THE SHRINKING SPACE FOR ANOMALIES

• Author: George J. Jiang,Andrew Jianzhong Zhang
• Date: 01 September 2013
• Published date: 01 September 2013
• DOI: http://doi.org/10.1111/j.1475-6803.2013.12012.x

THE SHRINKING SPACE FOR ANOMALIES

George J. Jiang

Washington State University

Andrew Jianzhong Zhang

University of Nevada Las Vegas

Abstract

The existing literature documents a number of cross‐sectional stock return anomalies.

This article examines how pervasive these anomalies are and whether factor models

provide valid inferences on anomalous returns. First, by shrinking the stock space along

the dimension of a predictive variable, we show that the book‐to‐market ratio (BM) and

net stock issues effects are pervasive, whereas the size, momentum, and illiquidity effects

are driven mainly by stocks on the long side, and the idiosyncratic volatility, accrual,

capital expenditure, and sales growth effects mainly by stocks on the short side. Second,

we provide evidence that commonly used factor models have limited explanatory power

of stock returns. Restricting to stock samples where the four‐factor model adequately

explains the size, BM, and momentum effects, we show that only the idiosyncratic

volatility, accrual, and net stock issues effects remain significant.

JEL Classification: G10, G12, G14

I. Introduction

A large body of existing studies has documented that certain firm‐specific characteristics

have predictive power of cross‐sectional stock returns. Many of these predictive patterns

are dubbed as anomalies because they cannot be explained by the capital asset pricing

model (CAPM) of Sharpe (1964) and Lintner (1965) or the multifactor models.

1

In this

article, we revisit 10 commonly documented return‐predictive variables and examine two

issues that are of important implications but have yet been adequately addressed in the

literature.

The first issue is whether the cross‐sectional return predictability is pervasive

among different stock samples. Although the existing literature has shown that these

anomalies are in the data, the concern is that they may be driven by a subsample of

extreme stocks, that is, stocks with extreme firm characteristics. The main focus of this

study is whether the anomalous returns are driven by stocks on the long side (those with

We are grateful to Tim Loughran (associate editor) and Jay Wellman (the referee) for valuable and constructive

comments and suggestions on the paper. We also wish to thank Turan Bali, Tyler Henry, Chris Lamoureux,

Guanzhong Pan, Theo Vermaelen, Leirong Xue, and seminar participants at the University of Arizona, University of

Oklahoma, and Fudan University for helpful comments and suggestions. The usual disclaimer applies.

1

See Schwert (2003) for further discussions on the relation between anomalies and market efficiency.

The Journal of Financial Research Vol. XXXVI, No. 3 Pages 299–324 Fall 2013

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© 2013 The Southern Finance Association and the Southwestern Finance Association

higher future returns) or stocks on the short side (those with lower future returns) or both.

To this end, we shrink the stock sample along the dimension of a predictive variable and

examine the pervasiveness of an anomaly.

For example, to examine the pervasiveness of the size effect, we first sort the

stock universe into percentiles based on the market cap in June of each year. We then

shrink the stock space from either the long or short side and examine how the size effect is

sensitive to the stock sample. Specifically, to shrink the stock space from the long side, we

first exclude 1 percentile of the smallest firms in the full stock sample and construct decile

portfolios on the remaining firms to compute return spreads between the top and bottom

size deciles over the next 12‐month period. The analysis is repeated sequentially with 1

additional percentile of the smallest firms excluded from the stock sample in each of the

subsequent steps. Similarly, to shrink the stock space from the short side, we first exclude

1 percentile of the largest firms in the full stock sample and construct decile portfolios on

the remaining firms to compute return spreads between the top and bottom size deciles

over the next 12‐month period. Again, the analysis is repeated sequentially with 1

additional percentile of the largest firms excluded from the stock sample in each of the

subsequent steps. Our approach is different from Fama and French (2008) in that they

divide the stock space according to market cap. By shrinking the stock space along the

dimension of the predictive variable, we are able to directly observe whether the return

spreads are driven by the long side or the short side or both.

The second issue is whether existing factor models provide valid inferences on

anomalous returns. Existing studies have proposed competing hypotheses for anomalies

associated with various stock characteristics. The rational models postulate that stock

characteristics are proxies for risk factors and differentials across stock returns are simply

the effect of risk premium. On the other hand, the behavioral models contend that

investors tend to misreact to information contained in certain firm characteristics and thus

form biased expectations of stock returns. To settle the debate, a standard practice is to

rely on factor models and examine whether abnormal returns remain significant even after

adjusting for risk premium. The commonly used factor models include the three‐factor

model of Fama and French (1993), the four‐factor model of Carhart (1997), and the five‐

factor model proposed in Pastor and Stambaugh (2003). The rationale is that if the cross‐

sectional stock return difference cannot be explained by a factor model (i.e., with a

significant alpha estimate), then such return differential is beyond the effect of risk

premium. As a result, the return‐predictive pattern is often referred to as an anomaly or is

evidence that there warrants a new risk factor to account for the difference in stock returns.

Therefore, it is crucial for factor models to provide valid inference on abnormal returns in

order to settle the debate between rational and behavioral camps. The main focus of this

study is which return‐predictive patterns are true anomalies and which are likely the result

of invalid inferences.

Our analysis helps to answer several important questions. First, separating the

long side versus the short side helps to pinpoint the causes of an anomaly. In addition to

rational and behavioral explanations, it is known that short sale constraint can be the direct

cause of stock return anomalies. Miller (1977) argues that in the presence of short sale

constraints, investors’heterogeneous beliefs can lead to stock overvaluation and these

stocks subsequently experience lower returns. Therefore, short sale constraint cannot be

300 The Journal of Financial Research