COVID-19 and the forward-looking
stock-bond return relationship
Xiaojing Caiab, Yingnan Congc, Ryuta Sakemotoad
March 23, 2021
aGraduate School of Humanities and Social Sciences, Okayama University, 3-1-1, Tsushima-naka,

Kita-ku, Okayama 700-8530, Japan. Email: caicai@okayama-u.ac.jp
bGraduate School of Economics, Kobe University, 2-1, Rokkodai, Nada-Ku, Kobe 657-8501, Japan.
cBusiness School, China University of Political Science and Law, 25 Xitucheng Lu, Haidian District,

Beijing, 100088, China.
dKeio Economic Observatory, Keio University, Minato-ku, Tokyo, 108-8345, Japan.

Abstract
This study analyzes the relationship between the forward-looking stock-bond returncorrelations and the number of COVID-19 cases using a quantile approach that isbeneficial to explore non-linear relationships. It shows that there are heterogeneous
responses across regions and countries. Specifically, the negative stock-bond correlations
weaken as the number of confirmed cases in the regions of North America (the U. S. andCanada) and Asia-Pacific (Australia and Japan) increases. These findings suggest that
uncertainty triggered by COVID-19 impacts the financial markets more significantly than
the actual confirmed cases. Our result also highlights that this pattern is not observed inEuropean countries.
JEL: C32; G01; G15
Keywords: Forward-looking stock-bond correlations; COVID-19; DCC-GARCH

11. Introduction
The World Health Organization (WHO) declared that the reported coronavirus disease(COVID-19) cases surpassed 61 million, and the total number of deaths was over 1
million globally by December 1, 2020.1 The outbreak of COVID-19 has a great impact
upon economic activities and burgeoning studies are exploring the impact of thepandemic on financial markets.2 For instance, Baker et al. (2020) report that the COVID19 pandemic raised stock market volatility, which was not observed in the previous
influenza pandemics. Ramelli and Wagner (2020) highlight that stock prices of firms
exposed to international trade risk underperformed at the beginning of the outbreak.
Gormsen and Koijen (2020) show that a forecast of annual growth in dividends
significantly declined since January 2020.
In this study, we focus on stock and bond correlations during the COVID-19 pandemic.
Previous studies have shown that a negative correlation between stock and bond returns
becomes stronger with high market uncertainty and illiquidity periods (Connolly et al.,2005, 2007; Baele et al., 2010, 2020). The COVID-19 outbreak causes high market
uncertainty and may influence the stock and bond correlations. Papadamou et al. (2020)
present empirical evidence that an increase in the confirmed COVID-19 cases results innegative stock and bond correlations. We extend the works of Connolly et al. (2005, 2007)
and Papadamou et al. (2020) to investigate the responses of stock-bond correlations
during the COVID-19 pandemic across international markets. Our study contributes tothe literature in the following manner.
Firstly, the study focuses on forward-looking correlations during the COVID-19
pandemic. Connolly et al. (2005, 2007) highlight that market uncertainty leads to more
frequent revisions of expected returns for investors, resulting in negative stock and bondcorrelations. The empirical evidence provided by Giglio et al. (2021) and Samels (2021)
supports our hypothesis that the market crash triggered by the pandemic changes investors’
expectations. Giglio et al. (2021) use data from the survey of Vanguard investors andreveal that investors perceive a more pessimistic outlook of the stock market after themarket crash triggered by the pandemic. Samels (2021) deploys Google search volume
for “coronavirus” and reports that the search volume is negatively linked to stock market
returns.
1

See Weekly epidemiological update - 1 December 2020 (who.int).

2 For example, Liu et al. (2021) measure the dynamic network strength during the coronavirus

pandemic, Albulescu (2021) investigates how official announcements regarding new cases of
COVID-19 impacted the financial markets, Zaremba et al. (2020) explore the relationship between
policy response to the COVID-19 pandemic and stock market volatility, and Goodell (2020)
summarizes the economic impact of COVID-19.
2

