Quantifying the impact of COVID-19 on the US stock market: An analysis from multi-source information
QQuantifying the impact of COVID-19 on the US stockmarket: An analysis from multi-source information
Asim K. Dey
1, 2 , G M Toufiqul Hoque , Kumer P. Das ,and Irina Panovska University of Texas at Dallas, Richardson, TX 75080 Princeton University, Princeton, NJ 08544 Lamar University, Beaumont, TX 77705 University of Louisiana at Lafayette, Lafayette, LA 70504
Abstract
We develop a novel temporal complex network approach to quantify theUS county level spread dynamics of COVID-19. The objective is to studythe effects of the local spread dynamics, COVID-19 cases and death, andGoogle search activities on the US stock market. We use both conventionaleconometric and Machine Learning (ML) models. The results suggest thatCOVID-19 cases and deaths, its local spread, and Google searches have im-pacts on abnormal stock prices between January 2020 to May 2020. In ad-dition, incorporating information about local spread significantly improvesthe performance of forecasting models of the abnormal stock prices at longerforecasting horizons. On the other hand, although a few COVID-19 relatedvariables, e.g., US total deaths and US new cases exhibit causal relationshipson price volatility, COVID-19 cases and deaths, local spread of COVID-19,and Google search activities do not have impacts on price volatility.
Keywords:
Covid-19, Stock market, Temporal network, Abnormal price,Volatility, Temporal network, Causality
1. Introduction
After the COVID-19 pandemic started spreading worldwide, the US stockmarket collapsed significantly with the S&P 500 dropping 38% betweenFebruary 24, 2020 and March 20, 2020. Similar declines have occurred inother stock indices. A number of recent studies attempt to assess the im-
Preprint submitted to Elsevier October 6, 2020 a r X i v : . [ q -f i n . S T ] O c t act of the COVID-19 outbreak on the stock market. Nicola et al. (2020)provide a review on the socioeconomic effects of COVID-19 on individualaspects of the world economy. Baker et al. (2020) analyze the reasons whythe U.S. stock market reacted so much more adversely to COVID-19 thanto previous pandemics that occurred in 1918 − − temporal network and network motifs . Thenetwork structure allows us to leverage much richer data set that includesinformation not only about the total number of cases, but also about thespread across counties over time.The stock market reacts to different local and global major events. Cagle(1996), Worthington and Valadkhani (2004), Worthington (2008), Cavalloand Noy (2009), and Shan and Gong (2012) study the impact of natural2isasters, e.g., hurricanes and earthquakes, on the stock market. Hudson andUrquhart (2015), Schneider and Troeger (2006), Chau et al. (2014), Beaulieuet al. (2006), and Huynh and Burggraf (2019) evaluate the effect of politicaluncertainty and war on the stock market. The influences of the outbreak ofinfectious diseases, e.g., Ebola and SARS, on the stock indices are assessedin Nippani and Washer (2004), Siu and Wong (2004), Lee and McKibbin(2004), and Ichev and Marinˇc (2018).Investor sentiment is another crucial determinant of stock market dynam-ics. However, quantifying investor sentiment is not an easy task because of itsunobservable and heterogeneous behaviors (Garc´ıa Petit et al. (2019), Gaoet al. (2020), Baker and Wurgler (2007), Bandopadhyaya and Jones (2005)).In recent years, due to data availability, Google search volume has becomea popular index of investor sentiment (Bijl et al. (2016), Kim et al. (2019),Preis et al. (2013)). Bollen et al. (2011) determine Twitter feeds as the moodsof investors and use the Twitter mood to predict the stock market. Alanyaliet al. (2013), Schumaker and Chen (2008), Bomfim (2003), and Albuquerqueand Vega (2008) evaluate the relationship between financial news and thestock market and find that news related to the asset significantly impact thecorresponding stock price and volatility. Cox et al. (2020) use a dynamicasset pricing model and high-frequency policy announcement news to studythe effects of policy on the stock market during the COVID-19 crisis, and findthat movements during the crisis have been more reflective of sentiment thansubstance, with the response to sentiment being a more important driver inthe stock market than the responses to the actual policy actions.Similarly, the economics literature has shown that the inclusion of addi-tional predictors for regional and local variables substantially improves now-casts and forecasts for aggregate activity (Hern´andez-Murillo and Owyang(2006)), with the gains typically being concentrated during periods of largenegative movements (Owyang et al. (2015)). Because local spread may beindicative both of disruption in local economic activity and might be linkedto local sentiment, we augment the standard aggregate models with variablesthat capture the local spread. We introduce the concept of network motifs to model the local spread. This allows us to utilize multi-source informationto quantify the impact of the spread on the US stock market. The rest ofthe paper is organized as follows. Section 2 describes the data, constructs atemporal network for COVID-19 spread, and defines the variables used in thestudy. The methodology is described in Section 3. Section 4 presents findingsand a discussion of the results. Finally, Section 5 provides a conclusion.3 . Data and Variables
The S&P 500 closing price from June 3, 2019 to May 29, 2020 data areobtained from Yahoo! Finance (Yahoo! (2020)). Google search data fromJanuary 2, 2020 to May 29, 2020 are obtained from Google Trends. We get USCounty level COVID-19 case data from the New York Times (NYT (2020))and US county information from the US National Weather Service (NWS(2020)).
