Seasonality

In this blog I’ll examine the old “sell in May and go away” seasonal pattern associated with risky assets. It’s timely to consider this pattern since the markets are now entering the seasonally weak period. Furthermore, stock market performance has been relatively weak in a number of recent “strong periods,” such as in January 2016, November 2015 through January 2016, and November 2015 through April 2016, which often provides a foreboding tell of additional weakness during the traditional seasonal weak period of May through October.

Seasonality as a trading edge is also worth considering because trend following has become very trendy these days, with billions of dollars flowing into this discipline every year via managed futures funds. The problem with these flows is that the effectiveness of trend following diminishes as more assets are devoted to the discipline, since trend following is naturally capacity constrained due to high turnover (>200%) and the liquid demanding nature of trading. It seems that trend following is crowded.

At this point in time, it may be interesting to examine other market timing signals as an alternative way to add and reduce risk exposure. One such approach is seasonality, which is probably underutilized by the asset class trading community and thus might be more effective than trend following over the near term.

The seasonal pattern has been well known for decades – the stock market’s best period is from November through April, and its poor-performing period is from May to October. This is not the case every year, but on average this seasonal pattern has held up really well with stock markets around the world for decades.

Academics call this pattern the Halloween effect since the buy signal is generated by buying at the close on October 31 every year and the sell signal is on every April 30. What’s amazing is that seasonality has not been arbitraged away, even though the cost of implementing a seasonal trading system has been low since the 1980s. The old adage of “sell in May and go away” still works!

I first read about this pattern in a variety of market timing books written in the 1980s, such as those by Zweig¹, Fosback², and Hirsch ³, which were all published in a variety of editions in the 1980s. The 1986 edition of Hirsch’s annual Stock Trader’s Almanac was the first to mention the seasonal pattern in the markets.⁴ Ben Jacobson and Cherry Zhang have studied this pattern in much more detail, including with UK stock market data going back over 300 years. ^5,6 Apparently, the sell-in-May adage was well known as far back as 1935 in the UK.

Table 1 shows the S&P 500 returns split into the two seasonal half-years (strong and weak) for three different time periods. The first time period is from 1954 to 2015, covering over 60 years of data. The second period covers 1984 to 2015, when the seasonality pattern was already well known and tradable with S&P 500 futures and ETFs with little cost. This is the time period where the effect should have been arbitraged away. The last time period, from 2003 to 2015, represents the most recent years when hedge funds came to dominate market dynamics, and again any approach to adding value trading the markets should have been arbitraged away. Table 1 also shows the S&P 500 minus T-bill returns for both seasonal half-years.

For all time periods, the strong seasonal half-year performed much better than the weak half-year. When factoring in T-bill returns, the S&P 500 barely beat the risk-free rate during the average weak period. S&P 500 returns during the weak months were a little better in the most recent time period, but the seasonal effect is still seen. Also, the start year of 2003 was taken somewhat arbitrarily; if I’d chosen 2000 instead, the effect of the 2000 to 2002 bear market would have produced much stronger results in the most recent period.

Table 1. S&P 500 performance during the strong and weak seasonal half-year periods

Figure 1 below shows the impact of the seasonality timing model on the S&P 500 from 1984 to 2015, a time period where such a model could actually be implemented with minimal transaction costs. The seasonality model would have produced similar returns ton the S&P 500, at quite a bit lower risk and a better Sharpe ratio. Figure 1 also shows the improvement made by adding seasonality to trend-following models (using monthly data): the six-month moving average and nine-month moving average. In the latter case, the S&P 500 was held when both seasonality and the trend-following model had buy signals.

Figure 1: Return-Risk chart for the S&P 500 and two trend-following models combined with seasonality (using standard deviation as the risk measure)

Figure 2 shows the same chart, but using worst drawdown as the risk measure.

Figure 2: Return-Risk chart for the S&P 500 and two trend-following models combined with seasonality (using worst drawdown as the risk measure)

Robustness Tests

So is seasonality a true trading edge? Is it worth betting on, especially considering it’s so well known and easy to implement? To answer this question, we start by evaluating seasonality with the following robustness tests:

1. Does seasonality add value during essentially all time periods?
2. Is the seasonality effect robust to the parameters used in the trading rules?
3. Does seasonality work for many different asset classes and securities?
4. Is there a rational explanation for why the effect exists?
5. Is there a rational explanation for why the effect is not arbitraged away?

