID-19 cases and deaths to the SRMs plot. The time series of cases and deaths share similar dynamics, though at different scales. But except for the initial shock in early 2020, the SRMs and the COVID time series do not appear to move closely with each other. For example, the SRMs surged to their highest levels in March 2020, while the case numbers peaked in early 2022 due to the wide spread of the contagious Omicron variant. In addition, the SRMs increased in the first half of 2022 and remained elevated in the second half of 2022, likely due to other risk factors, such as inflation, while both the case and death numbers decreased in the spring of 2022, and the death numbers remained low afterwards. These divergences imply difficulty in finding a positive and significant relationship between the SRMs and the COVID-19 variables over the full pandemic period, and we may need to zoom into March 2020 to find a significant effect.

To determine the appropriate time series model for the SRMs and the COVID-19 variables, we first show their time series properties. Figure 5 and Figure 6 plot the first 20 sample autocorrelations of the SRMs and the COVID-19 variables. The SRMs appear persistent, and may be unit root, as the sample autocorrelations remain close to 1 even at lag 20 for the levels and the logarithm of the levels. Their first differences appear to be stationary. The cumulative and the 7DMA COVID-19 numbers are persistent, too. The persistency of daily raw numbers is harder to detect, due to their weekly seasonality. The change in 7DMA appears stationary.

The above observations are confirmed by

Table 2. Unit root tests.

1. Financial variables
	ADF test			PP test		$M^{GLS}$ tests				KPSS test
	$Z_{\rho }$	t	F	$Z_{\rho }$	t	$M{Z}_{\rho }^{GLS}$	$MS{B}^{GLS}$	$M{Z}_t^{GLS}$	$M{P}^{GLS}$	$LM$
CoVaR	−23.5 ***	−3.5 ***	6.2 **	−81.6 ***	−6.5 ***	−2.7	0.40	−1.1	8.7	23.5 ***
DIP	−8.8	−2.5	3.2	−10.1	−2.7 *	−0.4	0.75	−0.3	31.4	17.8 ***
SRISK	−13.1 *	−3.1 **	5.1 **	−15.2 **	−3.1 **	−0.8	0.67	−0.5	24.1	9.6 ***
VIX	−58.1 ***	−5.3 ***	14.0 ***	−80.9 ***	−6.4 ***	−49.6 ***	0.10 ***	−5.0 ***	0.5 ***	2.7 ***
$\Delta$(3mT)	−622.4 ***	−10.8 ***	58.3 ***	−3690.6 ***	−60.1 ***	−7.6 *	0.26 *	−2.0 **	3.2 **	0.6 **
SOFR-T	−34.4 ***	−3.9 ***	7.8 ***	−43.2 ***	−4.6 ***	−29.2 ***	0.13 ***	−3.8 ***	0.9 ***	9.9 ***
$\Delta$(BAA-10yT)	−1315.6 ***	−15.5 ***	119.5 ***	−4955.1 ***	−61.2 ***	−19.6 ***	0.16 ***	−3.1 ***	1.3 ***	0.1
$\Delta$(10y-3m)T	−11,506.9 ***	−15.7 ***	123.3 ***	−4208.8 ***	−66.0 ***	−1.5	0.55	−0.8	15.5	0.1
Housing ret	−5569.3 ***	−79.6 ***	3165.7 ***	−5523.0 ***	−79.7 ***	−10.9 **	0.21 **	−2.3 **	2.5 **	0.2
S&P500 ret	−5784.1 ***	−83.2 ***	3457.0 ***	−5477.0 ***	−84.3 ***	−26.9 ***	0.14 ***	−3.7 ***	1.0 ***	0.0
CDS	−6.7	−2.0	2.1	−6.8	−2.1	−1.1	0.61	−0.7	19.7	12.4 ***
Corr	−68.4 ***	−5.5 ***	15.0 ***	−33.7 ***	−4.3 ***	−7.8 *	0.25 *	−1.9 **	3.3 **	10.2 ***
Quasi lev	−17.4 **	−3.1 **	4.7 **	−13.3 *	−2.7 *	−4.1	0.34	−1.4	6.0	7.8 ***
−MES	−38.4 ***	−4.2 ***	8.7 ***	−59.4 ***	−5.4 ***	−30.6 ***	0.13 ***	−3.9 ***	0.8 ***	7.2 ***
Mkt cap	−14.5	−2.5	3.4	−14.0	−2.5	−12.7	0.19	−2.4	7.7	4.6 ***
Book asset	−6.4	−2.6	4.6	−6.4	−2.6	−1.0	0.65	−0.7	79.0	7.7 ***
2. COVID-19
	ADF test			PP test		$M^{GLS}$ tests				KPSS test
	$Z_{\rho }$	t	F	$Z_{\rho }$	t	$M{Z}_{\rho }^{GLS}$	$MS{B}^{GLS}$	$M{Z}_t^{GLS}$	$M{P}^{GLS}$	$LM$
(1) Cases
Cumulative	−0.2	−0.2	3.5	0.3	1.3	−2.8	0.42	−1.2	32.8	19.0 ***
Daily	−42.5 ***	−3.8 ***	7.3 ***	−128.0 ***	−8.6 ***	−0.6	0.68	−0.4	26.0	1.1 ***
7DMA	−28.6 ***	−3.4 **	5.7 **	−10.2	−2.3	−0.1	0.97	−0.1	51.9	1.1 ***
$\Delta$7DMA	−1768.8 ***	−7.7 ***	30.0 ***	−859.3 ***	−23.5 ***	−88.7 ***	0.07 ***	−6.6 ***	0.3 ***	0.1
(2) Deaths
Cumulative	−1.1	−1.8	5.1 **	−0.5	−3.1 **	−10.6	0.20	−2.2	9.3	19.0 ***
Daily	−30.8 ***	−3.3 **	5.6 **	−141.3 ***	−9.1 ***	−0.8	0.62	−0.5	21.3	2.3 ***
7DMA	−46.2 ***	−3.9 ***	7.5 ***	−6.6	−1.9	−0.8	0.64	−0.5	22.5	2.4 ***
$\Delta$7DMA	−83.0 ***	−4.5 ***	10.0 ***	−843.2 ***	−24.3 ***	−19.9 ***	0.15 ***	−3.1 ***	1.6 ***	0.2