We evaluate the impact of COVID-19 on abnormalities in the S&P 500index. We define the daily abnormal S&P 500 price (AP) between January2, 2020 and May 29, 2020 by subtracting the average price of the last sevenmonths from the daily price and by dividing the resultant difference from thestandard deviation of the last seven months (i.e., 148 days) as follows: AP t = P t − (cid:80) i =1 P t − i σ P , (1)where, P t is the daily closing price for day t , σ P is the standard deviation ofthe closing price in the last 148 days (Kim et al. (2019), Bijl et al. (2016)).We use daily squared log returns of prices P t as a proxy for daily volatility( V ol ) (Brooks (1998), Barndorff-Nielsen and Shephard (2002)): r t = log (cid:18) P t P t − (cid:19) , V ol t = r t . (2) We study the impact of a number of COVID-19 variables ( C ), e.g., dailyUS total cases, daily US new cases, daily World total cases, etc. on AP t and V ol t . For a complete list of COVID-19 variables see Table 1. We standardizedeach COVID-19 variable on the basis of a rolling average of the past 7 daysand corresponding standard deviation as: CV t = C t − µ C σ C , (3)where, C t is a COVID-19 variable (e.g., US total cases) at day t , µ C and σ C are the mean and standard deviation of the corresponding variable withinthe sliding window of days [ t − k, t − .3. Local Spread through complex network analysis A complex network represents a collection of elements and their inter-relationship. A network consists of a pair G = ( V, E ) of sets, where V isa set of nodes, and E ⊂ V × V is a set of edges, ( i, j ) ∈ E represents anedge (relationship) from node i to node j . Here | V | is the number of nodesand | E | is the number of edges. The degree d u of a node u is the numberof edges incident to u i.e., for u,v ∈ V and e ∈ E, d u = (cid:80) u (cid:54) = v e u,v . A graph G (cid:48) = ( V (cid:48) , E (cid:48) ) is a subgraph of G , if V (cid:48) ⊆ V and E (cid:48) ∈ E . The largestconnected component (GC) is the maximal connected subgraph of G . Theelements of the n × n -symmetric adjacency matrix, A , of G can be writtenas A ij = (cid:40) , if ( i, j ) ∈ E , otherwise . (4)A higher-order network structure, e.g., motif , represents local interactionpattern of the network. In a disease transmission a network motif providessignificant insights about the spread of the diseases. For example, the pres-ence of a dense motif or fully connected motif can increase the spread of thedisease through the network, while a chain-like motif can decrease the spreadof the disease (Leitch et al. (2019)). A motif is a recurrent multi-node sub-graph pattern. A detailed description of network motifs and their function-ality in a complex network can be found in Milo et al. (2002), Ahmed et al.(2016), Rosas-Casals and Corominas-Murtra (2009), Akcora et al. (2018),and Dey et al. (2019b). Figure 1 shows all connected 3-node motifs (T) and4-node motifs ( M ). Figure 1:
All 3-node and 4-node connected network motifs.
Temporal Network is an emerging extension of network analysis which ap-pears in many domains of knowledge, including epidemiology (Valdano et al.(2015), Demirel et al. (2017), Enright and Kao (2018)), and finance (Battis-ton et al. (2010), Zhao et al. (2018), Beguˇsi´c et al. (2018)). A temporalnetwork is a network structure that changes in time. That is, a temporal5etwork can be represented with a time indexed graph G t = ( V ( t ) , E ( t )),where, V ( t ) is the set of nodes in the network at time t , E ( t ) ⊂ V ( t ) × V ( t )is a set of edges in the network at time t . Here t is either discrete or contin-uous. Figure 2 depicts a small 15-node temporal network with time t = 1 , Figure 2:
A changing network shown over three time steps.
In order to quantify the county level spread of COVID-19 we constructa complex network ( G t ) in each day ( t ) between Jan 2, 2020 to May 29,2020: G = { G , . . . , G T } , where T = 130. We evaluate the occurrences ofdifferent motifs in each G t . An increase number of motifs, i.e., T and M , andother network features e.g., E , indicate a higher spread in a local community.These increases of higher order network structures have potential impacts on AP and V ol .Let C be the set of counties in US, I is the set of COVID-19 new casesidentified in C on a day t , and D is the pairwise distance matrix in milesamong centroid of the counties in C . We use the following three steps toconstruct the COVID-19 spread network ( G t ) at time t and compute theoccurrences of motifs in G t :1. Each County in C with γ or more COVID-19 new cases, γ ∈ Z + , makesa node in the network ( G t ).2. Two counties (i.e., nodes), i and j , are connected by an edge if (1)both counties have λ or more COVID-19 new cases, λ ∈ Z + , and (2)the distance between i and j is less than δ , δ ∈ R ≥ . Therefore, theadjacency matrix, A t , is written as A tij = (cid:40) , if I i , I j > λ & D ij > δ , otherwise . (5)6 a) COVID-19 spread in US counties. (b) COVID-19 spread network. Figure 3: Local spread of COVID-19. (a) Shows US counties with 5 or more Coronaviruscases ( γ = 5) on April 11, 2020. (b) Represents the corresponding spread network ( λ = 5, δ = 100) with 514 nodes and 3831 edges.