Secondly, the study explores the heterogeneity of responses across various countries
based on the studies presenting the variation in responses of financial markets by regionand social structure. Zhang et al. (2020) explore international stock market correlations
and observe that Asian markets were more segmented than European and North American
markets. Erdem (2020) uses the political freedom index provided by Freedom House andfinds that counties receiving high scores suffered more severe stock market downturns.
Finally, the study’s approach explores a non-linear relationship between market
uncertainty and correlations. Adrian et al. (2019) highlight that an increase in expected
returns in the stock market is associated with a moderate, but not an extreme, rise inmarket uncertainty. Accordingly, we do not employ a linear regression model, as done by
Papadamou et al. (2020),3 and adopt a quantile approach instead.
The study showed that an increase in the number of confirmed COVID-19 cases
mitigates a negative relationship between stock and bond returns in the markets in North
America (the U.S. and Canada) and Asia-Pacific (Australia and Japan). Our finding isrelated to gradual information diffusion (Hong and Stein, 1999). Investors do not havesufficient information to evaluate how the pandemic affects stock markets, thus,
demanding safe Treasury bonds; i.e., they sell risky stocks and buy safe Treasury bonds
at the beginning of the pandemic, while they obtain more information about the pandemic
and adjust the risk level of their portfolios.
2. Data and methodology
This study investigates whether changes in the COVID-19 pandemic influence theforward-looking stock-bond correlations. The daily confirmed cases of the COVID-19
are obtained from https://ourworldindata.org (Roser et al., 2020). This dataset presents
statistics on the COVID-19 pandemic for all countries and is updated daily. Erdem (2020)
uses this dataset to investigate the stock market performance in 195 countries during the
COVID-19 outbreak.
We also employ the MSCI net total return local indices as stock market indices and theFTSE government bond local indices as bond market indices. These data are obtained
from Bloomberg. The returns are calculated as the first difference in the logarithmic prices.
This study’s sample period is from February 3, 2020, to December 3, 2020. This start dateis chosen because the first positive case was observed in Italy on January 30, 2020, andon January 31, 2020, in the U.K. Twenty-one developed financial markets from 3 regions,Cepoi (2020) also shows that relationships between stock market returns and COVID-19 news are
not linear.
33

including North America (the U.S. and Canada), Asia Pacific (Australia, New Zealand,
and Japan), and Europe (Austria, Belgium, Denmark, Finland, France, Germany, Greece,
Ireland, Italy, Netherland, Norway, Portugal, Spain, Sweden, Switzerland, and the U.K.)
are selected. Table A1 in the Online Appendix presents the descriptive statistics for alldata series.
We first estimate the dynamic correlations between stock and bond returns for eachcountry using the dynamic conditional correlation – generalized autoregressive
conditional heteroskedasticity (DCC-GARCH) model (Engle, 2002). Our interest is tounderstand how the expected returns on stocks and bonds are updated. The DCC-GARCH
provides time-varying correlations using the information of up to 𝑡 − 1. Considering 𝑟𝑡
as a vector of asset returns with the information set ℑ𝑡−1, the DCC-GARCH process is
described as
𝑟𝑡 |ℑ𝑡−1 ~ 𝑁(𝜇, 𝐷𝑡 𝑅𝑡 𝐷𝑡 )(1)

where 𝐷𝑡 is a diagonal matrix of the standard deviations of returns on the diagonal,
and 𝑅𝑡 is the conditional correlation matrix of the standardized residuals of returns,
given by𝑅𝑡 = 𝑑𝑖𝑎𝑔(𝑄𝑡 )−1/2 𝑄𝑡 𝑑𝑖𝑎𝑔(𝑄𝑡 )−1/2.
(2)
It is assumed that 𝑄𝑡 is an autoregressive process given by′
𝑄𝑡 = (1 − 𝑎 − 𝑏)𝑄̅ + 𝑏𝑄𝑡−1 + 𝑎𝜀𝑡−1 𝜀𝑡−1
, 𝑤𝑖𝑡ℎ 𝑎 ≥ 0, 𝑏 ≥ 0, 𝑎 + 𝑏 < 1 (3)where 𝑄̅ is the unconditional correlation coefficient matrix, and 𝜀𝑡−1 is the laggedfunction of standardized residuals of returns. Thus, the conditional correlation
coefficient in a bivariate case is obtained by
𝜌12,𝑡 =𝑞12,𝑡√𝑞11,𝑡 √𝑞22,𝑡(4)

