Investment and the Cross‐Section of Equity Returns

• Published date: 01 February 2019
• Author: GIAN LUCA CLEMENTI,BERARDINO PALAZZO
• DOI: http://doi.org/10.1111/jofi.12730
• Date: 01 February 2019

THE JOURNAL OF FINANCE •VOL. LXXIV, NO. 1 •FEBRUARY 2019

Investment and the Cross-Section of Equity

Returns

GIAN LUCA CLEMENTI and BERARDINO PALAZZO∗

ABSTRACT

The data show that, upon being hit by adverse profitability shocks, large public firms

have ample latitude to divest their least productive assets, reducing the risk faced

by shareholders and the returns that they are likely to demand. In the one-factor

production-based asset pricing model, when the frictions to capital adjustment are

shaped to respect the evidence on investment, the model-generated cross-sectional

dispersion of returns is only a small fraction of that documented in the data. Our

conclusions hold even when operating or labor leverage is modeled in ways shown to

be promising in the extant literature.

ANOTABLE GOAL OF MODERN APPLIED economics research has been to devise

internally consistent theories of choice, production, and exchange whose pre-

dictions for both quantities and prices are consistent with the evidence. For

example, much of the research in macroeconomics and asset pricing over the

last 25 years has sought to develop a unified model of the business cycle that is

able to generate empirically appealing time-series behavior for both aggregate

∗Gian Luca Clementi is with New York University’sStern School of Business and the National

Bureau of Economic Research. Berardino Palazzo is with the Capital Markets Section of the Fed-

eral Reserve Board. We thank the Editors, Kenneth Singleton and Stefan Nagel, one Associate

Editor, and two anonymous referees for suggestions that greatly improved the paper.We are also

grateful to Frederico Belo; Martin Boileau; Andrea Buffa; Ilan Cooper; Jo˜

ao Gomes; Dirk Hackbart;

Xiaoji Lin; Lars Lochstoer; Sydney Ludvigson; Felipe Saffie; and Stijn Van Nieuwerburgh; as well

as seminar attendants at NHH Bergen, Bank of Italy,Boston University, Federal Reserve Bank of

St. Louis, NYU, University of Minnesota, University of Southern California, Wharton, University

of Wisconsin, CAPR Workshop(Oslo), CIREQ Workshop (Montreal), Duke-UNC Asset Pricing Con-

ference, “Firm Dynamics and the Aggregate Economy” at the Becker-Friedman Institute, ENSAI

Economic Day (Rennes), EUI Macro Conference (Florence), Midwest Macro Meeting, NY/Philly

Workshop on Quantitative Macroeconomics, and meetings of the American Finance Association,

European Finance Association, Canadian Macro Study Group, and Society for Economic Dynam-

ics for their comments and insights. Marco Casiraghi and Peifan Wu provided excellent research

assistance. All remaining errors are our own responsibility. The views expressed are those of the

authors and do not necessarily reflect those of the Federal Reserve Board or the Federal Reserve

System.WehavereadtheJournal of Finance’s disclosure policy and have no conflicts of interest

to disclose.

DOI: 10.1111/jofi.12730

281

282 The Journal of Finance R

quantities—output, consumption, investment, and employment—and financial

assets returns.1

With respect to cross-sectional evidence on investment and financial asset re-

turns, the broadly intended neoclassical model of firm optimization has become

the analytical framework of choice for scholars interested in rationalizing one

or the other. Cooper and Haltiwanger (2006), among others, show that plant-

level investment data restrict modeling choices on capital adjustment costs.

Taking a different perspective, a series of papers starting with Carlson, Fisher,

and Giammarino (2004), Zhang (2005), and Cooper (2006) investigate the re-

strictions on the same choices coming from equity returns. The upshot of this

literature is that the same theoretical framework, when appropriately speci-

fied, has empirically sensible implications for quantities (investment rate) and

prices (equity returns).

In this paper, we examine whether the parametric restrictions imposed by

investment data are compatible with those derived from equity returns data.

We find that, for a large class of one-factor models, they are not. Loosely speak-

ing, the capital adjustment costs implied by the investment data are too small

to justify the observed dispersion in returns.