3. We compute occurrences of nodes ( V t ), edges ( E t ), different 3-nodemotif ( T ( t )), different 4-node motifs ( M ( t )), and size of the largestconnected component ( GC ( t )) in G t .In this study, we choose γ = 5, λ = 5, and δ = 100. That is, if twocounties both have 5 or more COVID-19 cases and if the distance betweenthese two counties is less than 100 miles they are connected by an edge.However, any appropriate choice of the parameters γ , λ , and δ can also beused to construct the COVID-19 spread network ( G t ). For illustration, Fig. 3shows the COVID-19 spread network in US counties on April 11, 2020. Weconsider different network features e.g., E , T , M , etc. as metrics of the localspread of COVID-19. We normalize each of the network variables based onEq. 3 as SP t = N t − µ N σ N , (6)where, N t is a network variable (e.g., E ) at day t , µ N and σ N are the mean andstandard deviation of the corresponding variable within the sliding windowof days [ t − k, t − A number of studies, e.g., Preis et al. (2010), Bijl et al. (2016), andKim et al. (2019), show that there is a significant correlation between stock7ariables (e.g., return, volume, and volatility) and related Google searches,and Google search data can be used to predict future stock prices.We investigate whether Google trend data affect the abnormal price, AP ,and volatility, V ol . We obtain the volume of the COVID-19 related dailyGoogle searches (e.g., “Coronavirus”) from Jan 2, 2020 to May 29, 2020. Weselect the location of a query in “US” and in the “World”. We standardizedeach Google search variable similar to Eq. 3 as GT t = G t − µ G σ G , (7)where, G t is a Google search variable at day t , µ G and σ G are the mean andstandard deviation of the corresponding variable within the sliding windowof days [ t − k, t − Table 1: Overview of the data sets.
Data type VariablesStock market and S&P 500 daily closing price,Economic Uncertainty Economic Policy Uncertainty (EPU) IndexCOVID-19 US total cases, US new cases, US total deaths,US new death, World total cases, World new cases,World total deaths, World new deathsGoogle Trends “Coronavirus” US, “Covid-19” US,“Covid 19” US, “Covid - 19” US, “ Coronavirus” World,“Covid-19” World, “Covid 19” World, “Covid - 19” World“Stimulus package” US, “Coronavirus stimulus” US,“Stimulus” US, “Stimulus check” US, “irs stimulus” USLocal Spread V , E , GC , T , T , M , M , M , M , M , M In a robustness check experiment, we also consider Google Trend searches for variouseconomic policy variables, and the news based economic policy uncertainty index fromBaker et al. (2016) as additional explanatory variables. However, while these variableswere significantly correlated with abnormal returns, they did not have a causal relationshipat any lag. For brevity, the results for the additional policy variables are reported in theAppendix. . Methodology We investigate the impact of COVID-19 cases and deaths, local spread ofCOVID-19, and COVID-19 related Google search volumes on the abnormalstock price and volatility.
A correlation test is widely used as an initial step to evaluate the relation-ship between the stock market and a potential covariate (Preis et al. (2010),Alanyali et al. (2013), Preis et al. (2013), Kim et al. (2019)). In this study,we use Spearman’s rank correlation to study correlation between stock data( AP and V ol ) and each of the COVID-19 related variables.To assess potential predictive utilities of COVID-19 cases, local spread,and Google search interests on abnormal price formation ( AP ) and V ol ,we apply the concept of Granger causality (Granger (1969)). The Grangercausality test evaluates whether one time series is useful in forecasting an-other. Let Y t , t ∈ Z + be a p × AP t or V t ) and let F t ( Y ) = σ { Y s : s = 0 , , . . . , t } denote a σ -algebra generated from all ob-servations of Y in the market up to time t . Consider a sequence of randomvectors { Y t , X t } , where X can be either COVID-19 cases, local spread orGoogle search volumes. Suppose that for all h ∈ Z + F t + h (cid:18) ·|F t − Y , X ) (cid:19) = F t + h (cid:18) ·|F t − Y (cid:19) , (8)where F t + h (cid:18) ·|F t − Y , X ) (cid:19) and F t + h (cid:18) ·|F t − Y (cid:19) are conditional distributions of Y t + h , given Y t − , X t − and Y t − , respectively. Then, X t − is said not toGranger cause Y t + h with respect to F t − Y . Otherwise, X is said to Grangercause Y , which can be denoted by G X (cid:26) Y , where (cid:26) represents the directionof causality (White et al. (2011), Dey et al. (2019a, 2020)).We fit two models where one model includes X and the other does notinclude X (base model), and compare their predictive performance to assesscausality of X to Y using an F -test, under the null hypothesis of no ex-planatory power in X . For univariate cases we compare the following twomodels: 9 t = α + d (cid:88) k =1 α k y t − k + d (cid:88) k =1 β k x t − k + e t , (9)versus the base model y t = α + d (cid:88) k =1 α k y t − k + ˜ e t . (10)If V ar ( e t ) is significantly lower than V ar (˜ e t ), then x contains additionalinformation that can improve forecasting of y , i.e., G x (cid:26) y . We can also fit twolinear vector autoregressive (VAR) models, with and without X , respectively,and evaluate the statistical significance of model coefficients associated with X . To quantify the forecasting utility of the covariates ( X ), i.e., COVID-19 cases, US county level spread of COVID-19, and