where 𝑞𝑖𝑗,𝑡 is the ij element of 𝑄𝑡 in Equation (3).
Forward-looking correlations are evaluated for three different time horizons. A dailychange in the correlations is calculated from the daily conditional correlations from t
to t+1. Similarly, a weekly (monthly) change in the correlations was obtained fromdaily conditional correlations from t to t+5 (t+22). Papadamou et al. (2020) explore
stock-bond correlations during the pandemic. However, they focus oncontemporaneous correlations. As investors may update their expected returns on
stocks and bonds when they obtain new information about the pandemic, and we use
the forward-looking stock-bond correlations (Connolly et al., 2005, 2007). The meanand standard deviation of the forward-looking correlations are calculated following the
average value of the confirmed cases in the previous week (from t-4 to t).

4

3. Empirical results
This section presents the means and standard deviations of the forward-looking
correlations following the given quantile values of confirmed COVID-19 cases. Table 1
presents the empirical results for North America (the U.S. and Canada), Asia-Pacific(Australia, New Zealand, and Japan). The data shows that all forward-looking stock-bondcorrelations are negative. Connolly et al. (2005, 2007) report that the forward-looking
stock-bond correlations vary over time and take negative values with high market
uncertainty states. The negative stock-bond correlations observed in our study indicatethat the market uncertainty is high during the pandemic, and investors prefer safe Treasury
bonds to risky stocks (flight-to-safety). Furthermore, the means of the daily and weekly
forward-looking correlations are lowest in all countries, except for New Zealand, where
the confirmed COVID-19 cases are below their 30% percentile. Notably, the forwardlooking correlations rise with the increase in the confirmed cases in North America (theU.S. and Canada) and the Asia-Pacific (Australia and Japan). Investors in these regions
are less risk averse as the pandemic worsens. This finding relates to the gradualinformation diffusion model in that information regarding the market is revealed toinvestors gradually (Hong and Stein, 1999). Investors sold risky stocks and bought safe
Treasury bonds at the beginning of the pandemic because they could not collect sufficient
information about how the pandemic would impact the financial markets, while they
adjusted the risk level of their portfolio as they obtained more information. Another point
to note from Table 1 is that the positive relationship between the forward-looking
correlations and the confirmed COVID-19 cases is less clear for the monthly results,suggesting that the flight-to-safety period is short-lived, as reported by Baele et al. (2020).
Table 2 shows the results in Europe. We observe that all forward-looking stock-bondaverage correlations are negative for countries in Panel A, while the average correlations
are positive for those in Panel B when the COVID-19 case levels are below their 30%
percentile. Panel B includes Greece, Ireland, Italy, Portugal, and Spain. The Treasury
bonds of these countries are riskier than those issued by the countries in Panel A. The
risky Treasury bonds positively comove with the stocks (Dufour et al., 2017). The
country-specific factors played a more important in the bond markets during the market
turmoil, observed in the euro bond market crisis (Pozzi and Wolswijk, 2012; Christiansen,
2014; Sakemoto, 2018). More importantly, the forward-looking average correlations in
Europe do not change with an increase in the number of confirmed COVID-19 cases,
contradicting the results observed for North America and the Asia-Pacific.
Figure 1 provides the evolution of the dynamic correlations and infection cases during
our sample period for four countries (the U.S., Australia, Germany, and Italy). The straight5

black line indicates the dynamic correlations, the values of which are reported by the left
vertical axis. The dashed red line indicates the weekly average values of the confirmed
COVID-19 cases, the values of which are reported by the right vertical axis. We confirm
that the negative stock-bond correlations weaken as the numbers of cases increase for the
U.S. and Australia. Contrastingly, no clear pattern is observed for Germany and Italy,
consistent with the empirical results presented in Tables 1 and 2.
In summary, the results in Tables 1 and 2 present empirical evidence that the responseof the stock-bond correlations observed during the COVID-19 pandemic is heterogeneous
across various regions and countries.
4. Conclusion
This paper investigated whether the forward-looking stock-bond return correlations
varied as the COVID-19 cases increased during the pandemic. We estimated thecorrelations using the DCC-GARCH model for 21 financial markets from 3 regions. We
focused on a non-linear relationship between the market states and the forward-looking
correlations proposed by Connolly et al. (2005, 2007). We found that a heterogeneous
relationship across regions and countries. Specifically, the negative forward-looking
stock-bond correlations weakened with the increase in the confirmed COVID-19 cases inNorth America (the U.S. and Canada) and the Asia-Pacific (Australia and Japan).
However, no clear relationships were observed between the confirmed COVID-19 cases
and the stock-bond correlations in European countries. The positive relationship wasparticularly strong for the U.S. The results were explained by the gradual information
diffusion model (Hong and Stein, 1999). Uncertainty triggered by the COVID-19
pandemic had a stronger impact on investors than the actual number of confirmed cases.
As investors lacked sufficient information, they became risk-averse, leading to flight-tosafety and strong negative stock-bond correlations. Investors adjusted their expected
returns on the stocks and the bonds as information was revealed, mitigating the negative
stock-bond correlations.

