Time‐series and cross‐sectional momentum in anomaly returns

• Published date: 01 September 2021
• Author: Feifei Wang,Xuemin (Sterling) Yan,Lingling Zheng
• Date: 01 September 2021
• DOI: http://doi.org/10.1111/eufm.12290

DOI: 10.1111/eufm.12290

ORIGINAL ARTICLE

Time‐series and cross‐sectional momentum

in anomaly returns

Feifei Wang

1

|Xuemin (Sterling) Yan

2

|Lingling Zheng

3

1

Farmer School of Business, Miami

University, Oxford, Ohio, USA

2

College of Business, Lehigh University,

Bethlehem, Pennsylvania, USA

3

School of Business, Renmin University

of China, Beijing, China

Correspondence

Lingling Zheng, School of Business,

Renmin University of China,

Beijing 100872, China.

Email: Zhenglingling@rmbs.ruc.edu.cn

Abstract

We find strong evidence of time‐series and cross‐sectional

momentum in the long–short returns of a comprehensive

sample of anomalies. Strategies that exploit such persis-

tence deliver significant abnormal returns that are robust

to the stock momentum effect, cannot be explained by

traditional asset‐pricing models, and are more pronounced

when arbitrage capital is scarcer or market liquidity is

lower. Momentum in anomaly returns dissipates but does

not reverse, in the long‐run. Our findings are consistent

with limits‐to‐arbitrage and slow‐moving capital causing

mispricing to persist. Supporting this explanation, we find

that both the level and persistence of anomaly returns are

positively related to idiosyncratic volatility.

KEYWORDS

anomalies, idiosyncratic volatility, limits to arbitrage,

momentum

JEL CLASSIFICATION

G10; G11; G14

1|INTRODUCTION

Finance researchers have documented hundreds of cross‐sectional return anomalies (Harvey

et al., 2016; Hou et al., 2020). An important debate in this literature is whether the abnormal

long–short returns are compensation for systematic risk, evidence of market inefficiency, or the

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© 2020 John Wiley & Sons Ltd.

We thank John Doukas (the editor), Ulrich Hammerich, Melvyn Teo, an anonymous referee, and seminar participants

at the 2017 CQAsia, 2018 FMA Annual Meetings, and the Renmin University of China for helpful comments. Lingling

Zheng acknowledges financial support from the National Natural Science Foundation of China (Project No. 71703164).

result of data mining. In this paper, we provide new evidence on this debate by examining the

persistence of absolute and relative performance of a comprehensive sample of cross‐sectional

return anomalies. Intuitively, if anomalies result from data mining, that is, they are spurious,

then any superior long‐short performance would be due to random chance, and hence is

unlikely to continue. In contrast, if the superior long–short returns represent compensation for

risk, then they should persist indefinitely. However, such persistence should weaken when we

remove the mean long–short return (an estimate of the expected return). Finally, if the anomaly

returns are due to mispricing, and, to the extent that arbitrage capital is limited and slow‐

moving, we would expect the superior long‐short performance to persist in the short run but

dissipate in the long run. Therefore, the data‐mining‐, risk‐, and mispricing‐based explanations

offer diametrically opposed predictions on whether superior anomaly returns should persist

and whether such persistence should be short‐lived or long‐lived.

We begin by examining time‐series momentum in our sample of 90 anomalies. We follow

Moskowitz et al. (2012) and estimate univariate regressions of anomaly returns on lagged

anomaly returns. We find strong evidence of persistence. Almost all of the auto‐regression

coefficients from lag 1 to 52 weeks are positive, with eight of them statistically significant at the

5% level. We also follow Moskowitz et al. (2012) and construct a diversified portfolio of time‐

series momentum strategies across all anomalies in our sample. This portfolio delivers sig-

nificant abnormal returns that are robust to different formation periods and holding periods

(both ranging from 1 to 52 weeks). For example, the CAPM αfor the time‐series momentum

strategy with a formation period of 4 weeks and a holding period of 4 weeks is 0.19% per week

(10% annualized) and is highly statistically significant. Although the time‐series momentum

profits are significant up to 52 weeks, they are most pronounced during the first 4 to 8 weeks,

suggesting the persistence of anomaly returns is relatively short‐lived.

Next, we examine whether anomaly returns exhibit cross‐sectional momentum, that is,

whether the relative performance of anomalies persists. The cross‐sectional momentum is

related to, but distinct from the time‐series momentum, which focuses entirely on an anomaly's

own past returns. We find strong evidence of cross‐sectional momentum among our sample of

anomalies. Anomalies that performed relatively well (poorly) during the past 1 to 52 weeks

continue to perform well (poorly) for the next 1 to 52 weeks. For example, the CAPM αfor the

cross‐sectional momentum strategy with a formation period of 4 weeks and a holding period of

4 weeks is 0.32% per week, and highly statistically significant. Similar to time‐series

momentum, we find that the cross‐sectional momentum is most pronounced during the first

4 to 8 weeks, suggesting that the persistence of relative anomaly returns is also short‐lived.