Google searches, wedevelop predictive models with and without X and compare their predictiveperformances. In order to conduct such a comparison, Box-Jenkins (BJ) classof parametric linear models are commonly used. However, different studies,e.g., Kane et al. (2014), Dey et al. (2020), show that flexible Random Forest(RF) models often tend to outperform the BJ models in their predictivecapabilities. We present the comparative analysis based on the RF models.However, any appropriate forecasting model (e.g., autoregressive integratedmoving average (ARIMA( p, d, q )), can also be used to compare the predictiveperformances of the covariates.A RF model sorts the predictor space into a number of non-overlappingregions R , R , · · · , R m and makes a top-down decision tree . A common di-viding technique is recursive binary splitting process, where in each split itmakes two regions R = { X | X j < k } and R = { X | X j ≥ k } by consider-ing all possible predictors X j s and their corresponding cutpoint k such thatresidual sum of squares (RSS) (Eq. 11) becomes the lowest. RSS = (cid:88) x i ∈ R ( j,k ) ( y i − ˆ y R ) + (cid:88) x i ∈ R ( j,k ) ( y i − ˆ y R ) , (11)10here ˆ y R and ˆ y R are the mean responses for the training observations inthe region R ( j, k ), and in R ( j, k ), respectively. To improve the predictiveaccuracy, instead of fitting a single tree, the RF technique builds a num-ber of decision trees and averages their individual predictions (Hastie et al.(2001)). RF is a non-linear model (piece-wise linear). Therefore, if thereis any nonlinear causality (Kyrtsou and Labys (2006), Anoruo (2012), Songand Taamouti (2018)) of X to AP and V , a RF model captures this causality.We compare the predictive performance of a baseline model (Model P ),which includes only the lagged values of the abnormal price, with other pro-posed models which additionally include a set of covariates. The covariatesare selected based on their significant correlations and causalities. Table 2represents a description of the five models we use in our analysis. Table 2: Model description for abnormal price AP and varying predictors. Model Predictors
Model P AP lag 1, AP lag 2, AP lag 3Model P AP lag 1, AP lag 2, AP lag 3 ,US total deaths lag 1, US total deaths lag 2, US total deaths lag 3,World new deaths lag 1, World new deaths lag 2, World new deaths lag 3Model P AP lag 1, AP lag 2, AP lag 3 ,Edges lag 1, Edges lag 2, Edges lag 3, GC lag 1, GC lag 2, GC lag 3, T lag 1, T lag 2, T lag 3, M lag 1, M lag 2, M lag 3Model P AP lag 1, AP lag 2, AP lag 3,“Covid-19” US lag 1, “Covid-19” US lag 2, “Covid 19” US lag 1,“Covid 19” US lag 2,“Covid-19” World lag 1, “Covid-19” World lag 2Model P AP lag 1, AP lag 2, AP lag 3,“Covid-19” US lag 1, “Covid-19” US lag 2, “Covid 19” US lag 1,“Covid 19” US lag 2, T lag 1, T lag 2,US total deaths lag 1, US total deaths lag 2We consider the root mean squared error (RMSE) as measure of predic-tion error. The RMSE for abnormal price modeling can be defined as RM SE = (cid:118)(cid:117)(cid:117)(cid:116) (1 /n ) n (cid:88) t =1 ( y t − ˆ y t ) , where y t is the test set of abnormal price ( AP ) and ˆ y t is the correspond-ing predicted value. We calculate the percentage change in prediction error11RMSE) for a specific model in Table 2 with respect to model P as∆ = (cid:16) − Ψ( P i )Ψ( P ) (cid:17) × , i = 1 , . . . , , (12)where Ψ( P i ) and Ψ( P ) are the RMSE of model P and model P i , re-spectively. If ∆ >
0, the covariate ( X ) is said to improve prediction of Y .We compare the ∆ for different models, calculated for varying predictionhorizons. We evaluate the utility of COVID-19 cases and deaths, US county levelspread of COVID-19, and Google searches in predicting stock market volatil-ity. Let the conditional mean of log return of S&P 500 price ( r t ) be givenas y t = E ( y t | I t − ) + (cid:15) t , (13)where I t − is the information set at time t −
1, and (cid:15) t is conditionallyheteroskedastic error. We build two exponential GARCH (EGARCH ( p, q ))models, Model 0 and Model X , where Model 0 is a standard EGARCH modelwith no explanatory variables, and Model X includes a set of explanatoryvariables: (cid:15) t = σ t η t , Model 0: log e ( σ t ) = ω + q (cid:88) i =1 (cid:0) ω i η t − j + γ j ( | η t − j | − E | η t − j | ) (cid:1) + p (cid:88) j =1 τ j log e ( σ t − j ) , Model X : log e ( σ t ) = ω + q (cid:88) i =1 (cid:0) ω i η t − j + γ j ( | η t − j | − E | η t − j | ) (cid:1) + p (cid:88) j =1 τ j log e ( σ t − j ) + Λ X t , (14)where η t ∼ iid (0,1), i = 1 , , · · · , q , j = 1 , , · · · , p (Nelson (1991),McAleer and Hafner (2014), Chang and McAleer (2017), Martinet and McAleer(2018), Bollerslev et al. (2020)). 12e select a set of eight explanatory variables: X = (cid:2) US total deaths lag1, US total deaths lag 2, T lag 1, T lag 1,“Covid 19” US lag 1, “Covid 19” US lag 2 (cid:3) with Λ = (cid:2) λ λ · · · λ (cid:3) (cid:48) . Allthe explanatory variables are in the form of log returns. For simplicity wechoose EGARCH (1,1) model. For EGARCH (1,1) with the assumption of η t ∼ iid (0,1) the two propose models (Eq. 14) reduce toModel 0: log e ( σ t ) = ω + ω i η t − j + γ j | η t − j | + τ j log e ( σ t − j ) , Model X : log e ( σ t ) = ω + ω i η t − j + γ j | η t − j | + τ j log e ( σ t − j ) + (cid:88) l =1 λ l x lt . (15)The performances of the two models are compared based on their loglikelihood, Akiake Information Criterion (AIC) and Bayesian informationcriterion (BIC).