Acknowledgments
This work was supported by JSPS KAKENHI Grant Number 19K1373801.

6

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8

Table 1
Confirmed COVID-19 cases and stock-bond return correlation in North American (theU.S. and Canada), and the Asia Pacific (including Australia, New Zealand, and Japan)
Case level

t+1
0~30%
30%~70%70%~100%
t+5
0~30%
30%~70%70%~100%
t+21
0~30%
30%~70%70%~100%

Mean
(SD)

Mean
(SD)

Mean
(SD)

Mean
(SD)

Mean
(SD)

U.S.

CanadaAustralia

New
ZealandJapan-0.407(0.022)-0.356(0.017)-0.24(0.103)-0.094(0.009)-0.357(0.084)-0.394(0.040)-0.29(0.016)-0.331(0.030)-0.312(0.016)-0.23(0.083)-0.213(0.070)-0.096(0.005)-0.097(0.005)-0.338(0.072)-0.326(0.081)-0.407(0.023)-0.397(0.038)-0.289-0.355(0.018)-0.333(0.03)-0.31-0.242(0.114)-0.233(0.093)-0.206-0.094(0.010)-0.096(0.006)-0.097-0.36(0.089)-0.342(0.076)-0.321(0.018)(0.016)(0.084)(0.007)(0.088)-0.411(0.016)-0.406(0.032)-0.298-0.363(0.012)-0.335(0.028)-0.302-0.235(0.123)-0.245(0.086)-0.188-0.095(0.008)-0.095(0.005)-0.098-0.338(0.089)-0.355(0.068)-0.321(0.017)(0.016)(0.086)(0.006)(0.083)

Notes: This table presents the means, and standard deviations (SD) of the forward-looking correlations
for North American and the Asia Pacific regions following the given quantile values of the average
number of confirmed COVID-19 cases from t-4 to t. The standard deviations are reported inparentheses.

9Table 2
Confirmed COVID-19 cases and stock-bond return correlation in Europe.
Case level
Panel A

Mean

Mean

Mean

Mean

Mean

Mean

Mean

Mean

Mean

Mean

Mean

(SD)

(SD)

(SD)

(SD)

(SD)

(SD)

(SD)

(SD)

(SD)

(SD)

(SD)

Austria

Belgium

Denmark

FinlandFranceGermany Netherlands

NorwaySwedenSwitzerland

U.K.

-0.253-0.122-0.145-0.325-0.076-0.366-0.292-0.45-0.323-0.216-0.315(0.058)(0.014)(0.132)(0.151)(0.027)(0.201)(0.130)(0.071)(0.097)(0.053)(0.046)-0.277-0.125-0.139-0.321-0.08-0.368-0.299-0.497-0.318-0.219-0.324(0.021)(0.004)(0.103)(0.081)(0.011)(0.130)(0.084)(0.036)(0.064)(0.046)(0.033)-0.289-0.126-0.137

-0.32

-0.08

-0.363-0.285-0.496-0.318-0.215-0.319(0.036)(0.006)(0.082)(0.063)(0.009)(0.096)(0.071)(0.032)(0.050)(0.021)(0.031)-0.253-0.122-0.144-0.321-0.076-0.373-0.290-0.450-0.326-0.216-0.316(0.062)(0.016)(0.174)(0.170)(0.032)(0.230)(0.146)(0.073)(0.119)(0.074)(0.052)-0.276-0.126-0.142-0.328-0.081-0.372-0.304-0.496-0.318-0.217-0.325(0.024)(0.004)(0.136)(0.100)(0.013)(0.153)(0.099)(0.038)(0.089)(0.065)(0.035)-0.291-0.126-0.13-0.318-0.08-0.351-0.28-0.497-0.315-0.216-0.317(0.040)(0.008)(0.105)(0.086)(0.011)(0.153)(0.085)(0.034)(0.075)(0.031)(0.038)t+1
0~30%
30%~70%70%~100%
t+5
0~30%
30%~70%70%~100%

Notes: See page 12.

