What Explains the COVID-19 Stock Market?

NBER WORKING PAPER SERIES

WHAT EXPLAINS THE COVID-19 STOCK MARKET? Josue Cox

Daniel L. Greenwald Sydney C. Ludvigson Working Paper 27784

NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 September 2020

Ludvigson is grateful to the CV Starr Center for Applied Economics, at NYU for financial support. We are grateful to Aleksandra Alferova for excellent research assistance. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. ? 2020 by Josue Cox, Daniel L. Greenwald, and Sydney C. Ludvigson. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including ? notice, is given to the source.

What Explains the COVID-19 Stock Market? Josue Cox, Daniel L. Greenwald, and Sydney C. Ludvigson NBER Working Paper No. 27784 September 2020 JEL No. G12,G28

ABSTRACT

What explains stock market behavior in the early weeks of the coronavirus pandemic? Estimates from a dynamic asset pricing model point to wild fluctuations in the pricing of stock market risk, driven by shifts in risk aversion or sentiment. We find further evidence that the Federal Reserve played a role in these fluctuations, via a series of announcements outlining unprecedented steps to provide several trillion dollars in loans to support the economy. As of July 31 of 2020, however, only a tiny fraction of the credit that the central bank announced it stood ready to provide in early April had been extended, reinforcing the conclusion that market movements during COVID-19 have been more reflective of sentiment than substance.

Josue Cox Department of Economics New York University josue.cox@nyu.edu

Daniel L. Greenwald MIT Sloan School of Management 100 Main Street, E62-641 Cambridge, MA 02142 dlg@mit.edu

Sydney C. Ludvigson Department of Economics New York University 19 W. 4th Street, 6th Floor New York, NY 10002 and NBER sydney.ludvigson@nyu.edu

1 Introduction

By February of 2020, the coronavirus 2019 (COVID-19) pandemic had set in motion a worldwide disruption in economic activity, causing the U.S. unemployment rate to reach 14.7% in April. The S&P 500 stock market index initially reacted to news of the disease by losing 33.7% of its value between February 19 and March 23 of 2020. But the market abruptly regained the vast majority of this lost value, rising 29% between March 24 and April 17, a surge that left the index back where it stood in August of 2019 when the U.S. economy was booming and the unemployment rate was 3.7%.

What explains this sharp V-shaped trajectory of the U.S. stock market that took place over a matter of weeks in the early stages of COVID-19? The objective of this study is to address this question. The investigation consists of two parts. The ...rst part employs the theoretical model of Greenwald, Lettau, and Ludvigson (2019) (GLL), along with updated estimates of that model, to decompose the market's changes into distinct component sources attributable to uctuations in aggregate economic fundamentals, interest rates, corporate earnings shares, and/or discount rate uctuations driven by the pricing of stock market risk. Estimates of this model imply that it is di? cult if not impossible to explain the market's V-shaped trajectory during the COVID-19 crisis with plausible uctuations in aggregate economic activity, corporate pro...t shares, or short-term interest rates. Instead, the estimates point toward wild volatility in the pricing of stock market risk, driven by uctuations in risk aversion or beliefs/sentiment.1

The second part of this study investigates what role, if any, Federal Reserve actions might have played in these uctuations.2 Speci...cally, we use a high-frequency event study to explore the role of central bank communications during March and April of 2020. We ...nd no evidence that "conventional"monetary policy announcements promulgating decisions to lower the target range for the federal funds rate to near zero or to increase the Federal

1Gormsen and Koijen (2020) reach a similar conclusion by studying S&P dividend futures to compute a lower bound on growth expectations.

2A widely shared belief among investment professionals is that the stock market is highly sensitive to the actions of the Federal Reserve. See Baker, Bloom, Davis, and Sammon (2019) who conduct systematic analysis of newspaper articles on the days after major stock market jumps.

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Reserve's holdings of Treasury securities and agency MBS were a contributing factor in the market rebound. Conversely, we do ...nd evidence that several "unconventional" monetary policy announcements outlining the central bank's unprecedented steps to provide several trillion dollars in loans to support the economy played a role in the market turnabout. Speci...cally, the 30-minute windows bracketing ...ve of these announcements are collectively associated with gains of approximately 8% in the S&P 500 stock market index and 12% in the Russell 2000 index.