Note: 1. ADF: augmented Dickey–Fuller test, PP: Phillips–Perron test, $M^{GLS}$: efficient modified PP test ($M{Z}_{\rho }^{GLS}$, $MS{B}^{GLS}$, and $M{Z}_t^{GLS}$) and modified feasible point-optimal test ($M{P}^{GLS}$), KPSS: (Kwiatkowski et al. (1992))’s Lagrange Multiplier (LM) test. 2. The null hypothesis for the ADF, PP, and $M^{GLS}$ tests is that the time series is unit root, while that for KPSS is the opposite. 3. There is no time trend in the test regression, except for market cap, book asset, and the cumulative COVID-19 variables. 4. SRMs and the daily and 7DMA COVID-19 variables are transformed as log(x + 1) to stabilize their distributions, before being put into the unit root tests. Similarly, VIX, CDS, and Quasi leverage are transformed as log(x). 5. *, **, and *** indicate statistical significance at the levels of 10%, 5%, and 1%, respectively. 6. VIX: CBOE Volatility Index, $\Delta$: first difference, 3mT: three-month Treasury yield, SOFR: Secured Overnight Financing Rate, BAA: Moody’s yield on BAA-rated seasoned corporate bonds, 10yT: ten-year Treasury yield, CDS: credit default swap spreads, Corr: average stock return correlations among the sample firms, Quasi lev = (book liability + market capitalization)/market capitalization, MES: marginal expected shortfall, Mktcap: market capitalization.

, which shows various unit root test results for the SRMs and their input variables and the COVID-19 variables. Each column corresponds to one test statistic. The first three columns are the three forms of the parametric Augmented Dickey–Fuller (ADF) test (Dickey and Fuller 1979). The fourth and fifth columns are the two forms of the nonparametric Phillips–Perron (PP) test (Phillips 1987; Phillips and Perron 1988). The sixth to ninth columns are the three forms of efficient modified PP test and the modified feasible point-optimal test, denoted as $M^{GLS}$ and proposed by Ng and Perron (2001). The last column is the KPSS Lagrange Multiplier (LM) test (Kwiatkowski et al. 1992). The null hypothesis for the ADF, PP, and $M^{GLS}$ tests is that the time series is unit root, while that for KPSS is the opposite, to solve the low-power problem for the unit root tests when the first autoregressive (AR) coefficient is less than, but very close to, 1. This means that we can treat a time series as stationary if all but the KPSS tests are significant. The statistic significance is determined by comparing the computed test statistics to the critical values we simulate with 100,000 Monte Carlo repetitions of sample sizes similar to our empirical samples.

Table 2 shows that the daily SRMs are unit root according to the $M^{GLS}$ and KPSS tests, which have better size and power properties than the basic ADF and PP tests. CDS spreads, market capitalization, and book asset are unit root under all test statistics. The first-difference or return type of variables, such as the change in the BAA-rated corporate bonds and 10-year Treasury yield spread ($\Delta$(BAA-10yT)), and the housing and the S&P 500 returns, are stationary. Other financial time series appear bordering stationary and unit root. Panel 2 in Table 2 shows that only the changes of 7DMA COVID-19 variables are stationary, while the cumulative, daily, and 7DMA are not.

The above observations imply that we should pair the levels of daily SRM with their input variables and with the 7DMA of cases or deaths to form commensurate regressions. We investigate these regressions in the following subsection.

5.2. Time Series Regressions

To formally study the relationship between the SRMs and their inputs in levels, we set up the following vector autoregression (VAR):13

$$\begin{array}{ccc}\hfill y_t& =& \mu +{\beta }^{\prime }{x}_t+u_t\hfill \end{array}$$

(18)

$$\begin{array}{ccc}\hfill x_{1,t}& =& x_{1,t-1}+v_{1,t}\hfill \end{array}$$

(19)

$$\begin{array}{ccc}\hfill x_{2,t}& =& c+{\zeta }^{\prime }{x}_{1,t-1}+v_{2,t},\hfill \end{array}$$

(20)

where $y_t$ is an SRM, $\mu$ is the intercept, and $x_t$ consists of SRMs’ input variables. $x_t$ = [$x_{1,t}$; $x_{2,t}$], $x_{1,t}$ consists of the input variables that are unit root, and $x_{2,t}$ consists of those that are stationary. Equation (18) estimates the cointegration (CI) relationship between SRMs and their inputs. All the residuals in Equations (18) to () are stationary and are allowed to be serially correlated and contemporaneously cross-correlated.

