Seasonality in markets: history, evidence and method

What seasonality means

Seasonality is the tendency of a market to behave in a recurring way at the same point in a calendar cycle: a time of day, day of the week, turn of the month, month of the year, a festival, a harvest or an election. It is one of the oldest ideas in markets and one of the most heavily tested.

It is different from two neighbouring ideas. Cycles, such as business or credit cycles, recur but with an irregular length, so they cannot be pinned to a date. Trends and momentum describe the direction of recent prices, not the position in the calendar.

Durable seasonal patterns usually have a plausible cause. Researchers group the causes into four families.

A pattern with a clear driver from this table deserves more attention than one that only appears in a back-test.

A short history of the seasonal factor

The idea travelled through four stages, and the tools used to measure it came from outside markets.

Two ideas from the statistical lineage matter to anyone reading a seasonal chart. Seasonality can evolve: official methods let the seasonal factor drift over time, which is why a 5-year and a 15-year seasonal line can disagree. Outliers distort averages: official methods down-weight extreme values, and a reader should be just as wary of one extreme year.

Every seasonal heatmap, including the one in Sezon, descends from the Buys Ballot table of 1847: years down one side, calendar periods across the other.

What the research says

Academic finance turned calendar folklore into testable patterns, then tested the tests. The landmark studies, oldest first:

• 1940s to 1980s: Wachtel (1942) on a January effect; Cross (1973) and French (1980) on weekend and Monday effects; Rozeff and Kinney (1976) and Keim (1983) on January and company size; Ariel (1987) on the turn of the month.
• 1988 to 1990: Lakonishok and Smidt review about 90 years of daily Dow data for patterns around the turn of the week, month and year, and Ariel (1990) examines the days before holidays.
• 2001: Sullivan, Timmermann and White show that calendar rules which look significant one at a time lose significance once the whole set of rules that was searched is counted.
• 2002 to 2003: Bouman and Jacobsen study the “Halloween” or “Sell in May” pattern across many countries, and Kamstra, Kramer and Levi link returns to hours of daylight.
• 2008 to 2016: Heston and Sadka, then Keloharju, Linnainmaa and Nyberg, find that assets which did relatively well in a calendar month tend to do relatively well in the same month in later years, across stocks, commodities and country indices.
• 2016: McLean and Pontiff study 97 published return predictors and find they weakened out of sample and weakened further after publication.
• 2019: Baur and co-authors study Bitcoin across seven exchanges and find volume patterns but no consistent return pattern.
• 2021: Keloharju, Linnainmaa and Nyberg find that seasonal patterns are offset by seasonal reversals in other months. Baltussen, Swinkels and Van Vliet test seasonality across 217 years; see our summary.

The arc of the research. Discovery in the 1940s to 1990s, stress-testing for data mining in the 2000s, then a more careful view in which seasonality shows up mainly as a relative pattern across assets and calendar windows, rather than a simple rule about one month.

Seasonality across asset classes

How strong a seasonal pattern is depends on how directly the calendar drives supply, demand or money flows. Physical commodities sit at the strong end, and liquid, globally traded financial assets at the weaker end.

Seasonality in Indian markets

The Indian evidence is real but inconsistent. Studies agree that calendar patterns exist, disagree on which ones persist, and often find patterns that differ from the US template. India’s April to March fiscal year, its festival calendar and its monsoon economy give it a seasonal fingerprint of its own.

• Index studies: work on the Sensex and Nifty reports a range of month effects. Some studies find a January effect, others do not. One study finds that earlier seasonality may be an artefact of extreme observations and does not persist once robust methods are used.
• Turn of the month: a thesis covering the Nifty, CNX 500, Sensex and BSE 500 reports that the first half of the month beats the middle of the month, with no significant holiday effect.
• Festival and lunar calendar: a 2023 IIM Bangalore study looks at Diwali Muhurat trading and new-moon days.

