Equilibrium Asset Pricing with Leverage and Default

• Published date: 01 April 2021
• Author: LUKAS SCHMID,JOÃO F. GOMES
• Date: 01 April 2021
• DOI: http://doi.org/10.1111/jofi.12987

THE JOURNAL OF FINANCE •VOL. LXXVI, NO. 2 •APRIL 2021

Equilibrium Asset Pricing with Leverage and

Default

JOÃO F. GOMES and LUKAS SCHMID∗

ABSTRACT

We develop a general equilibrium model linking the pricing of stocks and corporate

bonds to endogenous movements in corporate leverage and aggregate volatility. The

model features heterogeneous f‌irms making optimal investment and f‌inancing de-

cisions and connects f‌luctuations in macroeconomic quantities and asset prices to

movements in the cross section of f‌irms. Empirically plausible movements in leverage

produce realistic asset return dynamics. Countercyclical leverage drives predictable

variation in risk premia, and debt-f‌inanced growth generates a high value premium.

Endogenous default produces countercyclical aggregate volatility and credit spread

movements that are propagated to the real economy through their effects on invest-

ment and output.

IT IS NOW WELL UNDERSTOOD that leverage is a major driver of risk expo-

sure and a key contributor to macroeconomic f‌luctuations. Leverage pushes

many corporations to default during downturns, often with substantial losses.

Expectations of such losses affect the pricing of corporate debt, the issuance

of which is used to f‌inance growth options and accelerate expansions. Debt-

f‌inanced booms and debt-driven busts thus contribute to aggregate volatility

and are ref‌lected in asset returns, as the Great Recession of 2008 to 2009 has

reminded us. Yet, developing a framework suitable to study the joint deter-

mination of f‌irms’ investment and leverage decisions, macroeconomic f‌luctua-

tions, and risk premia on stocks and corporate bonds has proved challenging.

∗João F. Gomes is with the Wharton School of the University of Pennsylvania. Lukas Schmid

is with the Marshall School of Business, University of Southern California, and CEPR. This pa-

per replaces a previous version titled ”Equilibrium Credit Spreads.” We wish to thank the editors,

Ken Singleton and Stefan Nagel; an associate editor; and two anonymous referees for helpful feed-

back. We are also grateful for comments from Andy Abel; Hui Chen; Urban Jermann; Aubhik

Kahn; Dmitry Livdan; Neng Wang; participants at seminars in Calgary, Carnegie-Mellon, Duke,

Wharton, NY Fed, NYU, Richmond Fed, ECB, UBC, UCLA, and Imperial College; as well as par-

ticipants at the following conferences: AFA, SED,Minnesota Macro Week, NBER Capital Markets,

NYU Five Star, Rimini Macro-Finance, UCSB-LAEF, Venice C.R.E.D.I.T, and ESSFM Gerzensee.

Alexander Belyakov, Marco Grotteria, Alexandr Kopytov, and Haotian Xiang provided excellent

research assistance. We have read The Journal of Finance disclosure policy and have no conf‌licts

of interest to disclose.

Correspondence: Lukas Schmid, Marshall School of Business, University of Southern Califor-

nia; e-mail: lukas@marshall.usc.edu.

DOI: 10.1111/jof‌i.12987

© 2020 the American Finance Association

977

978 The Journal of Finance®

In this paper, we attempt to f‌ill this gap. We develop a general equilibrium

model with heterogeneous f‌irms that make optimal investment and f‌inancing

decisions under uncertainty. The model brings together many core insights

from asset pricing, capital structure, and macroeconomics, reconciling in a

unif‌ied framework several core stylized facts about asset returns while also

addressing many key features of aggregate and f‌irm-level investment and f‌i-

nancing variables. Specif‌ically, we show that our model produces a sizable av-

erage equity premium and credit spread, together with plausibly low average

returns on safe assets. In the time series, our model also implies that both

price-dividend ratios and credit spreads have substantial predictive power for

future stock returns, while the cross section of stock returns delivers a signif‌i-

cant value premium.

In the model, quantitatively realistic asset return dynamics are driven by

empirically plausible endogenous movements in leverage, both in the time se-

ries and in the cross section. Indeed, a major contribution of our model is that

it delivers an explicit connection between f‌luctuations in the cross-sectional

distribution of f‌irms and time-series movements in macroeconomic aggre-

gates and f‌inancial prices. This link is critical, as the mass of f‌irms close to

default, and hence the credit spread, becomes a key determinant of aggregate

volatility and asset prices.