To solve the problem of correlation between $x_{1,t}$ and $u_t$ in Equation (18) due to the correlation between $u_t$ and $v_{1,t}$, we follow Stock and Watson (1993)’s Dynamic OLS. That is, we project $u_t$ on $v_{1,t}$:

$$u_t={\gamma }_1{v}_{1,t}+w_t.$$

(21)

Then, by construction $w_t$ is uncorrelated with $v_{1,t}$. Equation () means $v_{1,t}=x_{1,t}-x_{1,t-1}=\Delta x_{1,t}$, so Equation (18) can be rewritten as

$$y_t=\mu +{\beta }^{\prime }{x}_t+{\gamma }_1\Delta x_{1,t}+w_t.$$

(22)

As the CI regression residual $w_t$ and the $x_{1,t}$ innovation $v_{1,t}$ are not correlated, $x_{1,t}$ is no longer correlated with $w_t$. Similarly, we add $x_{2,t-1}$ to the right-hand side (RHS) of Equation (22), but we do not first difference it because $x_{2,t}$ is stationary. The final CI regression is the following:

$$y_t=\mu +{\beta }^{\prime }{x}_t+{\gamma }_1\Delta x_{1,t}+{\gamma }_2{x}_{2,t-1}+{ϵ}_t.$$

(23)

The parameters of interest are included in $\beta$.

To account for the potential serial correlations in ${ϵ}_t$, the t statistics is computed as ${\displaystyle \frac{\widehat{\sigma }}{\widehat{\lambda }}}·$ t-stat, where t-stat is the standard t statistics, ${\sigma }^2$ is the variance of ${ϵ}_t$, and ${\lambda }^2$ is the long-run variance of ${ϵ}_t$. We estimate ${\sigma }^2$ by ${\widehat{\sigma }}^2={\displaystyle \frac{1}{T-n}}{\sum }_{t=1}^T{\widehat{{ϵ}_t}}^2$, where n is the number of the RHS variables, and $\widehat{{ϵ}_t}$ is the OLS residual of Equation (23). We estimate ${\lambda }^2$ by the AR spectral estimator:

$$\begin{array}{ccc}\hfill {\widehat{ϵ}}_t& =& {\varphi }_1{\widehat{ϵ}}_{t-1}+{\varphi }_2{\widehat{ϵ}}_{t-2}+...+{\varphi }_p{\widehat{ϵ}}_{t-p}+e_t\hfill \end{array}$$

(24)

$$\begin{array}{ccc}\hfill {\widehat{\sigma }}_e^2& =& {\displaystyle \frac{1}{T-p}}\sum _{t=1+p}^T{\widehat{e}}_t^2\hfill \end{array}$$

(25)

$$\begin{array}{ccc}\hfill \widehat{\lambda }& =& {\widehat{\sigma }}_e/(1-\widehat{{\varphi }_1}-\widehat{{\varphi }_2}-...-\widehat{{\varphi }_p}).\hfill \end{array}$$

(26)

The AR truncation lag p should be $op\left(T^{{\displaystyle \frac{1}{3}}}\right)$ (Said and Dickey 1984). That is, as T goes to infinity, p also goes to infinity, but $p/T^{{\displaystyle \frac{1}{3}}}$ goes to 0 in probability. Thus, as in Stock and Watson (1993), we set p to be the largest integer less than or equal to $T^{{\displaystyle \frac{1}{5}}}$.14

Table 3. Time series regressions over the full sample with finance variables only.

	CoVaR	DIP	SRISK
VIX	0.61 (17.0) ***	−0.08 (−1.5)	−0.04 (−0.6)
$\Delta$(3mT)	−0.39 (−1.1)	0.24 (0.5)	−0.38 (−0.6)
SOFR-T	−0.41 (−1.4)	0.23 (0.5)	−0.30 (−0.6)
$\Delta$(BAA-10yT)	−0.00 (−0.0)	0.14 (0.3)	0.04 (0.1)
$\Delta$(10y-3m)T	−0.08 (−0.6)	0.01 (0.0)	−0.03 (−0.1)
Housing ret	0.01 (1.0)	−0.00 (−0.1)	0.00 (0.1)
S&P500 ret	−0.00 (−0.3)	−0.00 (−0.0)	−0.00 (−0.1)
CDS	0.23 (11.0) ***	1.07 (33.7) ***	−0.01 (−0.2)
Corr	0.81 (9.0) ***	1.99 (14.6) ***	0.43 (2.6) ***
Quasi lev	0.50 (8.2) ***	−0.34 (−3.7) ***	−0.58 (−5.3) ***
−MES	−3.30 (−2.9) ***	−4.92 (−2.8) ***	8.69 (4.2) ***
Mkt cap	0.73 (10.2) ***	−0.36 (−3.4) ***	−1.19 (−9.3) ***
Book asset	0.22 (2.4) **	1.48 (10.7) ***	2.37 (14.2) ***