To gauge the relevance of our finding, consider that over the last decade or

so the one-factor investment-based model has been the dominant paradigm in

the quest to understand the drivers of cross-sectional heterogeneity in returns.

For example, Livdan, Sapriza, and Zhang (2009) use it to study the effect of

financial constraints on stock returns, Gomes and Schmid (2010) adopt it to

investigate the role of financial leverage, Schmid and Kuehn (2014) assess its

ability to rationalize credit spreads, and Tuzel and Zhang (2017) argue that it

can rationalize the impact of local factors on asset prices.

We start by documenting investment behavior among publicly traded U.S.

firms, that is, the subset of firms most studied by asset pricing scholars. This

exercise is akin to that conducted by Cooper and Haltiwanger (2006)onman-

ufacturing plants. The data display substantial cross-sectional dispersion for

the investment rate −28.5% at the annual frequency, almost twice the uncon-

ditional mean. Furthermore, each quarter on average 18.2% of firms record

negative gross investment. We take the latter as strong evidence against the

assumption of irreversibility.

We next consider a variant of the neoclassical investment model that is close

to that used by Zhang (2005). Our environment features decreasing returns

to scale, mean-reverting idiosyncratic shocks to profitability, and a flexible

formulation of capital adjustment costs. We select parameters to match the

cross-sectional dispersion and autocorrelation of the investment rate, as well

as the fraction of firms undertaking negative investment. Future cash flows

are priced by means of an exogenous stochastic discount factor parameterized

1See Rouwenhorst (1995) for a diagnosis of the inability of the prototypical real business cycle

model to generate sensible predictions for asset returns, and Jermann (1998) for an early attempt to

specify a model that comes to terms with the evidence on both quantity and asset return dynamics.

Investment and the Cross-Section of Equity Returns 283

to replicate the first two unconditional moments of the risk-free rate and the

Sharpe ratio.

In the cross-section, risk and returns are decreasing in productivity. Because

of mean-reversion, low-productivity firms derive most of their value from cash

flows with long maturity, which in this framework are riskier. Conversely, the

value of high-productivity firms comes mostly from short-run cash flows, which

are less risky.This rationalizes the size premium, that is, the finding that firms

with small market capitalization (in this environment, low productivity) elicit

higher returns.

Due to decreasing returns to scale, on average value firms (high book-to-

market) feature higher idiosyncratic productivity than growth firms (low book-

to-market). The model therefore produces a value discount. The equilibrium

association between productivity and book-to-market is inverted by assuming

that firms incur operating costs (invariant to firm size) that are large enough.

When calibrating the operating cost to match the unconditional mean firm’s

exit rate, we find that the unconditional cross-sectional correlation between

productivity and book-to-market does indeed turn negative. A value premium

thus obtains.

However, value firms are saddled with a large capital stock resulting from a

recent history of good shocks. The ability to relinquish capital—disciplined by

the evidence on investment—makes them less risky than small firms. Growth

firms feature high productivity but, thanks to a recent history of bad shocks,

relatively low capital. The ability to quickly grow their operating assets—once

again disciplined by the evidence on investment—makes them riskier than

large firms.

It follows that the resulting value premium is smaller than the size

premium. In particular, it is only one-third of the value we estimate from the

data. A higher dispersion of equity returns can be obtained by raising the

adjustment cost of capital, but at the cost of a counterfactually lower volatility

of investment.

This is the tension we focus upon. We show that for the value premium to

get close to its empirical counterpart, both the volatility of investment and

the fraction of firms undertaking negative investment must be very close to

zero. Consistent with these results, we document that for the model in Zhang

(2005) to generate a nontrivial value premium, the implied investment process

must be counterfactual. In particular, the unconditional standard deviation of

investment is one order of magnitude lower than in the data.

Zhang (2005), Carlson, Fisher, and Giammarino (2004), and Obreja (2013),

among others, emphasize the amplification role of operating leverage. In

our baseline model, the magnitude of the operating cost is disciplined by

matching the exit rate. Raising the cost to levels associated with coun-

terfactually higher exit rates has two countervailing effects on the disper-

sion of returns. On the one hand, it raises the variation among firms that

stay in the sample. On the other hand, the increased exit selection com-

presses the distribution. In our environment, the two effects cancel each other

out.