4. Results
We investigate the effect of COVID-19 public health crisis on the stockmarket, in particular, on the S&P 500 index. We primarily focus on theimpact of COVID-19 cases and deaths, local spread, and COVID-19 relatedGoogle searches on S&P 500. Figure 4 shows the movements of abnormalS&P 500 price and volatility from January 13, 2020 to May 29, 2020. Thetop panel illustrates the precipitous drop of S&P 500 price compared to themovements in prices during the last seven months (Eq. 1). The historic highvolatility (Eq. 2) is depicted in the bottom panel.We start our analysis with the Spearman’s rank correlation test. Wecalculate correlations between the daily abnormal S&P 500 closing price, AP and the daily COVID-19 cases and deaths, and daily occurrences of higherorder structures in the spread network at different time lags. For example, at lag AP at day t with COVID-19 cases and deaths,and higher order network structures, all at day t −
1. These lag correlationsevaluate the directionality of the relationships. Figure 5a shows the boxplots which combine correlations between each COVID-19 cases and deathsvariable and AP at different lag . Here we build two box plots at each lag:one for COVID-19 cases and deaths in the US (four variables), and anotherfor COVID-19 cases and deaths in the World (four variables). Similarly,13 igure 4: Time plots of abnormal price ( AP ) and volatility ( V ol ) from January 13 2020to May 29 2020.
Figure 5b represents the box plots that combined correlations between eacheleven local spread variable and AP at different lag . (a) AP and COVID-19 cases (b) AP and COVID-19 local spread. Figure 5: (Spearman) Correlations between Covid-19 and abnormal S&P 500. Correlationsof eight COVID-19 variables in each lags are summarized in a box plot.
We find that there exists significant (negative) correlation between COVID-19 cases and deaths in US and abnormal S&P 500 in all six lags, lag =1 , , · · · ,
6. However, there is no significant correlation between COVID-19cases and deaths in the entire world and abnormal S&P 500 ( p -value > p -value < lag = 1 , , · · · ,
6. That is, US county level spreadof COVID-19 adversely affects the price of S&P 500. However, it is antici-pated that the strength of correlations of local spread variables will graduallydecrease in higher lags, which is also reflected in Figure 5b. Some of theCOVID-19 related Google searches, e.g., “Covid-19” in US and “Corona” inworld are also significantly correlated ( p -value > (cid:26) .We find that US total new cases and US total death have significant pre-dictive impacts on price and volatility. US total number of cases have pre-dictive relationship only with volatility in few lags. Among world COVID-19cases and deaths only total new deaths have causality on price and volatility.Almost all the local spread variables have predictive impact on price, butnone of them except lag h = 1 , , . . . ,
6. For short term fore-casting horizons ( h = 1 ,
2, and 3) model P , which is based on Google searchvariables yields more accurate performance. For longer term forecasting hori-zons ( h = 4 ,
5, and 6), model P containing information from local spreaddelivers the most competitive results, followed by model P , which containsinformation from COVID-19 deaths, local spread, and Google searches.Figure 6 represents a comparison of the observed data with fitted valuesfrom baseline model (model P ) and four other models, i.e., model P , P ,15 able 3: Summary of G-causality analysis of COVID-19 cases and deaths on abnormalS&P 500 ( y ) on different lag effects (day). P and V ol denote significance in price andvolatility, respectively. Blank space implies no significance. Confidence level is 90%.
LagCausality (cid:26) y - - - V ol - V ol -US total deaths (cid:26) y P/ V ol V ol P/ V ol P/ V ol P/ V ol P/ V ol P/ V ol
US new cases (cid:26) y P/ V ol - -
V ol
P P/
V ol P/ V ol
US new deaths (cid:26) y - - - - - - -World total cases (cid:26) y - - - - - - -World total deaths (cid:26) y - - - - - - -World new cases (cid:26) y - - - - - - -World new deaths (cid:26) y - P P P V ol V ol - Table 4: Summary of G-causality analysis of COVID-19 spread on abnormal S&P 500( y ) on different lag effects (day). P and V ol denote significance in price and volatility,respectively. Blank space implies no significance. Confidence level is 90%.
LagCausality (cid:26) y V ol
P P P P P PGC (cid:26) y P P P P P P P T (cid:26) y P P - - - - - T (cid:26) y P P P P P P P V (cid:26) y - - P - - - - V (cid:26) y P P - P P - P V (cid:26) y - - - - - - - V (cid:26) y - P P P P P P V (cid:26) y - P P P P P P V (cid:26) y - - - P - - -Total V (cid:26) y - - - P - - - P , and P . For 1 day horizon model P yield a noticeably higher predictiveaccuracy followed by model P . For 2 day horizon, although it is expectedthat the prediction performances of all models deteriorates compare to theirperformances for 1 day horizon, model P again delivers the best predictionaccuracy.We now evaluate the influence of COVID-19 cases and deaths, US countylevel spread of COVID-19, and Google searches on S&P 500 volatility. A16 able 5: Predictive utilities (∆) of models in Table 2 over the baseline model (Model P )for different prediction horizons. h Model P Model P Model P Model P (a) h=1 day. (b) h=2 days. Figure 6: Abnormal price prediction for March 2020 to May 2020 with 1, and 2 dayhorizons. comparison of the two EGARCH models,
Model 0 and
Model X (Eq. 15),including the estimated parameters of the explanatory variables for
Model X are presented in Table 6. All EGARCH coefficients except the constant term( ω ) are statistically significant in both models. However, the coefficientsestimates of all the covariates in Model X are not statistically significant.We also examine the goodness of fit of the two models by comparing theirlog likelihood, Akiake Information Criterion (AIC) and Bayesian informationcriterion (BIC). We find that
Model 0 tends to describe the S&P 500 volatilitymore accurately than the volatility model with covariates,
Model X . That is,COVID-19 cases and deaths, its local spread and Google searches do notsignificantly influence the S&P 500 volatility. Figure 7 also suggests that
Model 0 captures the spikes of the price returns more accurately than