Note: 1. This table reports the estimation results for the Dynamic OLS: $y_t=\mu +{\beta }^{\prime }{x}_t+{\gamma }_1\Delta x_{1,t}+{\gamma }_2{x}_{2,t-1}+{ϵ}_t$, where $y_t$ is an SRM, $\mu$ is the intercept, and $x_t$ consists of SRMs’ input variables. $x_{1,t}$ consists of the variables in $x_t$ that are unit root, and $x_{2,t-1}$ consists of the rest variables lagged by one period. t statistics adjusted for the long-run variance are reported in parentheses. ** and *** indicate statistical significance at the levels of 5% and 1%, respectively. 2. −MES is the negative of its original negative values. 3. SRMs are transformed as log(x+1). VIX, CDS spreads, and Quasi leverage are transformed as log(x).

shows the regression results over the full sample period with the financial variables only. The inputs for each SRM have the first-order effects; thus, the signs of their coefficient estimates (if significant) are intuitive. The effects of other SRMs’ inputs on a given SRM have the residual effects, after partialing out the effects from the own input variables, so their signs may not always be intuitive. For example, the VIX effect is significantly positive for CoVaR, but not for DIP and SRISK, and MES (marginal expected shortfall) is significantly positive only for SRISK.15 Nevertheless, CDS spreads and equity correlation, if significant, always positively affect the SRMs. Most noticeably, book asset, which is a proxy for firm size, has significantly positive effects on all the SRMs. This observation will appear again in the cross-sectional analysis, showing the robustness of the size effect.

To study the effect of the COVID-19 pandemic, we add the 7DMA of cases and deaths (log transformed) separately on the RHS of Equation (23) as the exogenous variables and run the regression over the COVID-19 sub-sample period.

Table 4. Time series regressions over the COVID-19 sub-sample.

COVID-19 cases
	CoVaR	DIP	SRISK
Cases	0.03 (3.4) ***	−0.00 (−0.8)	−0.01 (−1.1)
IC and fin.	Yes	Yes	Yes
COVID-19 deaths
	CoVaR	DIP	SRISK
Deaths	0.05 (4.2) ***	−0.01 (−0.7)	−0.03 (−1.9) *
IC and fin.	Yes	Yes	Yes

Note: 1. This table reports the estimation results for the Dynamic OLS: $y_t=\mu +{\beta }_1^{\prime }{x}_t+{\beta }_2^{\prime }COVI{D}_t+{\gamma }_1\Delta x_{1,t}+{\gamma }_2{x}_{2,t-1}+{ϵ}_t$, where $y_t$ is an SRM, $\mu$ is the intercept (IC), $x_t$ consists of SRMs’ input variables, and $COVI{D}_t$ is either COVID-19 cases or deaths. $x_{1,t}$ consists of the variables in $x_t$ that are unit root, and $x_{2,t-1}$ consists of the rest variables lagged by one period. For conciseness, only ${\beta }_2$ estimates are reported. The t statistics adjusted for the long-run variance are reported in parentheses. * and *** indicate statistical significance at the levels of 10% and 1%, respectively. 2. SRMs and the COVID-19 variables are transformed as log(x + 1).

reports the regression results. As the effects of the financial variables remain similar to those in the full sample, we omit them in the output to avoid repetitions. The effects of both cases and deaths on CoVaR are positive and significant, which is intuitive. However, they become insignificant or marginally negative for DIP and SRISK. Thus, there is no consistent effect of the COVID-19 variables on the SRMs, a result hinted by Figure 4.

5.3. March 2020

Figure 4 suggests that it is more promising to look into the first wave of the pandemic to detect the COVID-19 effect on the SRMs than to use the complete pandemic period. To determine the first wave of the pandemic, we check both the pandemic and the broader market data. In terms of the pandemic data, the daily 7DMA of the confirmed cases exploded from single digits in February, 2020, to thousands in March, peaking at 32,028 on 7 April. That of the new deaths also grew quickly from single digits in February to hundreds in March, peaking at 2237 on 20 April. In terms of the broader market data, the VIX index, also known as the fear gauge and reflecting market uncertainty, surged from the range of 10% to 20% in January and most of February to 39% on 12 February, then hovered in the range of 60% to 80% between 12 and 27 March, and decreased to the range of 50% then 40% from 30 March into April.16 Putting everything together, March 2020 is the calendar month when the pandemic situation quickly worsened and the broader market actively responded to this exogenous shock. Thus, it is an ideal period to detect the pandemic effect on the SRMs.

In this short period of one month, the long-run relationship among the financial variables is less of a concern. Given the exogeneity of the COVID-19 variables, we run a simple OLS regression of each SRM on a constant and the 7DMA of cases or deaths. All the time series are divided by their sample standard deviations in this period for ease of coefficient display.

Table 5. Regressions for March 2020.