A trading strategy that can pass these robustness tests has a good chance of being a truly exploitable edge, rather than another case of data mining.

The sell-in-May seasonality effect generally passes robustness tests 1-3. Academic studies have shown the effect to work in stock markets around the world spanning decades, with many markets dating back to the 1800s.⁵ Further studies show that the sell-in-May effect applies to all risky assets and risk premiums, such as the size and value premiums, credit risk premium, currency carry and the equity volatility risk premium.⁷ The bond market’s term premium has the opposite pattern, which makes sense due to the risk-off nature associated with treasuries.⁷

Table 1 above provides one example of the results being robust to the time period. Examining the effect with non-overlapping periods also shows the seasonality effect to be independent of time period. While not shown in this blog, varying the start and stop months of the seasonal pattern does not change the pattern significantly.

The problem lies with robustness tests 4 and 5. While there are many explanations for why the effect exists, most are unconvincing, and the more viable explanations are speculative. In addition, since such a strategy is easy to implement (at least for small traders and funds), the effect should have been marginalized long ago.

Explanations for the Seasonality Effect

Developing a rationale for trading edges and risk premiums is relatively easy, especially when employing a behavioral explanation. The problem with behavioral explanations is they can be arbitraged away over time when more and more market participants attempt to exploit the effect. The seasonality effect has a number of explanations that are all behavioral. Here is a summary of explanations.

Investor mood shifts

Various authors^1,2,5,6 have suggested people are happier and more optimistic around the year-end holiday season associated with Thanksgiving and Christmas, and that people tend to be less happy when summer vacations end.

While I agree people tend to gamble more when happy, it’s hard to see how this effect can push stocks higher in the February to April time frame when holiday happiness has waned and the dreary winter months settle in. I’m also not convinced investor moods become gloomy at the end of summer. Markets in the Southern Hemisphere appear to follow the same sell-in-May pattern, which doesn’t make sense if the end of the summer was the cause of this effect.

Seasonal variation of equity risk premium

Perhaps the likeliness of a stock market crash increases for some reason in the fall of each year. Certainly some of the stock market’s biggest crashes have occurred in October. The explanation is that investors adjust stock prices lower in the summer months to account for this possibility.

Table 2 below shows a month-by-month count of the worst 43 months of U.S. stock market performance since 1871, using the data from Robert Shiller’s website.⁸ These months represent the worst 2.5% out of the 1,742 total months during this time period. The third column below shows the fraction of all worst months – for example, 23.3% of all worst months occurred in October.

Table 2: Monthly distribution of the 2.5% worst performing months since 1871.

Table 2 clearly shows that the worst stock market month is October, and the worst two-month combo is September and October together. More generally, 70% of the worst months occur during the weak period of May to October. This is not a great explanation for the seasonal effect.

Fund flows

There’s a seasonal pattern to fund flows that’s consistent with the sell-in-May pattern. I can speculate that flows into risky assets are high at the beginning of the year due to the free cash available from year-end bonuses, and due to IRA contributions. There can also be flows associated with tax-loss selling and year-end window dressing.

Figure 3, from Ned Davis Research, shows the seasonality effect with mutual fund flows since 1978. Notice that the strongest four months are January to April. In addition, IPO activity generally shuts down in December and January, which may reduce the supply of stock for sale during that time period.

Another fund-flows related phenomenon is that traders and hedge funds anticipate this cycle and begin buying risky assets in November and December. This behavior is enhanced by the tournament behavior of fund managers near the end of the year.^9,10 In the 1980s and 1990s, this activity was played among mutual fund managers trying to land at the top of the performance tables for the year. The payoff with future inflows was huge during that time, especially in the late 1990s, when new funds often ramped from $50 million to over a billion dollars in assets after winning the previous year’s performance competition.