Momentum in anomaly returns is not merely a reflection of the stock momentum

(Jegadeesh & Titman, 1993). Profits to our time‐series and cross‐sectional momentum strategies

are slightly reduced but remain highly significant after controlling for the momentum factor.

Our results are also robust to alternative asset pricing models including the Fama and French

(2015)5‐factor model and the Hou et al. (2015)q‐factor model. In addition, our findings are not

driven by small, illiquid stocks. In constructing anomaly returns, we remove all stocks with a

price less than $5 or with a market capitalization ranked in the lowest NYSE decile, and we use

value weights. In addition, our results remain significant when we skip a week after portfolio

formation, mitigating a concern that our results are driven by microstructure effects. Finally,

we find that the persistence in anomaly returns is attributable to both long and short legs.

Our finding of significant momentum in anomaly returns is inconsistent with the view that

stock return anomalies are a product of data mining or statistical biases. We follow McLean and

Pontiff (2016) and use the term “statistical biases”to describe a wide range of biases that are

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inherent in academic research. These biases may lead to discoveries of “significant”return

predictability that is in fact spurious. If the anomalies in our sample are spurious, then any

superior long‐short performance would be a chance result, and therefore, should not persist.

Momentum in anomaly returns could be due to differences in unconditional expected returns

(Conrad & Kaul, 1998 and Jegadeesh & Titman, 2001). We test this possibility in two ways. First, we

examine whether the persistence in anomaly returns extends beyond the initial holding period.

Intuitively, if anomaly A exhibit higher returns than anomaly B because anomaly A is un-

conditionally riskier, then, everything else equal, we would expect the relative performance of these

two anomalies to persist for a long time. Our evidence is inconsistent with this prediction. Second, if

momentum in anomaly returns is due to differences in unconditional expected returns, then it should

disappear when we use demeaned long–short returns to construct our momentum strategies. We do

not find such evidence. We find that both the time‐series and cross‐sectional momentum in anomaly

returns are essentially unchanged. This finding is not only inconsistent with explanations based on

constant expected returns but also casting doubts on risk‐based explanations in general, because, to

theextentthattheaveragelong–short return contains information about the riskiness of an anomaly,

one would expect momentum in anomaly returns to be weaker in demeaned long–short returns.

Alternatively, momentum in anomaly returns may be driven by a time‐varying risk pre-

mium. To explore this possibility, we estimate rolling CAPM, Fama and French 3‐factor, and

Carhart 4‐factor models and remove the time‐varying expected returns based on these models

from each anomaly's long–short returns. We then test whether time‐series and cross‐sectional

momentum exist in the residual anomaly returns. If the persistence in anomaly returns solely

results from the persistence in factor exposures to the market, size, value, and momentum

factors, then we would expect the residual anomaly returns to exhibit no time‐series or cross‐

sectional momentum. Our results are inconsistent with this prediction—both the time‐series

and cross‐sectional momentum remain highly significant in residual anomaly returns.

1

We argue that momentum in anomaly returns is more consistent with behavioral ex-

planations in which limits to arbitrage and slow‐moving arbitrage capital cause mispricing to

persist. In the presence of costly arbitrage, mispricing will not be completely eliminated

(Pontiff, 2006; Shleifer & Vishny, 1997). We show in a simple model that such incomplete

arbitrage leads to persistence in anomaly returns in the short run. In the long run, the arrival of

information or additional arbitrage capital brings mispricing toward zero. Therefore, behavioral

arguments predict that anomaly returns will be persistent in the short‐run but dissipate in the

long run. Our results are consistent with these predictions.

If momentum in anomaly returns is related to time‐varying arbitrage capital, as predicted by

behavioral explanations, then it should be more pronounced when the arbitrage capital is

scarcer. To test this hypothesis, we construct two proxies for the amount of arbitrage capital,

that is, hedge fund total assets under management and aggregate short interest ratio. Consistent

with the prediction of behavioral explanations, we find that the persistence in anomaly returns

is negatively related to these proxies for arbitrage capital. Behavioral explanations also predict

that momentum in anomaly returns should be more pronounced when the market is less

liquid. Using the aggregate Amihud ratio, aggregate turnover, and a postdecimalization in-

dicator as proxies for market liquidity, we find evidence consistent with this prediction.

Our model also makes two predictions related to idiosyncratic volatility (IVOL), an im-

portant limit to arbitrage. First, anomalies with greater IVOL exhibit higher anomaly returns.

1

We acknowledge that, without knowing the true asset pricing model, we cannot completely rule out the possibility of time‐varying risk premium.

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