COVID-19 cases
	CoVaR	DIP	SRISK
Cases	0.76 (3.7) ***	0.29 (1.2)	0.57 (2.8) **
Intercept	2.32 (8.7) ***	2.55 (5.7) ***	4.66 (11.5) ***
${\mathrm{R}}^2$	0.58	0.08	0.32
COVID-19 deaths
	CoVaR	DIP	SRISK
Deaths	0.65 (2.9) ***	0.20 (1.0)	0.51 (2.8) **
Intercept	2.47 (8.3) ***	2.63 (6.0) ***	4.75 (12.1) ***
${\mathrm{R}}^2$	0.42	0.04	0.26

Note: This table reports the estimation results of regressing each SRM on a constant and the COVID-19 cases or deaths in March 2020. All the time series are divided by their sample standard deviations in this period. The t statistics with the HAC (Heteroskedasticity and Autocorrelation Consistent) standard errors are reported in parentheses. ** and *** indicate statistical significance at the levels of 5% and 1%, respectively.

reports the estimation results. Except for DIP, both cases and deaths have positive and significant effects on CoVaR and SRISK, and the corresponding $R^2$ are decent, ranging from 0.26 to 0.58.

To understand the significant effects, we plot the SRMs and the COVID-19 cases and deaths for March 2020 in Figure 7. The case and death numbers increased sharply in this period. In comparison, the SRMs increased from the beginning of March to around 20 March, then DIP decreased significantly, while CoVaR exhibited some decreasing patten toward the end of March, but SRISK continued to increase. The increasing patterns of CoVaR and SRISK in most or all of March 2020 explain the positive and significant relationship between them and the COVID-19 variables. The decreasing pattern of DIP in the final one-third of March 2020 offsets its increase in the early and middle parts of that month, resulting in the insignificant COVID-19 effect.

The question now is what led to the decreases of DIP and CoVaR toward the latter part of March 2020. The obvious candidates are the government interventions introduced in this period in response to the stress caused by the pandemic. In an emergency move on Sunday, 15 March, the Federal Reserve announced it had dropped its benchmark interest rate to zero and launched a new round of quantitative easing (Liesman 2020). On 17 March, the Federal Reserve established the first two facilities: the Primary Dealer Credit Facility (PDCF), “to support the credit needs of American households and businesses” (Federal Reserve 2020b), and the Commercial Paper Funding Facility (CPFF), “to support the flow of credit to households and businesses” (Federal Reserve 2020a). These two dates are marked by vertical lines in Figure 7. Shortly after these policy measures, the SRMs started to decrease, showing the effectiveness of these government interventions in mitigating the COVID-19 effects on the SRMs.17

6. Cross-Sectional Analysis of the SRMs at the Beginning of the COVID-19 Pandemic

In the cross-sectional dimension, we analyze each firm’s SRMs and identify firm characteristics that explain their contributions or predict the surge in their contributions to the SRMs at the beginning of the pandemic. We focus on the beginning of the pandemic because the SRMs all peaked in this period, and as Section 5 shows, this is the period during which the COVID-19 effects are likely significant.

Figure 8 shows each firm’s SRMs from 1 December 2019 (pre-pandemic) to 31 March 2020. Across almost all firms, the SRMs surge in March 2020. This dynamic pattern matches what we observe in the aggregate SRMs in Section 5.

To visualize the relative magnitudes of the firms’ SRMs, Figure 9 compares their values in December 2019 to their values in the first three months of 2020, the period leading up to the major peak of the financial crisis during the pandemic. The values are from the last business day of each month. Before COVID-19 took a major toll, the relative rankings of firms were more or less stable, as the plotted dots in the first row of Figure 9 follow a relatively straight 45-degree line. However, as time passed, the second and third rows show more and more dispersed patterns. This implies that the different firms fared differently when the pandemic initially hit the financial system. Figure 10 magnifies this comparison by showing the firms’ rankings on 31 December 2019 and on 31 March 2020, with the firms’ tickers added. Among the three SRMs, CoVaR is the one showing the least distribution change, as the firms line up relatively well along the 45-degree line. DIP shows a little more distribution change, with Barclays moving up the most in its DIP ranking. Indeed, it is the only firm whose CDS spreads and equity correlation more than doubled over the three-month period. SRISK exhibits the most significant distribution change, with a clear pattern. The largest four firms—JPM, BAC, WFC, and C—shoot up in their SRISK rankings. The implication is that even though these largest U.S. banks were doing very well during the calm period right before the pandemic, their expected capital shortfalls during the system stress time could easily overtake other firms when an unexpected crisis hit.

Given the different experiences of different firms, we first identify firm characteristics that can explain the cross-sectional differences in SRMs during the crisis in March 2020 by the following panel regression:

$$y_{i,t}={\mu }_i+{\beta }^{\prime }{x}_{i,t}+{\gamma }^{\prime }COVI{D}_t+{ϵ}_{i,t},$$

(27)

where $y_{i,t}$ is an SRM for firm i on day t, ${\mu }_i$ is the fixed effect for firm i, $x_{i,t}$ is firm i’s characteristics on day t, and $COVI{D}_t$ is the 7DMA of either the cases or deaths on day t. As book asset does not vary within a month, and there is a firm fixed-effect term, to avoid multicollinearity, book asset is not included in $x_{i,t}$.

