Return Seasonalities

• DOI: http://doi.org/10.1111/jofi.12398
• Published date: 01 August 2016
• Date: 01 August 2016

THE JOURNAL OF FINANCE •VOL. LXXI, NO. 4 •AUGUST 2016

Return Seasonalities

MATTI KELOHARJU, JUHANI T. LINNAINMAA, and PETER NYBERG∗

ABSTRACT

A strategy that selects stocks based on their historical same-calendar-month returns

earns an average return of 13% per year. Wedocument similar return seasonalities in

anomalies, commodities, and international stock market indices, as well as at the daily

frequency.The seasonalities overwhelm unconditional differences in expected returns.

The correlations between different seasonality strategies are modest, suggesting that

they emanate from different systematic factors. Our results suggest that seasonalities

are not a distinct class of anomalies that requires an explanation of its own, but rather

that they are intertwined with other return anomalies through shared systematic

factors.

FIGURE 1PLOTS THE AVERAGE COEFFICIENTS from cross-sectional regressions of

monthly stock returns against one-month returns of the same stock at differ-

ent lags. What is remarkable about this plot, which is an updated version of

that in Heston and Sadka (2008), is not the momentum up to the one-year

mark or the long-term reversals that follow, but rather the positive peaks

that disrupt the long-term reversals at every annual lag. This seasonal pat-

tern, documented for many countries,1emerges in pooled regressions with

stock fixed effects but disappears when the regressions include stock-calendar

∗Matti Keloharju is with Aalto University School of Business, CEPR, and IFN. Juhani T. Lin-

nainmaa is with the University of Southern California Marshall School of Business and NBER.

Peter Nyberg is with the Aalto University School of Business. We thank John Cochrane, Mark

Grinblatt, Chris Hansen, Steven Heston (discussant), Maria Kasch (discussant), Jon Lewellen

(discussant), Anders L¨

oflund, Toby Moskowitz, Stefan Nagel, ˇ

Luboˇ

sP

´

astor, Tapio Pekkala, Ruy

Ribeiro, Ken Singleton (Editor), Rob Stambaugh, an Associate Editor, and two anonymous ref-

erees for insights that benefited this paper; seminar participants at Aalto University, Chinese

University of Hong Kong, City University of Hong Kong, Deakin University, Hong Kong Poly-

technic University, Hong Kong University, INSEAD, Lancaster University, LaTrobe University,

Luxemburg School of Finance, Maastricht University, Monash University, Nanyang University of

Technology, National University of Singapore, Singapore Management University, University of

Arizona, University of Chicago, University of Houston, University of Illinois at Chicago, University

of Melbourne, University of New South Wales, University of Sydney, and University of Technology

in Sydney, as well as conference participants at 2013 FSU SunTrust Beach Conference, Financial

Research Association 2013 meetings, 2014 European Finance Association Meetings, Inquire UK

2015 Conference, and AQR Insight AwardCompetition for valuable comments; and Yongning Wang

for invaluable research assistance. Earlier versions of this paper were circulated under the titles

“Common Factors in Stock Market Seasonalities” and “The Sum of All Seasonalities.” The authors

did not receive financial support for this research, and have no financial interests in its outcomes.

1See Heston and Sadka (2010).

DOI: 10.1111/jofi.12398

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1558 The Journal of Finance R

Lag, months

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bt

12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240

−0.01

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Figure 1. Seasonalities in individual stock returns. This figure plots slope coefficients from

univariate Fama and MacBeth (1973) regressions of month treturns against month t−kreturns,

ri,t=at+btri,t−k+ei,t, with kranging from 1 to 240 months. The circles denote estimates at

annual lags. The regressions use monthly data from January 1963 through December 2011 for

NYSE, Amex, and NASDAQ stocks.

month fixed effects. Thus, the estimates in Figure 1do not mean that stocks

“repeat” shocks from the past, but instead suggest that expected returns vary

from month to month. A strategy that chooses stocks based on their historical

same-calendar-month returns earns an average return of 13% per year between

1963 and 2011.