India-specific calendar drivers worth knowing about: Diwali and Muhurat trading, a one-hour ceremonial session on Diwali; the Union Budget on 1 February; fiscal year-end in March and the quarterly advance-tax dates; the monsoon from June to September, to which some sectors are sensitive; and global flows around US year-end and quarter-ends.

Test Indian seasonal patterns on Indian data and on recent windows. Rules born in the US, such as the January effect, do not transfer automatically.

How seasonality is measured

Every seasonal statistic answers one question: across N past years, how did this market behave in this calendar window compared with the rest of the time? Four numbers do most of the work.

• Average seasonal return: the mean result of the window across the N years.
• Median seasonal return: less sensitive to one crash or spike year. Compare it with the mean to spot an average driven by an outlier.
• Win rate (hit ratio): the share of years in which the window was positive, or beat a benchmark.
• Significance (t-statistic): the average divided by its standard error, which is the spread across years divided by the square root of N. It shows whether the average differs from zero by more than chance would explain.

How good is a win rate, really?

With 15 years of history, a pure coin flip gives 9 or more winning years about 30% of the time, and 10 or more about 15% of the time. The table shows how often chance alone reaches each win rate.

Around 12 winning years out of 15 is where luck becomes unlikely for one window. But a scan across hundreds of instruments and windows will turn up some 12-of-15 results by chance alone. That is why Sezon also shows a multiple-testing adjusted q-value, and checks earlier years separately.

Building a seasonal chart

1. Collect daily closes for N years and measure each year from its first trading day.
2. Align the years by calendar day, or by trading-day number.
3. Average the aligned paths to get the composite seasonal line.
4. Compare a short composite (for example 5 years) with a long one (15 years or more). Disagreement suggests the pattern is changing.
5. Look at each individual year, not only the average line.

Formal tests researchers use

Critiques and pitfalls

Seasonality is easy to find and hard to rely on. Six problems explain most of the gap.

1. Data mining. Test enough calendar windows and some will look significant by chance. Sullivan, Timmermann and White (2001) showed that rules with impressive individual p-values stop being significant once the whole universe of rules searched is counted.
2. Decay after discovery. McLean and Pontiff (2016) found that published return predictors weakened out of sample and weakened further after publication. Other work on the Dow since 1900 found calendar anomalies peaking in the mid-20th century and fading from the 1980s.
3. Outliers. One crash year, such as 1987, 2008 or 2020, can create or erase a monthly effect. Critics argued the original Halloween result leaned on the 1987 crash and the 1998 LTCM crisis, and later replications disagree on how much.
4. Small samples. Fifteen or twenty observations per window give wide margins of error, and a win rate needs many years to mean much.
5. Costs and timing. Brokerage, taxes and slippage can exceed a small seasonal edge, and published seasonal results often leave them out.
6. Regime change. Tax rules, market hours, settlement cycles, index composition and new participants such as algorithms and ETFs change the causes behind a pattern.

Reading a seasonal pattern with care

Sezon applies this measurement toolkit so that you can see a pattern’s history, and the chance that it is luck, for yourself. These questions are a simple credibility checklist for any seasonal pattern, in Sezon or elsewhere.

• Is there an economic or behavioural reason for the pattern?
• Does it hold in both halves of the sample, and in the most recent 5 to 10 years?
• Does the median agree with the mean, so that no single year is doing the work?
• Does it appear in related markets or assets?
• Would it survive realistic costs and taxes?
• Is the win rate well above what chance would produce for that number of years, even after allowing for how many windows were searched?

This guide is educational. Historical patterns do not guarantee future results, and nothing here is investment advice. Please read the disclaimer, and consider speaking to a SEBI-registered adviser before making investment decisions.

Glossary

Reference library

For readers who want the original sources. Titles are given so that you can find the publisher’s record or an open version.

Books and practitioner sources

• Hirsch, J. A. and Mistal, C. Stock Trader’s Almanac, annual since the 1968 edition. Wiley.
• Haugen, R. and Lakonishok, J. (1988). The Incredible January Effect. Dow Jones-Irwin.
• Moore Research Center, seasonal patterns and strategy reports, since 1989.
• Ladiray, D. and Quenneville, B. (2001). Seasonal Adjustment with the X-11 Method. Springer.
• Ghysels, E. and Osborn, D. (2001). The Econometric Analysis of Seasonal Time Series. Cambridge University Press.