To allow for the autocorrelations of ${ϵ}_{i,t}$ for each firm i, and the contemporaneous correlations across different firms on day t, the variance–covariance matrix of the parameter estimates are clustered both at the firm and the day dimensions (Thompson 2011; Cameron et al. 2011). Accordingly, we apply the small-sample adjustment to the t statistic by multiplying it with the constant $c={\displaystyle \frac{J}{J-1}}{\displaystyle \frac{N-1}{N-K}}$, where J is the minimum number of groups along both dimensions. As there are 13 firms in our sample and 22 days in March 2020, $J=13$. N is the total number of observations, and K is the number of the RHS variables. The corresponding t distribution has $13-1=12$ degrees of freedom (Hansen 2007; Cameron et al. 2011).

Table 6. Explanatory panel regressions (March 2020).

COVID-19 cases
	CoVaR	DIP	SRISK
CDS (%)	3.24 (0.8)	5.09 (3.1) ***	−5.59 (−1.2)
Corr (%)	−0.22 (−1.5)	−0.02 (−0.4)	0.20 (1.0)
Quasi lev	−0.03 (−0.2)	0.09 (2.0) *	−0.23 (−1.0)
−MES (%)	1.33 (0.9)	0.06 (0.2)	1.31 (1.0)
Mkt cap (USD BN)	−0.57 (−3.1) ***	−0.18 (−7.0) ***	−0.96 (−11.3) ***
Cases	1.01 (3.1) ***	−0.02 (−0.6)	0.30 (1.6)
FE	Yes	Yes	Yes
COVID-19 deaths
	CoVaR	DIP	SRISK
CDS (%)	2.18 (0.6)	5.03 (3.2) ***	−4.83 (−1.3)
Corr (%)	−0.19 (−1.3)	−0.02 (−0.4)	0.19 (1.2)
Quasi lev	−0.06 (−0.4)	0.09 (2.0) *	−0.24 (−1.4)
−MES (%)	2.13 (1.5)	0.06 (0.2)	1.34 (1.2)
Mkt cap (USD BN)	−0.56 (−4.7) ***	−0.18 (−7.2) ***	−0.96 (−11.3) ***
Deaths	26.58 (2.5) **	−0.68 (−0.9)	11.23 (2.3) **
FE	Yes	Yes	Yes

Note: This table reports the estimation results for the panel regression $y_{i,t}={\mu }_i+{\beta }^{\prime }{x}_{i,t}+{\gamma }^{\prime }COVI{D}_t+{ϵ}_{i,t}$, where $y_{i,t}$ is an SRM for firm i on day t, ${\mu }_i$ is the fixed effect for firm i, $x_{i,t}$ is firm i’s characteristics on day t, and $COVI{D}_t$ is the 7DMA of either the cases or deaths on day t. The data are for March 2020. The t statistics with the variance–covariance matrix of the parameter estimates clustered at the firm and day dimensions are reported in parentheses. *, **, and *** indicate statistical significance at the levels of 10%, 5%, and 1%, respectively.

reports the explanatory regression results. Most of the firm characteristics are insignificant in explaining the firm-level SRMs. The only exception is market capitalization. Though it is an input only for SRISK, it turns out to have negative and significant effects on all three SRMs. This implies that market capitalization can serve as a cushion that protects firms from negative shocks and, thus, helps to stabilize the financial system. Like in Section 5.3, COVID-19 cases and deaths have significantly positive effects on firms’ CoVaR and SRISK, but not on DIP. So the COVID-19 effects on the aggregate SRMs remain at the firm level.

To study how the effects of the firm characteristics on their SRMs evolve when the COVID-19 pandemic hits the system, we run the following event study type of panel regression by adding an interactive term between the firm characteristics and the COVID-19 indicator ($I\left(COVI{D}_t\right)$) to the RHS of Equation (27):

$$y_{i,t}={\mu }_i+{\beta }^{\prime }{x}_{i,t}+{\gamma }^{\prime }{x}_{i,t}\times I\left(COVI{D}_t\right)+{ϵ}_{i,t}.$$

(28)

The data are from December 2019 and March 2020. $I\left(COVI{D}_t\right)=0$ for December 2019 and 1 for March 2020. We apply the same clustering used in Equation (27) to Equation (28).

Table 7. Event study panel regressions (December 2019 + March 2020).

	CoVaR	DIP	SRISK
CDS (%)	−0.47 (−0.2)	3.67 (2.7) **	−3.95 (−1.4)
Corr (%)	−0.08 (−0.5)	−0.05 (−0.7)	−0.09 (−0.6)
Quasi lev	−0.25 (−1.6)	0.10 (3.2) ***	−0.11 (−0.6)
−MES (%)	1.93 (1.4)	0.40 (1.2)	9.61 (3.8) ***
Mkt cap (USD BN)	−0.51 (−5.8) ***	−0.15 (−7.5) ***	−0.82 (−10.4) ***
CDS (%) × COVID	−2.31 (−1.1)	1.03 (1.5)	−1.26 (−1.2)
Corr (%) × COVID	−0.07 (−0.6)	−0.03 (−0.7)	0.39 (3.0) **
Quasi lev × COVID	0.16 (5.2) ***	0.03 (3.2) ***	−0.10 (−3.5) ***
−MES (%) × COVID	2.01 (1.0)	−0.06 (−0.1)	−7.92 (−3.3) ***
Mkt cap (USD BN) × COVID	−0.02 (−0.7)	−0.01 (−1.9) *	−0.05 (−1.4)
FE	Yes	Yes	Yes