10

Table 2
Continued

Austria

Belgium

Denmark

FinlandFranceGermany Netherlands

NorwaySwedenSwitzerland

U.K.

-0.268-0.121-0.118-0.317-0.073-0.351-0.273-0.429-0.32-0.213-0.313(0.034)(0.017)(0.149)(0.184)(0.035)(0.224)(0.123)(0.061)(0.120)(0.053)(0.056)-0.277-0.126-0.15-0.325-0.081-0.385-0.311-0.505-0.323-0.222-0.331(0.025)(0.004)(0.138)(0.102)(0.014)(0.156)(0.092)(0.034)(0.089)(0.062)(0.033)-0.277-0.124-0.118-0.307-0.079-0.331-0.262-0.478-0.305-0.214-0.307(0.018)(0.004)(0.100)(0.089)(0.011)(0.150)(0.091)(0.031)(0.072)(0.049)(0.038)t+21
0~30%
30%~70%70%~100%

Notes: See page 12.

11

Table 2
Continued
Panel Bt+1
0~30%
30%~70%70%~100%
t+5
0~30%
30%~70%70%~100%
t+21
0~30%
30%~70%70%~100%

GreeceIreland

Italy

Portugal

Spain

0.431
(0.074)0.243(0.062)0.162(0.043)0.095(0.010)-0.055(0.047)0.011(0.040)0.308(0.013)0.284(0.008)0.278(0.009)0.201(0.023)0.186(0.011)
0.185(0.019)0.09(0.050)0.047(0.035)-0.012(0.048)0.43(0.077)0.25(0.062)0.162(0.046)0.098(0.101)-0.056(0.049)0.008(0.042)0.308(0.013)0.285(0.009)0.278(0.009)0.201(0.025)0.185(0.012)0.186(0.020)0.089(0.051)
0.049(0.036)-0.007(0.048)0.454(0.055)0.047(0.067)0.312(0.010)0.202(0.026)0.11(0.035)0.248(0.052)0.177(0.028)-0.062(0.051)-0.007(0.038)0.285(0.007)0.28(0.007)0.184(0.012)0.192(0.012)0.049(0.031)
0.015(0.011)

Notes: This table presents the means, and standard deviations (SD) of the forward-looking correlations
for European countries following given quantile values of the average number of confirmed COVID19 cases from t-4 to t. The standard deviations are reported in parentheses.

12Fig. 1. Dynamic correlations (left vertical axis and the straight black line) and confirmed COVID-19 cases (right vertical axis anddashed red line) from February 3, 2020, to December 3, 2020.

13

COVID-19 and the forward-looking
stock-bond return relationship
March 23, 2021

Xiaojing Cai, Yingnan Cong and Ryuta Sakemoto

Online Supplement, Not for Publication
This material provides additional results not reported in the main text. Table A1 presents
the descriptive statistics. Figure A1 shows the evolution of dynamic correlations and thenumber of confirmed COVID-19 cases from February 3 to December 3, 2020, for
Canada, New Zealand, Japan, Austria, Belgium, Denmark, Finland, France, theNetherlands, Norway, Sweden, Switzerland, the U.K., Greece, Ireland, Italy, Portugal,
and Spain.

14

Table A1
Descriptive statistics for MSCI total net return index, FTSE government bond index, andconfirmed COVID-19 cases.
OECD countries

Obs.