However, as of July 31 of 2020, only a tiny fraction of the credit that the central bank announced it stood ready to provide in early April had been extended. And as of August 19 of 2020, the market had yet to give up any of the gains it made starting in late March; indeed several indexes had reached record highs. Taken together, this evidence suggests that Federal Reserve communications during the early weeks of the coronavirus pandemic inuenced markets mainly by altering risk tolerance, reinforcing the model-based conclusion that market movements during COVID-19 have been more reective of sentiment than substance.

The rest of this paper is organized as follows. The next section describes the GLL asset pricing model, its estimation, and model results pertaining to the COVID-19 economic shock. Section 3 discusses the event study of Federal Reserve announcements during March and April of 2020. Section 4 concludes.

2 Modeling Market Movements

This section provides an adumbrated description of the GLL model and its estimation, along with how its modi...ed to study the COVID-19 shock to the economy. We refer the reader to GLL for the full model details.

The GLL model is designed to address the question: What are the economic foundations of stock market uctuations? The framework is set up so that it can answer the question regarding uctuations over any desired horizon. It is therefore straightfoward to focus on speci...c episodes. To translate raw data into a quantitative decomposition of the sources of growth in stocks, GLL construct and estimate a exible parametric model of the U.S. equity market that allows for inuence from a number of mutually uncorrelated latent factors,

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including not only factors driving overall economic output and corporate pro...t shares, but also independent factors driving risk premia and risk-free interest rates.

Equity in GLL is priced, not by a representative household, but by a representative shareholder, akin in the data to a wealthy household or large institutional investor. Shareholder preferences are subject to shocks that alter their patience and appetite for risk, driving variation in both risk-free interest rates and the equity risk premium. Shareholders understand the laws of motion for these shocks and internalize them when forming expectations. The representative shareholder consumes cash ows from ...rms, the variation of which is driven by shocks to the total rewards generated by productive activity, but also by shocks to how those rewards are divided between shareholders and other claimants.

The intertemporal marginal rate of substitution of shareholder consumption, Ct; is the stochastic discount factor (SDF) and takes the form

ln Mt+1 = 10 t dt xt ln Ct+1

(1)

where the subjective time discount factor t exp ( [ t + dt]). The stochastic process t = 10 t, where t is a bivariate vector containing low- and high-frequency components, is a latent shock to the subjective time-discount factor that moves the risk-free rate independently of the aggregate economic state. The parameter dt is a compensating factor chosen to ensure that the log risk-free rate rf;t = ln Et exp (mt+1) obeys an empirically accurate process that exactly matches an observed proxy for the risk-free rate of interest. The parameter xt is a latent state variable that governs the pricing of stock market risk. Since an SDF always reects both preferences and beliefs, an increase in xt may be thought of as either an increase in e?ective risk aversion or an increase in pessimism about shareholder payout. The GLL model allows this variable to contain a component that is correlated with the earnings share of output, and a component that is uncorrelated with all other economic state variables. The mutually uncorrelated latent risk price shock is denoted x?;t 10x?;t, and is modeled as the sum of estimated low- and high-frequency components contained in the 2 1 vector x?;t.

In equilibrium, shareholder consumption Ct+1 is equal to equity payout, which we refer to simply as "cash ow."Let lowercase letters denote log variables, e.g., ln (Ct) = ct: Denote

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the log stock price pt. The log di?erence of cash ows in the model obeys ct = 0 st + yt;

where yt is log of aggregate economic output. The vector st contains low- and high-frequency components of the after-tax corporate earnings share, while 0 ( ; )0 is a constant vector that contains an "operating leverage"parameter > 1 that arises from the need for ...rms in aggregate to retain part of their earnings for reinvestment before making any payout.

Although the estimates of output growth in GLL suggest that their autocorrelations hover around zero, thereby suggesting a near i.i.d. process for yt; the Covid-19 economic crisis might reasonably be interpreted as having a large transitory component to it. To accommodate a transitory drop in output, we augment the GLL model with a transitory component, denoted zt, that follows

zt+1 = zzt + "z;t+1;

"z;t+1

N (0;

2 z

)

which implies

zt+1 = (1 z)zt + "z;t+1:

Total output growth is de...ned by

yt+1 = g + zt+1 + "a;t+1 = g (1 z)zt + "z;t+1 + "a;t+1:

The transitory "z;t+1 shock is designed to capture any temporary output drop attributable to the Covid-19 event, which, although sharp, may be short-lived due to the temporary nature of lockdowns and the possibility of a vaccine arriving in the relatively near future. To incorporate the unexpected nature of this shock without adjusting our previous estimates, we assume that agents perceive z = 0, and are completely surprised by a nonzero realization of this shock in 2020:Q1. For simplicity, we assume that agents maintain their belief z = 0 going forward, and interpret the drop in output following the arrival of Covid-19 as a one-time event.