Foundations of seasonal statistics

• Buys Ballot, C.H.D. (1847). Les Changements Périodiques de Température. Utrecht.
• Persons, W. (1919) and Macaulay, F. (1931), early seasonal-index methods.
• Shiskin, J., Young, A. and Musgrave, J. (1967). The X-11 Variant of the Census Method II Seasonal Adjustment Program.
• Cleveland, R. B., Cleveland, W. S., McRae, J. and Terpenning, I. (1990). STL: a seasonal-trend decomposition procedure based on loess. Journal of Official Statistics.
• IMF (2017). Quarterly National Accounts Manual, chapter 7 on seasonal adjustment.

Indian market studies

• Pandey, I. M. (2002). Seasonality in the Indian stock market (Sensex).
• Sasidharan, A. (2009). Does seasonality persist in Indian stock markets? MPRA.
• Kumar, H. and Jawa, R. Efficient market hypothesis and calendar effects: evidence from the Indian stock markets. Business Analyst, SRCC.
• Acharya, P. N. and Kaliyaperumal, S. Capturing the month of the year effect in the Indian stock market using GARCH models.
• Ghalke, A., Kumar, S., Kakani, R. K. and Modekurti, K. (2023). New moon day anomalies of Amavasya and Muhurat trading. IIMB Management Review.

Landmark academic papers

• Wachtel, S. (1942). Certain observations on seasonal movements in stock prices. Journal of Business.
• Cross, F. (1973). The behavior of stock prices on Fridays and Mondays. Financial Analysts Journal.
• Rozeff, M. and Kinney, W. (1976). Capital market seasonality: the case of stock returns. Journal of Financial Economics.
• French, K. (1980). Stock returns and the weekend effect. Journal of Financial Economics.
• Keim, D. (1983). Size-related anomalies and stock return seasonality. Journal of Financial Economics.
• Ariel, R. (1987). A monthly effect in stock returns. Journal of Financial Economics. Ariel, R. (1990). High stock returns before holidays. Journal of Finance.
• Lakonishok, J. and Smidt, S. (1988). Are seasonal anomalies real? A ninety-year perspective. Review of Financial Studies.
• Sullivan, R., Timmermann, A. and White, H. (2001). Dangers of data mining: the case of calendar effects in stock returns. Journal of Econometrics.
• Bouman, S. and Jacobsen, B. (2002). The Halloween indicator, “Sell in May and go away”: another puzzle. American Economic Review.
• Kamstra, M., Kramer, L. and Levi, M. (2003). Winter blues: a SAD stock market cycle. American Economic Review.
• Heston, S. and Sadka, R. (2008). Seasonality in the cross-section of stock returns. Journal of Financial Economics.
• Keloharju, M., Linnainmaa, J. and Nyberg, P. (2016). Return seasonalities. Journal of Finance. And (2021) Are return seasonalities due to risk or mispricing? Journal of Financial Economics.
• McLean, R. D. and Pontiff, J. (2016). Does academic research destroy stock return predictability? Journal of Finance.
• Baur, D., Cahill, D., Godfrey, K. and Liu, Z. (2019). Bitcoin time-of-day, day-of-week and month-of-year effects in returns and trading volume. Finance Research Letters.
• Baltussen, G., Swinkels, L. and Van Vliet, P. (2021). Global factor premiums. Journal of Financial Economics, 142, 1128–1154. doi.org/10.1016/j.jfineco.2021.06.030

We cite these works for reading and do not claim they endorse AI Amplify or Sezon. Findings are summarised in our own words. Please read the originals before relying on any detail.

AI Amplify’s guides are for education and self-directed research. They are not investment advice, a recommendation or an offer. Historical patterns do not predict future results.

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