Portfolio managers will ultimately conclude that the best way to win such a competition near year-end is to put on more risk by adding equity exposure and buying high beta or high-momentum stocks. Academic evidence supports this view. ^9,10 Funds that are close to beating a benchmark will also be motivated to increase risk exposure near year-end.

Figure 3: Seasonality of fund flows (from Ned Davis Research).

Over the last 10 to 15 years, hedge funds have taken over this activity, where beating a previous year’s high water mark can make the difference of being in business the following year, or not. As long as there are funds competing with each other, adding risk will be the logical year-end approach to meeting performance goals among a large segment of professional market participants.

Late-year flows from managers competing with each other, followed by cash inflows during the first four months of the year, is a reasonable explanation for the seasonality of S&P 500 performance. As discussed in a previous blog, the effect of fund flows is hard to arbitrage away if it represents price-insensitive buying, which appears to be the case here. Perhaps, as more market participants have incorporated these thoughts into their decision making, the seasonal cycle becomes self-fulfilling.

Seasonal optimism cycle

Doeswijk offers another explanation that’s very interesting. The idea is that investors, market strategists, fund managers and pretty much all humans frame their thinking in calendar years rather than rolling 12-month periods.¹¹ By thinking in calendar years, market participants tend to be systematically over-optimistic at the beginning of each calendar year.

By mid-year, reality sets in, and the probability of downgrades to future expectations increases. Asset prices react to changes in expectations, and since on average there are more downgrades during the summer and fall, we can expect weaker returns during that time period. This thinking is consistent with Table 2 showing the distribution of worst performing months since 1871. We can expect the largest downward shift in expectations to occur during the summer-fall time period. Toward year-end, optimism about the upcoming year sets in, and the cycle repeats itself.

Figure 4 shows a chart of the average monthly change in the 12-month rolling expected earnings growth rate of the MSCI World index from 1988 to 2003.¹¹ This chart clearly shows that marginal changes in earnings expectations have a seasonal pattern that is consistent with the stock market seasonality effect.

At the corporate finance level, it’s easy to imagine this effect in action. As the calendar year ends, goals are established regarding sales and profits for the following year. Corporate chiefs are likely to set goals to be stretchy or ambitious to motivate employees. These numbers are ultimately reported to analysts, which feed into earnings expectations, and into stock prices. Later in the year, when these goals look ever more ambitious, expectations are downgraded.

I think this view can be generalized beyond optimism around earnings to humans being systematically over-optimistic as the year begins. Humans naturally want a fresh start in January as evidenced by the tradition of New Year’s resolutions. This may explain the seasonality effect a hundred years ago when there were no analysts issuing earnings estimates or funds competing for assets.

In summary, the seasonality effect is best explained by fund flows and the general seasonal optimism cycle. We have certainly not proven that these are the causes, yet part of the art of asset class trading is to exploit effects that have not been accepted by academics and large institutional investors. Just because an effect can’t be proven doesn’t mean that it doesn’t exist. Betting on unproven trading edges can be a worthwhile pursuit since it will naturally be much less crowded.

Figure 4: The average % monthly change in the 12-month rolling forward expected earnings growth rate for the MSCI World index from 1988 to 2003.¹¹

Why Hasn’t Seasonality Been Arbitraged Away?

Does the lack of a clear explanation for seasonality keep away competition? Perhaps one competitive edge associated with seasonality is that no professional manager can advertise using this approach to add value. The pattern doesn’t work every year and can underperform by a wide margin. As Table 1 shows, the weak period still provided gains in 69% of years since 1954.

From a career risk point of view, few professional managers can make such a bet, at least in a size large enough to make a difference in performance. Furthermore, large money managers may have difficulty buying and selling a large amount of exposure twice a year without transaction costs eroding the benefits.

For these reasons, I don’t know of any big-money hedge funds, trading desks or mutual funds exploiting the seasonal pattern. The lack of a good explanation for the effect, the low win % of holding cash during the weak period, and high transaction costs may provide barriers-to-entry preventing large funds from exploiting seasonality. This may be why seasonality continues to work.

The lack of “seasonality arbitrage activity” thus allows the little guys to exploit seasonality, while the big guys miss out. When someone designs an ETF to exploit seasonality, and it becomes popular, then we’ll have to worry about future effectiveness.