ModelX . 17 able 6: Estimates of EGARCH models for S&P 500 price volatility. ∗∗∗ p < . ∗∗ p < . ∗ p < . Model X Model 0Parameter Coef. t value Coef. t value ω -0.611 -1.287 -0.392 -1.394 ω -0.517 -3.249 ∗∗∗ -0.484 -3.443 ∗∗∗ γ ∗∗∗ ∗∗∗ τ ∗∗∗ ∗∗∗ US total deaths lag 1 ( λ ) -0.867 -0.864US total deaths lag 2 ( λ ) -0.558 -0.609 λ ) -0.260 -1.235 λ ) 0.050 0.221 T lag 1 ( λ ) -0.514 -0.939 T lag 1 ( λ ) -0.067 -0.120“Covid 19” US lag 1 ( λ ) -0.132 -0.167“Covid 19” US lag 2 ( λ ) -0.476 -0.621Log-likelihood 214.049 218.258AIC -4.540 -4.709BIC -4.205 -4.599COVID-19 related factors do not seem to play a role when it comes toexplaining the dynamics of the volatility. One potential explanation for thisis that the movements in the volatility are driven by national-level sentimentabout policy or about policy uncertainty. As a robustness check, we performan experiment where we explore the correlations and Granger causality be-tween Google trend searches for macroeconomic policy variables. Becausethe data for the COVID-19 spread is available at daily frequency, we usedaily data in all of our specifications. Therefore, we proxy for investor senti-ment about policy by using Google Trend searches and the policy uncertaintyindex from Baker et al. (2016) rather than higher frequency 30 minute win-dows around policy announcements as in Cox et al. (2020). The results arereported in the Appendix. Our results are very similar to the results forthe benchmark specifications with the volatility being affected by nationalfactors. While sentiment about policy is correlated with abnormal prices, we18 igure 7: Time plots of AP and V ol from January 13 2020 to May 29 2020. only find Granger causality in several cases related to fiscal policy searches,and only at higher lags. On the other hand, sentiment about policy Granger-causes volatility at all lags.
5. Conclusion
The aim of this paper is to evaluate whether COVID-19 cases and deaths,local spread of COVID-19, and Google search activity explain and predictUS stock market plunge in the spring of 2020.We develop a modeling frame-work that systematically evaluates the correlation - causality - predictiveutility of each of the COVID-19 related features on stock decline and stockvolatility. In order to quantify local spread of COVID-19 we construct atemporal spread network and study the dynamics of higher order networkstructures as a measure of local spread. We find that COVID-19 cases anddeaths, its local spread, and Google search activities related to COVID-19have contemporary relationships and predictive abilities on abnormal stockprices. Our results indicate that COVID-19 cases and deaths, and its localspread not only unprecedentedly disrupt economic activity and cause a col-lapse in demand for different goods but also they make investors panic andincrease their anxiety. The anxiety is also reflected in Google search intensityfor COVID-19. These shocks affect investment decisions and the subsequentstock price dynamics. On the other hand, very few COVID-19 variables have19ausal relationship on volatility. However, standard EGARCH models forthe volatility show that COVID-19 cases and deaths, its local spread , andGoogle search volumes do not have impact on volatility. Different forms forthe volatility measure Moln´ar (2012), Kim et al. (2019), Bijl et al. (2016)lead to the same conclusions.Overall, the volatility is mostly affected by national factors and incor-porating higher-order information about local spread does not significantlyimprove the forecasting performance of the models. However, the local spreadare significantly linked to abnormal price returns. Furthermore, incorporat-ing information about the local spread significantly improves the predictiveperformance of the models for the abnormal price level.
6. Appendix
Table 7: Spearman correlations between COVID-19 cases and abnormal S&P 500. bluecolor indicates significant correlation ( p -values < p -values > Lag
ReferencesReferences
Ahmed, N.K., Neville, J., Rossi, R.A., Duffield, N., Willke, T.L.,2016. Graphlet decomposition: Framework, algorithms, and applications.Knowledge and Information Systems (KAIS) 50, 1–32.Akcora, C.G., Dey, A.K., Gel, Y.R., Kantarcioglu, M., 2018. Forecastingbitcoin price with graph chainlets, in: PAKDD, pp. 1–12.20 able 8: Spearman correlations between Local spread variables and abnormal S&P 500.blue color indicates significant correlation ( p -values < p -values > Lag T T M M M M M M T ot M Table 9: Spearman correlations between google trend and abnormal S&P 500. A significantcorrelation ( p -values < p -values > Lag
Alanyali, M., Moat, H.S., Preis, T., 2013. Quantifying the relationship be-tween financial news and the stock market. Scientific Reports 3, 3578.Albuquerque, R., Vega, C., 2008. Economic News and International StockMarket Co-movement*. Review of Finance 13, 401–465.Anoruo, E., 2012. Testing for linear and nonlinear causality between crude oil21 able 10: G-causality analysis of Google searches on abnormal S&P ( y ) on different lageffects (day). P and V ol denote significance in price and volatility, respectively. Blankspace implies no significance. Confidence level is 90%.
LagCausality (cid:26) y - - - - - - -“Covid-19” US (cid:26) y P P P P P P P“Covid 19” US (cid:26) y V ol
P P P P - -“Covid - 19” US (cid:26) y - P - - - - -“Coronavirus” World (cid:26) y - - P - - - -“Covid-19” World (cid:26) y P P P P P P P“Covid 19” World (cid:26) y - - - - - - -“Covid - 19” World (cid:26) y P P P P - - -
Table 11: Spearman correlations between Economic Policy Uncertainty (EPU) Index andgoogle trend in US related to economic policy, and abnormal S&P 500. A significantcorrelation ( p -values < p -values > Lag price changes and stock market returns. International Journal of EconomicSciences and Applied Research (IJESAR) 4, 75–92.Arias-Calluari, K., Alonso-Marroquin, F., Nattagh-Najafi, M., Harr´e, M.,2020. Methods for forecasting the effect of exogenous risk on stock markets.arXiv preprint arXiv:2005.03969 .Baker, M., Wurgler, J., 2007. Investor sentiment in the stock market. TheJournal of Economic Perspectives 21, 129–151.22 able 12: G-causality analysis of Economic Policy Uncertainty (EPU) Index and googletrend in US related to economic policy on abnormal S&P ( y ) on different lag effects (day). P and V ol denote significance in price and volatility, respectively. Blank space implies nosignificance. Confidence level is 90%.