Note: This table reports the estimation results for the event study type of panel regression $y_{i,t}={\mu }_i+{\beta }^{\prime }{x}_{i,t}+{\gamma }^{\prime }{x}_{i,t}\times I\left(COVI{D}_t\right)+{ϵ}_{i,t}$, where $y_{i,t}$ is an SRM for firm i on day t, ${\mu }_i$ is the fixed effect for firm i, $x_{i,t}$ is firm i’s characteristics on day t, and $I\left(COVI{D}_t\right)$ is the COVID-19 indicator, equal to 0 for December 2019 and 1 for March 2020. The t statistics with the variance–covariance matrix of the parameter estimates clustered at the firm and day dimensions are reported in parentheses. *, **, and *** indicate statistical significance at the levels of 10%, 5%, and 1%, respectively.

reports the estimation results. The cushion effect of market capitalization continues to hold in this event study regression. For DIP, market capitalization has an additional negative effect when the COVID-19 pandemic hits, though this effect is only marginal. The effects of other firm characteristics remain sporadic or inconsistent across the SRMs.

Finally, to identify firm characteristics that predict the surge in a firm’s SRMs when the pandemic initially hits the financial system, we regress the firms’ SRMs of 31 March 2020 on their characteristics of 31 December 2020. As this is a cross-sectional regression, we add book asset back to the RHS.

Table 8. Predictive regressions (31 December 2019 versus 31 March 2020).

	CoVaR	DIP	SRISK
CDS (%)	2.70 (0.9)	1.16 (1.6)	5.13 (0.9)
Corr (%)	0.54 (1.5)	−0.06 (−2.3) *	−0.52 (−1.4)
Quasi lev	−0.32 (−1.4)	0.00 (0.0)	0.20 (0.7)
−MES (%)	−0.33 (−0.1)	2.26 (2.9) **	7.75 (1.0)
Mkt cap (USD BN)	0.06 (0.7)	0.00 (0.4)	−0.12 (−1.3)
Book asset (USD BN)	0.04 (3.0) **	0.01 (6.1) ***	0.08 (6.2) ***
Intercept	−33.09 (−2.4) *	−4.54 (−1.7)	−4.82 (−0.2)

Note: This table reports the estimation results for regressing the firms’ SRMs of 31 March 2020 on their characteristics of 31 December 2020. The t statistics with the HAC standard errors are reported in parentheses. *, **, and *** indicate statistical significance at the levels of 10%, 5%, and 1%, respectively.

reports the estimation results. The effects of most firm characteristics remain sporadic, but book asset turns out to have positive and significant effects on all three SRMs, even though it is an input only for SRISK. This result shows the significant power of firm size in predicting a firm’s SRM surge when a negative shock hits the financial system, echoing the results observed in Figure 10.

7. Discussion

As Section 5 and Section 6 study the pandemic effect on SRMs along the time series and cross-sectional dimensions, we discuss our results and compare them to those in the literature along these two dimension in this section.

Along the first dimension of time series, we study the effect of the pandemic, as well as those of other financial variables, on the three SRMs separately. The results show some similarity and difference across different SRMs. The main similarity is that the SRMs are significantly affected by their input financial variables in the same way as shown in the papers proposing these measure (Adrian and Brunnermeier 2016; Huang et al. 2009; Acharya et al. 2012), even when we substantially extend the sample period from the 2007–2009 GFC to the post pandemic period of 2024. In addition, we observe that CDS spreads, equity correlation, and firm size have positive and significant effects on the SRMs for which they are not the input variables. Thus, we extend the empirical findings in the above SRM papers from their own SRM into other SRMs, showing robust explanatory power of these variables.

For the pandemic effect, we find the COVID-19 variables have significant and positive effects on CoVaR over the full sample period, but not on DIP or SRISK. If we restrict the sample to March 2020, the pandemic effect is also positive and significant for SRISK. Our significance result on CoVaR and SRISK in March 2020 is consistent with most of the literature studying the pandemic effect in early 2020, such as Borri and di Giorgio (2022), Gomis-Porqueras et al. (2023), and Acharya et al. (2023). Our observation of the significant effect on CoVaR over the complete pandemic period is consistent with the finding of Bevilacqua et al. (2023), who also use CoVaR, although their data covers 10 countries and is limited only to 2020. However, the lack of significant effect on DIP and SRISK over the complete pandemic period highlights the importance of using more than one SRM to obtain a robust result of the pandemic effect on FSR and avoid observations driven only by a particular SRM.