Mean

SD

Skewness

Kurtosis

Panel A: MSCI total net return index
U.S.
CanadaAustralia

218
218
218

0.001
0
0

0.023
0.023
0.021

-0.864-1.113-0.967

10.19916.206
8.185

New Zealand

199

0

0.015

0.274

5.456

Japan
Austria
Belgium
Denmark
FinlandFranceGermany
GreeceIreland
Italy

218
202
217
162
180
180
218
215
198
218

0
0
-0.0010.001
0-0.0010-0.002
0.001
0

0.015
0.029
0.025
0.015
0.02
0.023
0.021
0.03
0.022
0.024

-0.001-0.844-1.761-1.157-0.926-1.259-1.089-0.993-1.186-2.622

6.787
8.464
12.446
8.054
8.052
9.978
11.9238.414
8.54
21.992

Netherlands
NorwayPortugal
Spain
Sweden

208
201
214
218
218

0
0
0
-0.001
0

0.018
0.018
0.021
0.023
0.019

-1.08
-0.896-0.823-1.252-1.079

9.423
6.738
11.77
12.482
8.798

Switzerland

202

0

0.016

-1.19311.816

U.K.

218

0

0.02

-0.964

9.869

Notes: SD stands for standard deviation.

15

Table A1
Continued
OECD countries

Obs.

Mean

SD

Skewness Kurtosis

Panel B: FTSE government bond index
U.S.
CanadaAustralia

218
218
218

0
0
0

0.004
0.003
0.003

-0.32
0.657
-0.75310.3599.038
10.161New Zealand

199

0

0.005

1.247

19.924Japan
Austria
Belgium
Denmark
FinlandFranceGermany
GreeceIreland
Italy

218
202
217
162
180
180
218
215
198
218

0
0
0
0
0
0
0
0
0
0

0.002
0.005
0.004
0.003
0.003
0.004
0.003
0.013
0.004
0.005

-1.292-0.767-0.9610.05-0.832-0.734-0.5822.675-0.479-0.36514.347
7.429
8.212
6.909
7.577
7.457
7.762
49.22
7.043
11.542

Netherlands
NorwayPortugal
Spain
Sweden

208
201
214
218
218

0
0
0
0
0

0.003
0.002
0.004
0.004
0.002

-0.875
0.82
0.091
0.039
-0.411

8.105
6.349
12.902
10.5499.674

Switzerland

202

0

0.001

-1.52311.294

U.K.

218

0

0.008

1.414

20.24

Notes: SD stands for standard deviation.

16

Table A1
Continued
OECD countries

Obs.

Mean

SD

Skewness Kurtosis

Panel C: COVID-19 confirmed cases
U.S.

218

4,085,739

3,795,376

0.764

2.622

CanadaAustralia

218
218

113,634.70
14,151.35

94,253.05
10,704.42

0.947
0.155

3.669
1.345

New Zealand

199

1,483.79

538.967-1.755

5.283

Japan
Austria
Belgium

218
202
217

43,033.53 42,352.24
46,054.46 66,358.33
121,193.20 160,818.90

0.822
2.415
1.899

2.483
7.909
5.244

Denmark
FinlandFranceGermany
GreeceIreland
Italy
Netherlands

162
180
180
218
215
198
218
208

12,634.43
7,537.18
5,450.74
3,366.31
204,875.50 172,742.70
252,978.10 243,573
23,109.38 36,773.68
29,848.91 19,161.11
323,815.60 354,321.30
132,993.70 166,949.90

0.49-0.498
1.139
1.88
1.878
0.677
2.292
1.607

3.336
1.972
4.317
6.397
5.155
3.001
7.845
4.181

NorwayPortugal
Spain
SwedenSwitzerland
U.K.

201
214
218
218
202
218

11,532.11
8,050.33
90,747.43
103,750452,006.30 459,217.90
66,203.82 59,366.84
64,220.24 80,855.95
387,526.60 412,997.10

1.483
1.664
1.291
1.206
2.201
1.671

5.078
4.546
3.578
4.633
6.656
5.04

Notes: SD stands for standard deviation.

17

Fig. A1. The dynamic correlations (left vertical axis and the straight black line) and the number of confirmed COVID-19 cases (rightvertical axis and dashed red line) in North America, the Asia Pacific, and Europe from February 3, 2020, to December 3, 2020.

18

Fig. A1. Continued.

19

Fig. A1. Continued.

20

Fig. A1. Continued.

21

Fig. A1. Continued.

22