Return Seasonalities

Return Seasonalities – A Stock Selection Strategy

Matti Keloharju
Aalto University – School of Business; Research Institute of Industrial Economics (IFN); Centre for Economic Policy Research (CEPR)

Juhani T. Linnainmaa
University of Chicago – Booth School of Business; National Bureau of Economic Research (NBER)

Peter M. Nyberg
Aalto University

July 6, 2015

Journal of Finance, Forthcoming

Fama-Miller Working Paper

Chicago Booth Research Paper No. 13-15

Abstract:

A strategy that selects stocks based on their historical same-calendar-month returns earns an average return of 13% per year. We document similar return seasonalities in anomalies, commodities, international stock market indices, and 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 – rather, they are intertwined with other return anomalies through shared systematic factors. A theory that is able to explain the risks behind any systematic factor is thus likely able to explain a part of the seasonalities.

Return Seasonalities: A Stock Selection Strategy – Introduction

Figure 1 plots the average coefficients from cross-sectional regressions of monthly stock returns against one-month returns of the same stock at different 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 the positive peaks that disrupt the long-term reversals at every annual lag. This seasonal pattern, documented for many countries1, emerges in pooled regressions with stock fixed effects, but it disappears when the regressions include stock-calendar month fixed effects. The estimates in Figure 1 thus do not mean that stocks repeat” shocks from the past but that expected returns vary from calendar 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 monthly frequency. We show that seasonality strategies that trade well-diversified portfolios 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 portfolios2 and at the daily frequency. Moreover, we show that the returns on most anomalies-accruals, equity issuances, and others-exhibit tremendous seasonal variation. A meta-strategy 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); an alternative strategy that selects anomalies based on their other-calendar-month premiums earns a slightly negative return! That is, knowing how well an anomaly has performed in other calendar months is uninformative about how it will perform in the cross section of anomalies this month. Seasonal variation in expected returns for these anomalies thus completely swamps cross-sectional differences in unconditional expected returns.

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 control, one at the time, 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 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 sizes. 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 what their origins. 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. 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, we show that 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 prominence 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.