Solving the model under these assumptions yields the solution for the log price-payout ratio pt ct, denoted pct:

pct = A0 + A0s~st + A0x?x~?;t + A0 ~t + Azzt

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where tildes denote demeaned variables,

Az =

1 1

z 1z

and where all other coe? cients are unchanged from the baseline model of GLL.

The state space representation of the model takes the form

Yt = H0t t + b

(2)

t = F t 1 + "t;

(3)

where Yt (eyt; rft; pyt; rpt; yt)0 is an observation vector that contains observations on

the corporate earnings share of output, the risk-free rate, the price-output ratio, a measure

of the equity risk premium implied by options data due to Martin (2017), and corporate

output growth. The latent state vector is t

s~t0; ~0t; x~0?;t;

0

y~t . If we let Hi denote the

row/element of Ht corresponding to the log ratio of the stock price to output (pyt), then the

log di?erence in the stock price according to the model is given by

pt+1 = pyt+1 + yt+1

= Hi0 t+1 + g (1 z)zt + "z;t+1 + "a;t+1

(4)

= g + Hi0 (I F) t + "t+1 (1 z)zt + "z;t+1 + "a;t+1:

GLL estimate the full dynamic model in (2) and (3) using state space methods, allowing us to precisely decompose the market's observed growth into these distinct component sources. The model is exible enough to explain 100% of the change in equity values over the sample and at each point in time. To capture the inuence of primitive shocks to latent variables at di?erent horizons, we model each as a mixture of multiple stochastic processes driven by lowand high-frequency variation. GLL apply and estimate the model using data on the U.S. corporate sector over the period 1952:Q1-2017:Q4, where their focus is on understanding why stocks relative to measures of aggregate economic activity have risen so much over the post-war period.

Here we are interested understanding stock market behavior in the COVID-19 economic crisis. To address this episode, we ...rst update the data with observations through 2019:Q4.

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We then decompose the growth in the market equity values for the corporate sector into sources attributable to di?erent latent components. This is accomplished by either ...xing one component during a particular period, or by allowing only one component to vary.

We begin by asking what factors could have plausibly driven the sharp decline in stock market values pt+1 in 2020:Q1. For this we need to ...ll in the terms of (4). This is accomplished by replacing the the time-t latent state vector t with its estimated value tjt for 2019:Q4 assuming that zt = 0 prior to the arrival of the COVID-19 shock, yielding

pt+1 = g Hi0(I F) tjt + Hi0"t+1 + "z;t+1 + "a;t+1:

(5)

Since the model decomposition is expressed in logs, the observed decline in the stock market between February 19 and March 23 of 33.7% in levels converts to log market equity growth of pt+1 = log(1 0:337) = 0:414. We may then ask which combinations of shocks could plausibly explain this sharp decline, where our candidate set includes the transitory COVID-19 output shock "z;t+1, the permanent output shock "a;t+1, and the remaining shocks contained in "t+1, which include shocks to both low- and high-frequency components of the corporate earnings share, st, of real interest rates, rf;t, and of the orthogonal price of stock market risk x?;t.

Unlike the other elements of "t+1, we specify the transitory COVID-19 output shock "z;t+1 as a one-time event rather than estimating it from the data in each period. We do this to account for the fact that this shock to the macroeconomy appears to be of a unique scale following the outbreak of COVID-19, and therefore would not be well approximated by a Gaussian process with constant volatility in all periods. We therefore need to calibrate, rather than estimate, the size of this shock to output, as perceived by market participants in real time. To obtain a measure of this object, we consult the Survey of Professional Forecasters (SPF). The May 2020 wave of this survey indicates a median forecast of -32.2% annualized growth in 2020:Q2, which is quite close to what the Bureau of Economic Analysis "advance"estimate of -32.9% turned out to be when it was released on July 30, 2020. The annualized decline of 32.2%, once converted to a quarterly growth rate in logs is

"z;t+1 = 0:25 log(1 0:322) = 0:0972:

(6)

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