Sticky Expectations and the Profitability Anomaly

• Author: DAVID THESMAR,PHILIPP KRÜGER,AUGUSTIN LANDIER,JEAN‐PHILIPPE BOUCHAUD
• Published date: 01 April 2019
• DOI: http://doi.org/10.1111/jofi.12734
• Date: 01 April 2019

THE JOURNAL OF FINANCE •VOL. LXXIV, NO. 2 •APRIL 2019

Sticky Expectations and the Profitability

Anomaly

JEAN-PHILIPPE BOUCHAUD, PHILIPP KR ¨

UGER, AUGUSTIN LANDIER,

and DAVID THESMAR∗

ABSTRACT

We propose a theory of the “profitability” anomaly. In our model, investors forecast

future profits using a signal and sticky belief dynamics. In this model, past profits

forecast future returns (the profitability anomaly). Using analyst forecast data, we

measure expectation stickiness at the firm level and find strong support for three

additional model predictions: (1) analysts are on average too pessimistic regarding

the future profits of high-profit firms, (2) the profitability anomaly is stronger for

stocks that are followed by stickier analysts, and (3) the profitability anomaly is

stronger for stocks with more persistent profits.

ANUMBER OF STUDIES IN THE asset pricing literature document the existence of

stock return predictability: Several stock-level characteristics beyond market

betas significantly predict future stock returns. However, the origin of such ab-

normal returns, and how they can exist in equilibria without being arbitraged

away, is subject to debate. One strand of the literature interprets abnormal

returns as risk premia (see, for instance, Cochrane (2011)), which implies that

they are only seemingly abnormal. Other authors attribute abnormal returns

to behavioral biases combined with limits to arbitrage (see, e.g., Barberis

and Thaler (2003) or references therein, such as Daniel, Hirshleifer, and

Subrahmanyam (1998,2001) and Hirshleifer (2001)). Mispricing then relies on

investors making systematic expectation errors, while rational arbitrageurs

are unable to fully accommodate their demand because arbitrage is not

risk free. In this literature, the behavioral biases of the nonrational market

participants typically take the form of non-Bayesian expectations grounded

in the psychology literature (see, e.g., Hong and Stein (1999) or Barberis,

Shleifer, and Vishny (1998)).

In this paper, we focus on the profitability anomaly, whereby stocks with high

profitability ratios tend to outperform on a risk-adjusted basis (Novy-Marx

∗Jean-Philippe Bouchaud is with Capital Fund Management. Philipp Kr¨

uger is with the Univer-

sity of Geneva and Swiss Finance Institute. Augustin Landier is with HEC Paris. David Thesmar

is with MIT Sloan and CEPR. We thank Nick Barberis, Bruno Biais, and Eric So, as well as the two

referees and Stefan Nagel for their very detailed and constructive feedback. We are also grateful to

seminar audiences at AFA, UC Berkeley, and NBER. Disclosure statement: Bouchaud is chairman

of Capital Fund Management. Kr¨

uger has nothing to disclose. Landier and Thesmar were doing

research at Capital Fund Management when they started this paper.

DOI: 10.1111/jofi.12734

639

640 The Journal of Finance R

(2013,2015)). Recent research suggests that profitability is one of the stock

return anomalies that has the largest economic significance. The correspond-

ing long-short arbitrage strategy features high Sharpe ratios, no crash risk

(Lemperiere et al. (2017)), and very high capacity due to the high persistence

of the profitability signal (e.g., operating cash flows to asset ratio on which the

strategy sorts stocks (Landier, Simon, and Thesmar (2015)). Our goal in this

paper is to test whether the profitability anomaly can be directly related to a

simple model of sticky expectations in which investors update their beliefs too

slowly.

We start by building a simple model in which risk-neutral investors price a

stock whose dividend is predictable with a persistent signal. These investors

have “sticky” expectations. Each period, their expectations are given by λ

times their previous belief and 1 −λtimes the rational expectation (i.e.,

the individual-level version of the consensus forecast model of Coibion and

Gorodnichenko (2012,2015)). As Coibion and Gorodnichenko (2015)show,

this model has the advantage of nesting rational expectations as a particular

case and offers a simple way to measure expectation stickiness using the

link between forecast errors and past forecast revisions. It can thus be easily

applied to the data. When solving this simple model, we find that future stock

returns can be forecasted using past profits and past changes in profits. The

model therefore provides a rationalization for the profitability anomaly. It also

makes other predictions.