Endogenous movements in leverage amplify and propagate aggregate

consumption risk and volatility. Debt-f‌inanced booms and busts amplify ag-

gregate volatility, while a realistic long-term maturity structure of corporate

debt signif‌icantly increases the persistence of f‌luctuations. This amplif‌ication

increases the volatility of the market price of risk and produces quantitatively

realistic risk premia. Importantly, endogenous default also increases the

volatility of consumption during recessions, as the mass of f‌irms burdened

by excessive leverage and closer to default grows. As a consequence, the

equilibrium market price of risk also becomes sharply countercyclical.

Endogenous movements in leverage also explain much of our f‌indings about

predictability in both the time series and the cross section. Countercyclical

leverage drives up risk premia on f‌inancial assets during downturns, which, in

the time series, is naturally ref‌lected in both price-dividend ratios and credit

spreads. Cross-sectionally, because investment is f‌inanced at least in part with

debt, value f‌irms tend to have higher leverage ratios and these cross-sectional

differences in leverage between growth and value f‌irms amplify the dispersion

in equity risk and are a major determinant of the value premium.

Some of these mechanisms are shared by several partial equilibrium models

of equity returns, even if leverage is exogenous and there are no f‌inancing fric-

tions.1However, in such models leverage affects assets’ conditional betas only

through a direct cash f‌low effect, which is often magnif‌ied by correlated, but

exogenous, movements in discount rates. By contrast, in our general equilib-

rium setting, the main impact of leverage is felt indirectly though its general

1Carlson, Fisher, and Giammarino (2004), Zhang (2005), Livdan, Sapriza, and Zhang (2009),

Gomes and Schmid (2010), Ozdagli (2012), Obreja (2013),andKuehnandSchmid(2014).

Equilibrium Asset Pricing with Leverage and Default 979

equilibrium effect on the stochastic discount factor. This is because movements

in leverage are endogenously linked to the dynamics of aggregate consumption.

Indeed, in our model, both cash f‌low and discount rate effects are important

and interact with each other. Nevertheless, it is the general equilibrium move-

ments in consumption dynamics and the stochastic discount rate effect that

are quantitatively more important determinants of asset return dynamics.

Because defaults tend to cluster in downturns, when the market price of

risk is high, credit spreads contain a signif‌icant and volatile credit risk pre-

mium that compensates consumers for losses in bad states. Accordingly, credit

spreads exhibit signif‌icant time-series variation that spills over into the real

economy. In expansions, default risk and the market price of risk are low, and

hence debt-f‌inanced investment is cheap, while in recessions, increases in de-

fault rates and the credit risk premium lead credit spreads to spike up. These

endogenous movements in credit prices amplify the effects of shocks and gener-

ate more pronounced business cycle f‌luctuations. Much like in the data, credit

spreads predict business cycles, providing an early warning of impending re-

cessions. This is because the risk premium is informative about the tail of the

cross-sectional f‌irm distribution beyond aggregate productivity.2

Our model informs empirical work linking capital structure and returns by

highlighting potential pitfalls associated with the measurement of leverage.

Specif‌ically, we show that while there is a close theoretical connection between

true market leverage and equity returns, these linkages are much weaker

when we construct leverage using only the book value of debt and market value

of equity. This f‌inding suggests that using the lagged (book) value of debt as

a proxy for market leverage, as empirical studies generally do, may help ex-

plain the failure to f‌ind a strong link between leverage and returns in the

data.

A growing body of work provides an integrated discussion of asset prices,

leverage, and aggregate cycles in a modern setting, but our emphasis on risk

premia is fairly unique. Existing general equilibrium macro models that ex-

plain the cyclical behavior of credit markets and their correlation with macroe-

conomic aggregates largely abstract from variation in risk premia and asset

prices.3Unlike these classic f‌inancial accelerator papers, movements in credit

spreads in our paper are due mostly to variation in credit risk premia and

do not require large spikes in observed default events. In fact, in our model

changes in risk premia drive about two thirds of the credit spread and account

for most of its predictive power.

A parallel literature seeks to link credit risk to f‌irms’ f‌inancing decisions

and, more recently, to exogenous movements in risk premia and aggregate

2Examples of the ability of credit spreads to forecast economic activity include studies by Keim

and Stambaugh (1986), Stock and Watson (1999), Famaand French (1992), Lettau and Ludvigson

(2002), and Gilchrist and Zakrajsek (2012).

3Classic examples include Kiyotaki and Moore (1997) and Bernanke, Gertler, and Gilchrist

(1999). More recent contributions are Jermann and Quadrini (2012) and Khan and Thomas (2013).