Lag (cid:26) y - - - - - - -“Unemployment benefit” (cid:26) y - - - - - - -“Stimulus package” (cid:26) y V ol V ol V ol V ol V ol V ol V ol “Coronavirus stimulus” (cid:26) y V ol V ol V ol P/ V ol P/ V ol P/ V ol V ol “Stimulus” (cid:26) y V ol V ol V ol V ol V ol V ol V ol “Stimulus check” (cid:26) y - - - - - - -“irs stimulus” (cid:26) y P - - -
V ol V ol
Baker, S.R., Bloom, N., Davis, S.J., 2016. Measuring economic policy uncer-tainty. Quarterly Journal of Economics 131(5), 1593–1636.Baker, S.R., Bloom, N., Davis, S.J., Kost, K.J., Sammon, M.C., Viratyosin,T., 2020. The Unprecedented Stock Market Impact of COVID-19. WorkingPaper 26945. National Bureau of Economic Research.Bandopadhyaya, A., Jones, A., 2005. Measuring investor sentiment in equitymarkets. Journal of Asset Management 7.Barndorff-Nielsen, O.E., Shephard, N., 2002. Econometric analysis of realizedvolatility and its use in estimating stochastic volatility models. Journal ofthe Royal Statistical Society. Series B (Statistical Methodology) 64, 253–280.Battiston, S., Glattfelder, J.B., Garlaschelli, D., Lillo, F., Caldarelli, G.,2010. The Structure of Financial Networks. Springer London, London. pp.131–163.Beaulieu, M.C., Cosset, J.C., Essaddam, N., 2006. Political uncertaintyand stock market returns: evidence from the 1995 quebec referendum.Canadian Journal of Economics/Revue canadienne d’´economique 39, 621–642.Beguˇsi´c, S., Kostanjcar, Z., Kovac, D., Stanley, H., Podobnik, B., 2018. In-23ormation feedback in temporal networks as a predictor of market crashes.Complexity 2018, 1–13.Bijl, L., Kringhaug, G., Moln´ar, P., Sandvik, E., 2016. Google searches andstock returns. International Review of Financial Analysis 45, 150 – 156.Bollen, J., Mao, H., Zeng, X., 2011. Twitter mood predicts the stock market.Journal of Computational Science 2, 1 – 8.Bollerslev, T., Patton, A.J., Quaedvlieg, R., 2020. Multivariate leverageeffects and realized semicovariance garch models. Journal of Econometrics217, 411 – 430. Nonlinear Financial Econometrics.Bomfim, A.N., 2003. Pre-announcement effects, news effects, and volatility:Monetary policy and the stock market. Journal of Banking & Finance 27,133 – 151.Brooks, C., 1998. Predicting stock index volatility: can market volume help?Journal of Forecasting 17, 59–80.Cagle, J.A., 1996. Natural disasters, insurer stock prices, and market dis-crimination: The case of hurricane hugo. Journal of Insurance Issues 19,53–68.Cao, K.H., Li, Q., Liu, Y., Woo, C.K., 2020. Covid-19’s adverse effects on astock market index. Applied Economics Letters 0, 1–5.Cavallo, E., Noy, I., 2009. The Economics of Natural Disasters - A Survey.Working Papers 200919. University of Hawaii at Manoa, Department ofEconomics.Chang, C.L., McAleer, M., 2017. The correct regularity condition and inter-pretation of asymmetry in egarch. Economics Letters 161, 52 – 55.Chau, F., Deesomsak, R., Wang, J., 2014. Political uncertainty and stockmarket volatility in the middle east and north african (mena) countries.Journal of International Financial Markets, Institutions and Money 28, 1– 19.Cox, J., Greenwald, D., Ludvigson, S.C., 2020. What Explains the COVID-19 Stock Market. Working Paper 27784. National Bureau of EconomicResearch. 24emirel, G., Barter, E., Gross, T., 2017. Dynamics of epidemic diseases ona growing adaptive network. Scientific Reports 7, 42352.Dey, A.K., Akcora, C.G., Gel, Y.R., Kantarcioglu, M., 2020. On the roleof local blockchain network features in cryptocurrency price formation.Canadian Journal of Statistics n/a.Dey, A.K., Edwards, A., Das, K.P., 2019a. Determinants of high crude oilprice: A nonstationary extreme value approach. Journal of StatisticalTheory and Practice 14, 1–14.Dey, A.K., Gel, Y.R., Poor, H.V., 2019b. What network motifs tell us aboutresilience and reliability of complex networks. Proceedings of the NationalAcademy of Sciences 116, 19368–19373.Enright, J., Kao, R.R., 2018. Epidemics on dynamic networks. Epidemics24, 88 – 97.Gao, Z., Ren, H., Zhang, B., 2020. Googling investor sentiment around theworld. Journal of Financial and Quantitative Analysis 55, 549–580.Garc´ıa Petit, J.J., Vaquero Lafuente, E., R´ua Vieites, A., 2019. How in-formation technologies shape investor sentiment: A web-based investorsentiment index. Borsa Istanbul Review 19, 95 – 105.Granger, C.W.J., 1969. Investigating causal relations by econometric modelsand cross-spectral methods. Econometrica 37, 424–438.Hastie, T., Tibshirani, R., Friedman, J., 2001. The Elements of StatisticalLearning. Springer Series in Statistics, Springer New York Inc., New York,NY, USA.Hern´andez-Murillo, R., Owyang, M.T., 2006. The information content ofregional employment data for forecasting aggregate conditions. EconomicsLetters 90, 335 – 