What Drives Anomaly Returns?

• DOI: http://doi.org/10.1111/jofi.12876
• Published date: 01 June 2020
• Date: 01 June 2020
• Author: PAUL C. TETLOCK,LARS A. LOCHSTOER

THE JOURNAL OF FINANCE •VOL. LXXV, NO. 3 •JUNE 2020

What Drives Anomaly Returns?

LARS A. LOCHSTOER and PAUL C. TETLOCK∗

ABSTRACT

We decompose the returns of five well-known anomalies into cash flow and discount

rate news. Common patterns emerge across the five factor portfolios and their mean-

variance efficient (MVE) combination. Whereas discount rate news predominates in

market returns, systematic cash flow news drives the returns of anomaly portfolios

and their MVE combination with the market portfolio. Anomaly cash flow and dis-

count rate shocks are largely uncorrelated with market cash flow and discount rate

shocks and with business cycle fluctuations. These rich empirical patterns restrict the

joint dynamics of firm cash flows and the pricing kernel, thereby informing models of

stocks’ expected returns.

OVER THE PAST 30 YEARS, researchers have uncovered robust patterns in stock

returns that contradict classic asset pricing theories. A prominent example is

that value stocks outperform growth stocks, even though they are similarly

exposed to fluctuations in the overall stock market. To exploit such anomalies,

investors can form long-short portfolios (e.g., long value and short growth) with

high average returns and near-zero market risk. These long-short anomaly

portfolios are an important part of the mean-variance efficient (MVE) portfolio

and thus the stochastic discount factor (SDF). In the five-factor Fama and

French (2015) model, nonmarket factors account for 85% of the variance in the

model’s implied SDF.1

Researchers sharply disagree about the source of these nonmarket factors.

Several different models, both risk-based and behavioral, can explain why

∗Lochstoer is at the UCLA Anderson School of Management. Tetlock is at Columbia Business

School. We thank Jules van Binsbergen; John Campbell; Mikhail Chernov; James Choi; Zhi Da;

Kent Daniel; Francisco Gomes; Leonid Kogan; Stefan Nagel; Stijn van Nieuwerburgh; Christopher

Polk; Shri Santosh; Luis Viceira; Amir Yaron; an anonymous referee and associate editor; as well as

seminar participants at the AFA, Case Western,Columbia, Copenhagen Business School, Cornell,

FRB, LBS, McGill, Miami Behavioral Conference, Miami University, NBER LTAM, NY Fed, Ohio

State, Q-group, SFS Finance Cavalcade, Swedish House of Finance, UBC, UCLA, UC Irvine,

University of Massachusetts Amherst, and UVAfor helpful comments. Lochstoer and Tetlock have

no conflicts of interest to disclose.

Correspondence: Paul Tetlock, Columbia Business School, Department of Finance, 3022 Broad-

way, 811 Uris Hall, New York, NY 10027; e-mail: pt2238@columbia.edu.

This is an open access article under the terms of the Creative Commons Attribution License, which

permits use, distribution and reproduction in any medium, provided the original work is properly

cited.

1Using data from 1963 to 2017, a regression of the MVE combination of the five Fama-French

factors on the market factor yields an R2of 15%.

DOI: 10.1111/jofi.12876

C2020 The Authors. The Journal of Finance published by Wiley Periodicals, Inc. on behalf of

American Finance Association

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1418 The Journal of Finance R

long-short portfolios based on valuation ratios and other characteristics earn

high average returns.2In this paper, we introduce an efficient empirical tech-

nique for decomposing anomaly portfolio returns, as well as their MVE combi-

nation, into cash flow (CF) and discount rate (DR) shocks (news) as in Campbell

(1991). These decompositions provide a wide array of new facts that can guide

specifications of asset pricing theories.

To see how this CF-DR decomposition relates to extant theories, consider at

one extreme the model of noise trader risk proposed by De Long et al. (1990). In

this model, firm CFs are constant, implying that all return variation arises from

changes in DRs. At the other extreme, consider the simplest form of the Capital

Asset Pricing Model (CAPM) in which firm betas, the market risk premium,

and the risk-free interest rate are constant. In this setting, expected returns

(DRs) are constant, which implies that all return variation arises from changes

in expected CFs. More generally, models that explain how firm characteristics

like book-to-market (BM) or investment are related to expected firm returns

have implications for the joint distribution of firm CFs and the pricing of these

CFs. Applying our empirical methodology to simulated data from any such

theory allows one to test whether the model matches the empirical properties

of CF and DR shocks to anomaly portfolios and their MVE combination.