The detailed examination of March 2020 and comparison of this month to the complete pandemic period reveal the mitigating effect of government interventions, which help to break the link between the COVID-19 variables and the three SRMs, thus leading to the insignificance pandemic effect on DIP and SRISK over the complete pandemic period. The effectiveness of government interventions in early 2020 echoes several existing papers. For example, Borri and di Giorgio (2022) find that the Pandemic Emergency Purchasing Programme (PEPP) announced by the European Central Bank (ECB) on March 18 calmed the European banking sector. Bevilacqua et al. (2023) point out that fiscal and regulatory policies helped to reduce CoVaR across 10 countries in 2020. The mitigating effect of government interventions on SRMs may be due to the fact that these policies help stabilize individual FIs. For example, Rahman and Warusawitharana (2023) study the effect of Federal Reserve’s temporary leverage ratio relief program, which allowed banks to exclude U.S. Treasuries and deposits at Federal Reserve Banks from their Supplementary Leverage Ratio (SLR). The authors observe that this program helped to stabilize the stock prices of the banks subject to the SLR rule. The authors interpret it as the positive view of this announcement by market participants. This result directly applies to all the banks in our sample, as they are G-SIBs and thus subject to both the basic and additional SLR requirements.

Along the second dimension of cross-sections, we observe that firm size, measured by book asset, significantly predicts the surge of a firm’s contribution to FSR at the initial shock of the pandemic. This result is robust across all three SRMs, and consistent with the finding of Borri and di Giorgio (2022) that larger European banks contribute more to the FSR (measured by CoVaR) of the European banking sector in their short sample ending in September 2020.

In addition to the size effect, we also observe that market capitalization helps to reduce a firm’s contribution to FSR during the initial shock of the pandemic. This observation is relatively new to the pandemic literature, but central to the foundation of SRISK, a capital shortfall-based SRM proposed during the GFC. Thus, our observation generalizes the idea behind SRISK to other SRMs and to the new crisis of the COVID-19 pandemic.

8. Conclusions

The COVID-19 pandemic has caused major disruption to our daily life, creating an economic and financial crisis. This is a unique situation, as the pandemic can be treated as an exogenous shock to the system, which is rare among various explanatory variables that researchers typically have. Hence, it is important and interesting to study how the FSR evolves before and during the pandemic, and how COVID-19, as well as the financial variables, affect the dynamic of the aggregate FSR, and which firm characteristics explain or predict the cross-sectional differences of the firms’ FSR contributions.

In view of the timeliness and forward-looking nature of market data, we use three market-based SRMs—CoVaR, DIP, and SRISK—to obtain a relatively complete picture of the aggregate and firm-level FSR. For explanatory variables, we include the financial variables that are inputs of these SRMs as well as two COVID-19 variables—daily confirmed cases and deaths.

In the time series dimension, when we include only the financial variables for the full sample period, we find that financial risk factors, such as CDS spreads, equity correlation, and firm size, have positive and significant effects on the SRMs. For the COVID-19 variables, it is relatively hard to find their explanatory power over the complete pandemic period. There are at least two reasons. First, the Federal Reserve intervened in late March 2020, which calmed down the market and reduced the SRMs, while the COVID-19 variables continued to surge. The mitigating effect of government interventions is consistent with the findings of Borri and di Giorgio (2022) for ECB’s PEPP announcement and Bevilacqua et al. (2023) for fiscal and regulatory policies across 10 countries. Second, the improved public measures against the COVID-19 pandemic prevent another surge in the COVID-19 cases and deaths since the beginning of 2022. Meanwhile, other risk factors, such as inflation, push up SRMs in 2022, driving a wedge between the SRMs and the COVID-19 variables.

However, at the first wave of the pandemic in March 2020, the surge in the SRMs and the COVID-19 variables align relatively well. This is the period when we conduct the cross-sectional analysis of the firms’ FSR contributions. In the contemporaneous explanatory regression, we find that market capitalization has negative and significant effects on all three SRMs, showing the cushion effect of market capitalization that protects firms from negative shocks. COVID-19 cases and deaths have significantly positive effects on firms’ CoVaR and SRISK, just like their effects on the aggregate SRMs in this period. In terms of prediction, size turns out to have the most robust predictive power for each firm’s SRMs when the pandemic first hits the system. The positive and statistical significance of the size effect echoes the finding of Borri and di Giorgio (2022) for European banks.

The policy implications of the empirical observations include the following. First, proper market interventions, such as the ones carried out by the Federal Reserve in March 2020, can help to bring down the FSR level, restore the resilience of the firms, and mitigate the negative effects from the pandemic. Second, the current financial regulation of required capital holding is effective in protecting firms against negative shocks, thus stabilizing the financial system. Third, the current designation of SIFIs based on their sizes (as well as other considerations) is a good practice. Large firms may do well in the calm period, but their SRM contributions can surge more than those of smaller firms when a large, unexpected shock hits the system.

This paper focuses on the U.S. FSR over the sample period from early 2000s to 2024. There are two directions for future research. First, our sample can be extend cross-sectionally. Researchers can study the pandemic effect on other countries or regions. This will provide a broader picture of the pandemic around the world. We may observe similarities, but also reveal distinct results arising from different financial systems, economies, or other social or natural factors. These results will help regulators in different areas to come up with measures that are most suitable for their situations. Second, if good-quality market data are available, we can extend the sample further back in history, and compare the effects of different historical crises on FSR. By incorporating more episodes of historical stress events, we may be able to discover patterns that are consistent across different crises, which may help us design robust measures in response to future crises.