339.Hudson, R., Urquhart, A., 2015. War and stock markets: The effect of worldwar two on the british stock market. International Review of FinancialAnalysis 40, 166 – 177.Huynh, T., Burggraf, T., 2019. If worst comes to worst: Co-movement ofglobal stock markets in the us-china trade war. SSRN Electronic Journal .25chev, R., Marinˇc, M., 2018. Stock prices and geographic proximity of in-formation: Evidence from the ebola outbreak. International Review ofFinancial Analysis 56, 153 – 166.Kane, M.J., Price, N., Scotch, M., Rabinowitz, P., 2014. Comparison ofARIMA and Random Forest time series models for prediction of avianinfluenza H5N1 outbreaks. BMC Bioinformatics 15, 276.Kim, N., Luˇcivjansk´a, K., Moln´ar, P., Villa, R., 2019. Google searches andstock market activity: Evidence from norway. Finance Research Letters28, 208 – 220.Kyrtsou, C., Labys, W.C., 2006. Evidence for chaotic dependence betweenus inflation and commodity prices. Journal of Macroeconomics 28, 256 –266. Nonlinear Macroeconomic Dynamics.Lee, J.W., McKibbin, W.J., 2004. Globalization and disease: The case ofsars. Asian Economic Papers 3, 113–131.Leitch, J., Alexander, K., Sengupta, S., 2019. Toward epidemic thresholdson temporal networks: a review and open questions. Applied NetworkScience 4.Martinet, G.G., McAleer, M., 2018. On the invertibility of egarch(p, q).Econometric Reviews 37, 824–849.McAleer, M., Hafner, C.M., 2014. A one line derivation of egarch. Econo-metrics 2, 92–97.Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.,2002. Network motifs: simple building blocks of complex networks. Science298, 824–827.Moln´ar, P., 2012. Properties of range-based volatility estimators. Interna-tional Review of Financial Analysis 23, 20 – 29.Nelson, D.B., 1991. Conditional heteroskedasticity in asset returns: A newapproach. Econometrica 59, 347–370.26icola, M., Alsafi, Z., Sohrabi, C., Kerwan, A., Al-Jabir, A., Iosifidis, C.,Agha, M., Agha, R., 2020. The socio-economic implications of the coron-avirus and covid-19 pandemic: A review. International Journal of Surgery78.Nippani, S., Washer, K.M., 2004. Sars: a non-event for affected countries’stock markets? Applied Financial Economics 14, 1105–1110.NWS, 2020. U.s. counties. URL: .accessed May 15, 2020.NYT, 2020. Covid-19 data. URL: https://developer.nytimes.com/covid .accessed May 15, 2020.Onali, E., 2020. Covid-19 and stock market volatility doi: http://dx.doi.org/10.2139/ssrn.3571453 .Owyang, M.T., Piger, J., Wall, H.J., 2015. Forecasting national recessionsusing state-level data. Journal of Money, Credit and Banking 47, 847–866.Preis, T., Moat, H.S., Stanley, H.E., 2013. Quantifying trading behavior infinancial markets using google trends. Scientific Reports 3, 1684.Preis, T., Reith, D., Stanley, H., 2010. Complex dynamics of our economic lifeon different scales: Insights from search engine query data. Philosophicaltransactions. Series A, Mathematical, physical, and engineering sciences368, 5707–19. doi: .Rosas-Casals, M., Corominas-Murtra, B., 2009. Assessing European powergrid reliability by means of topological measures. WIT Transactions onEco. and the Env. 121, 527–537.Schneider, G., Troeger, V.E., 2006. War and the world economy: Stockmarket reactions to international conflicts. Journal of Conflict Resolution50, 623–645.Schumaker, R.P., Chen, H., 2008. Evaluating a news-aware quantitativetrader: The effect of momentum and contrarian stock selection strategies.Journal of the American Society for Information Science and Technology59, 247–255. 27han, L., Gong, S.X., 2012. Investor sentiment and stock returns: Wenchuanearthquake. Finance Research Letters 9, 36 – 47.Siu, A., Wong, Y.C.R., 2004. Economic impact of sars: The case of hongkong. Asian Economic Papers 3, 62–83.Song, X., Taamouti, A., 2018. Measuring nonlinear granger causality inmean. Journal of Business & Economic Statistics 36, 321–333.Valdano, E., Ferreri, L., Poletto, C., Colizza, V., 2015. Analytical compu-tation of the epidemic threshold on temporal networks. Phys. Rev. X 5,021005.Wagner, A., 2020. What the stock market tells us about the post-covid-19world. Nature Human Behaviour 4. doi: .White, H., Chalak, K., X., L., 2011. Linking Granger causality and the Pearlcausal model with settable systems, in: JMLR, pp. 1–29.Worthington, A., Valadkhani, A., 2004. Measuring the impact of nat-ural disasters on capital markets: an empirical application using in-tervention analysis. Applied Economics 36, 2177–2186. doi: .Worthington, A.C., 2008. The impact of natural events and disasters on theaustralian stock market: a garch-m analysis of storms, floods, cyclones,earthquakes and bushfires. Global Business and Economics Review 10,1–10.Yahoo!, 2020. S&P 500. URL: https://finance.yahoo.com/https://finance.yahoo.com/