Return seasonalities are not confined to individual stocks or to the monthly

frequency.We show that seasonality strategies that trade well-diversified port-

folios formed by characteristics such as size and industry are about as profitable

as those that trade individual stocks. Seasonalities also exist in the returns of

commodities and country portfolios2and at the daily frequency. Moreover, we

show that the returns on most anomalies—accruals, equity issuances, and

others—exhibit tremendous seasonal variation. For instance, a metastrategy

that takes long and short positions on 15 anomalies based on their historical

same-calendar-month premiums earns an average return of 1.88% per month

(t-value =6.43), while an alternative strategy that selects anomalies based on

their other-calendar-month premiums earns a slightly negative return! The lat-

ter result suggests that knowing how well an anomaly has performed in other

calendar months is uninformative about how it will perform in the cross sec-

tion of anomalies this month. Seasonal variation in expected returns for these

anomalies thus completely swamps cross-sectional differences in unconditional

expected returns.

2Heston and Sadka (2010) document significant seasonalities within 14 international stock

markets. Our analysis differs from theirs in that we measure seasonalities in the cross section of

country indexes, that is, we test whether a stock market in a country that typically performs well

in a particular month relative to the other countries is more likely to do so in the future.

Return Seasonalities 1559

Although both individual stocks and factors exhibit return seasonalities, at

first glance, the connection between the two realms seems surprisingly weak in

the data. Heston and Sadka (2008) consider the possibility that seasonalities

reflect systematic risks but find that they survive tests that separately control

for firm size, industry, exposures to the Fama and French (1993) factors, and

calendar month. At the same time, they find that return seasonalities are

not driven by seasonalities in certain firm-specific events such as earnings

announcements and dividends.

We show that the seeming disconnect between seasonalities in individual

stock returns and those in factor premiums is due to the fact that none of

the factors alone is responsible for the seasonal patterns in individual stocks.

Individual stocks aggregate seasonalities across the various factors. To see this,

consider the seasonality in stock returns as a function of firm size. Small stocks

tend to outperform large stocks in January,so firms’ historical January returns

are noisy signals of their size. A sort of stocks into portfolios by their past

January returns thus predicts variation in future January returns because

it correlates with firm size. The same intuition applies if the seasonalities

originate from many factors. A sort on past returns picks up all seasonalities

no matter their origin. A regression of returns on past same-calendar-month

returns is equivalent to a regression of returns on a noisy combination of

attributes associated with return seasonalities.

Two simple empirical tests suggest that the seasonalities in monthly

U.S. stock returns originate in large part from systematic factors. First, the

variance of a strategy that trades seasonalities is five times higher than what

it would be if it took on just idiosyncratic risk. Second, seasonalities are strongly

present in returns on well-diversified portfolios. We estimate that at least one-

half of the seasonalities in monthly U.S. stock returns derive from systematic

factors associated with salient firm characteristics such as size, dividend-to-

price, and industry. Moreover, the seasonalities that remain after controlling

for these factors continue to be exposed to other systematic risks. The promi-

nence of systematic factors suggests that seasonal strategies have to remain

exposed to systematic risk—attempts to hedge those risks would likely reduce

(or even eliminate) the seasonalities as well.

The return seasonalities are also remarkably pervasive. Whereas many

anomalies falter in some corners of the market, seasonalities permeate the

entire cross section of U.S. stock returns, varying little from one set of stocks

to another. Moreover, unlike every anomaly studied by Stambaugh, Yu, and

Yua n (2012), return seasonalities are approximately equally strong in periods

of high and low sentiment. In spite of this, different seasonality strategies

are at best weakly correlated with each other. Within U.S. equities, for exam-

ple, the correlation between strategies trading seasonalities in small stocks

and high-dividend-yield stocks is 0.17. The correlations are negligible across

asset classes: the seasonalities in country index and commodity returns, for

example, are unrelated to those in U.S. equities. Similarly, a strategy that

trades daily seasonalities is uncorrelated with a strategy that trades monthly

seasonalities.