Our empirical work focuses on the annual returns of five well-known

anomalies—value, size, profitability, investment, and momentum—from 1929

to 2017. We uncover three sets of novel findings for theories to explain. First,

for all five anomalies, CF news explains most (64% to 80%) of the variation in

anomaly returns. This finding builds on Cohen, Polk, and Vuolteenaho (2003,

2010; hereafter CPV), who show that CFs explain most of the variance in the

returns of the value anomaly. It also builds on Fama and French (1995), who

show that portfolios formed on size and value experience systematic shocks to

earnings. We find that such systematic earnings shocks occur not only in size

and value factor portfolios but also in profitability,investment, and momentum

portfolios. Moreover, unlike Fama and French (1995), we are able to explicitly

link systematic shocks to firms’ earnings to the returns of the anomaly portfo-

lios. Toevaluate implications for the SDF, we combine all five anomalies into an

MVE anomaly portfolio and continue to find that CF shocks explain most (73%)

of the MVE portfolio’s return variance. This finding contrasts with the stylized

fact that DR shocks explain most of market return variance (see, e.g., Camp-

bell (1991) and Cochrane (2011))—a fact that we replicate. The CF shock to

the anomaly MVE portfolio represents a large and common source of variation

in firms’ CF shocks that spans anomaly boundaries, which runs counter to the

conclusion in Vuolteenaho (2002; hereafter V02) that “cash-flow information is

largely firm specific” (p. 259).

Second, the CF and DR components in anomaly returns exhibit only

weak correlations with the corresponding components in market returns.

2See, for example, Barberis, Shleifer, and Vishny (1998); Berk, Green, and Naik (1999); Hong

and Stein (1999); Daniel, Hirshleifer, and Subrahmanyam (2001); Zhang (2005); Lettau and

Wach ter (2007); and Kogan and Papanikolaou (2013).

What Drives Anomaly Returns? 1419

Conceptually,there are four correlations of interest between anomaly and mar-

ket CF and DR components, all of which affect an anomaly’s market beta. The

correlations between market CFs and the five anomaly CFs range from −0.22

to 0.13. We can reject the hypothesis that CF shocks to the MVE portfolio that

consists of all five anomalies are positively correlated (above 0.11) with market

CF shocks, indicating that the anomaly MVE portfolio and the market portfolio

are exposed to distinct fundamental risks. In addition, we estimate that the

correlation between anomaly MVE DR news and market DR news is just 0.06

(SE =0.12).

Our third finding is that, for most anomalies, CF and DR shocks are neg-

atively correlated. That is, firms with negative news about future CFs tend

to experience persistent increases in DRs. This association contributes signif-

icantly to return variance in anomaly portfolios. A notable caveat is that this

result applies to anomaly portfolios based on stocks with market capitaliza-

tion not in the bottom quintile of New York Stock Exchange (NYSE) stocks,

which roughly corresponds to excluding stocks popularly known as microcaps.

In an alternative specification that includes microcaps, these stocks exert a

large influence on some findings because they are numerous and have volatile

characteristics and returns. Although our first two findings are essentially un-

changed in this alternative specification, the correlation between anomaly CF

and DR news abecomes positive.3

Our main findings cast doubt on three types of anomaly theories. First,

theories in which DR news is the primary source of anomaly returns, such as

De Long et al. (1990), are inconsistent with evidence that CF news dominates

over returns. The main reason anomaly portfolios’ returns are volatile is that

CF shocks are highly correlated across firms with similar characteristics. For

example, the long-short investment portfolio is volatile mainly because the CFs

of a typical high-investment firm are more strongly correlated with the CFs of

other high-investment firms than with those of low-investment firms. The small

variance of anomaly DR news does not imply small variation in the conditional

expected returns to anomaly portfolios. Indeed, we find substantial variation

in anomalies’ one-year expected returns, consistent with, for example, Haddad,

Kozak, and Santosh (2018). However, because this expected return variation is

not highly persistent, it has a small impact on stock prices and thus realized

anomaly returns.

Second, theories that emphasize commonality in DRs, such as theories of

time-varying risk aversion (e.g., Santos and Veronesi (2010)) and theories of

common investor sentiment (Baker and Wurgler (2006)), are difficult to recon-

cile with the low correlations between anomaly and market DR shocks. Third,

theories in which anomaly CF news is strongly correlated with market CF

news, in particular CF beta stories such as Zhang (2005), are inconsistent with

3At the firm level, our results with and without microcaps are consistent with the finding in

V02 that the correlation between CFs and DRs is highest for the smallest firms as well as with

the finding in Mendenhall (2004) that postearnings announcement drift is concentrated in the

smallest firms.