We test the predictions of the model using observed earnings per share (EPS)

forecasts by financial analysts from I/B/E/S. Directly observable expectations

contained in financial analysts’ EPS forecasts is a natural setting to study how

beliefs of market participants deviate from rational expectations. Analysts are

professional forecasters whose forecasts are not cheap talk, which mitigates

the legitimate concerns about subjective answers found in surveys (see

Bertrand and Mullainathan (2001)). However, we do make the assumption

that analysts’ data are representative of investors’ expectations. Using these

data, we find that the average forecaster puts an excess weight of 16% on

earlier annual forecasts.

The data are consistent with key cross-sectional predictions of the model.

First, we expect analysts to systematically underestimate future profits when

current profits are high. Second, we expect the profitability anomaly to be

stronger for firms that are subject to stickier EPS forecasts. Third, firms with

more persistent earnings should be more prone to the profitability anomaly.

Fourth, the previous three predictions should also hold for two significant sig-

nals besides the profitability level, namely,earnings momentum (profit change)

and returns momentum (past returns). All of these predictions are robust out-

comes of the model, and they all hold in the data. They thus support our

interpretation of this anomaly.

Our analysis’s greatest contribution is to the behavioral finance literature,

which documents both under- and overreaction of analyst forecasts. There is

an old tradition of papers on investor underreaction. Abarbanell and Bernard

(1992) find that analysts underreact to past earnings, in line with our own

Sticky Expectations and the Profitability Anomaly 641

results. Ali, Klein, and Rosenfeld (1992) find a similar result for annual

earnings forecasts. Like us, such positive serial correlation is most often

interpreted in the literature as a sign that analysts are underreacting in a

non-Bayesian manner when setting expectations of future earnings (see, e.g.,

Ali, Klein, and Rosenfeld (1992) or Markov and Tamayo (2006) for a summary

of the literature). An exception is Markov and Tamayo (2006), who argue that

the positive autocorrelation of forecast errors is compatible with Bayesian

updating if analysts do not know the true data-generating process for earnings

but rather learn about it slowly. Consistent with this hypothesis, Mikhail,

Walther, and Willis (2003) find that analysts with more experience underreact

less to prior earnings. To our knowledge, this literature does not establish a

link between the persistence of forecast errors and the profitability anomaly.

Also, our analyst-level regressions are harder to reconcile with Bayesian

learning. In addition, using the insight of Coibion and Gorodnichenko (2015),

we propose a model of expectation formation where underreaction is captured

by a single parameter, which we estimate. Finally, we add to the literature

by documenting heterogeneity in analyst biases at the firm level and by

relating this heterogeneity to the intensity of stock market anomalies. In this

sense, our results are consistent with finance papers that document the slow

diffusion of information in markets (see, e.g., Hong, Lim, and Stein (2000),

Hou (2007)).

The literature also provides abundant evidence of overreaction. For instance,

Debondt and Thaler (1990) document patterns of overreaction by looking at an-

alyst revisions. Most relevant to our present work is a group of papers starting

with Debondt and Thaler (1985) and Lakonishok, Shleifer, and Vishny (1994)

that seek to explain the value premium by extrapolating beliefs. La Porta

(1996) and Bordalo et al. (2017) show that stocks with high expected growth

(as measured by analyst consensus on long-term earnings growth) tend to

be glamour stocks and to have low expected returns. Alti and Tetlock (2014)

calibrate a model in which overreaction and overconfidence distort agents’ ex-

pectations of firm productivity. Weber (2018) documents abnormal returns of

portfolios sorted on cash flow duration and shows that this anomaly can be

explained by extrapolation bias in analysts’ long-term forecasts. Gennaioli,

Ma, and Shleifer (2015) and Greenwood and Shleifer (2014) find that errors

in CFO expectations of earnings growth are not rational and are compatible

with a model of extrapolative expectations. They focus on the time sequence

of forecasts and on expectations of long-term growth and returns. These pa-

pers differ from ours in two respects. First, they seek to explain the value

premium or the duration premium while we offer a theory of the profitabil-

ity anomaly. Second, they find evidence of extrapolative behavior regarding

long-term earnings growth forecasts, while we provide evidence of stickiness

of near-term EPS forecasts. Consistent with this, Bordalo et al. (2017)run

regressions similar to our Table III on both EPS forecasts (our focus here)

and long-term growth forecasts (their focus), and confirm both our finding of

stickiness in the short run and their hypothesis of overreaction of long-run

expectations.