Seasonal Tell

We are always looking for “market tells” as a trading edge. A tell is an instance where the market does something that is out of the ordinary, which under certain conditions can provide an early warning of a future price move. I will write a future blog on this very effective way to find a trading edge.

One criteria for considering a market behavior as a tell is that the “usual action” must occur at least 75-80% of the time. Then when the 20-25% of the time that the unusual occurs, we can examine this behavior to determine if there’s a potential trading edge associated with it. If the usual behavior occurs just 55-60% of the time, then it’s much harder to distinguish a market tell from just random price action.

For now, let’s consider a possible tell that seasonality can provide. The tell is to watch the stock market during the seasonally strong period, which as Table 1 shows, is positive over 80% of the time. In those periods where the seasonal strong period is weak (a six-month return that is less than 0%), we can expect a much worse subsequent weak period.

Table 3 shows a summary of the results using this seasonal tell for two time periods: 1954 to 2015, and 1984 to 2015. From 1954 to 2015, the weak period win % falls from 69% to 42%, and from 61% to 33%, compared to T-bills when the seasonal tell is triggered. In addition, average returns during the weak period are significantly less when the seasonal tell is triggered – falling from 2.82% to -2.55%, and to -5.19% when compared to T-bills.

In the more recent period, during a time when seasonality was well known among market participants and implementable with S&P 500 futures and ETFs, we see a similar effect when the seasonal tell is triggered. The weak period win % drops to 40% from 75% and the average return falls from 3.01% to -4.78%. Interestingly, for both periods, the standard deviation of returns jumps dramatically during these tell periods.

How could this seasonal tell be used? For those portfolio managers looking for certain moments in time to implement seasonality, rather than doing it every year, waiting for this tell could be useful. The seasonal tell could serve as one of a slew of indicators used by investment strategists to determine when to lighten up on risky assets. For small traders, the tell can be used to adjust trading to a negative bias when the tell is triggered.

Table 3: Weak period performance when previous strong period returns are less than 0%.

Additional value can be added by ignoring seasonality when expectations are already so low that the potential for further downgrades seems unlikely; and if anything, upgrades are more likely. One such point in time is after a severe bear market, when stocks have already lost greater than 35%+ of their value. We can plan to ignore the upcoming weak period, especially if stocks have showed signs of bottoming because future expected returns are much higher now, the market is under-owned, and perhaps there are compelling long-term values among a variety of risky asset classes, sectors and individual securities.

Summary

The seasonality of equity returns appears to be an exploitable trading edge. All risky assets and risk premiums appear to follow the seasonal pattern of strong returns from November to April, and weak returns from May to October. Seasonal fund flows and the seasonal optimism cycle appear to be reasonable explanations for why this effect is still strong and exploitable. These explanations are behaviorally based, and thus are at risk of eventually being arbitraged away.

While the sell-in-May adage has been around for decades, and we usually see the sell-in-May news stories every year around this time, there doesn’t seem to be much big money managed using seasonality. Career risk, inconsistency of results and transaction costs likely keep many arbitrageurs from exploiting this effect. If the seasonality timing strategy became popular among institutions, large money managers and hedge funds, then it would be time to stop using this pattern to make investment decisions. In addition, if new products (ETFs) are developed to invest with the seasonal pattern, then the seasonal edge would also be at risk of going away, much like what happened with momentum over the last ten years.

 

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References

1. Zweig, M. “Winning on Wall Street”, 1986.
2. Fosback, N.G., “Stock Market Logic: a Sophisticated Approach to Profits on Wall Street”, 1985.
3. Hirsch, J.A., “Stock Trader’s Almanac 2015”, 2015. Yearly almanac originally created by Yale Hirsch.
4. Maberly, E.D. and Pierce, R.M., “Stock Market Efficiency Withstands another Challenge: Solving the “Sell in May/Buy after Halloween” Puzzle”, Econ Journal Watch, Vol. 1, No. 1, April 2004, pp. 29-46.
5. Jacobsen, B. and Zhang, C.Y., “The Halloween indicator, “Sell in May and go Away”: an even bigger puzzle”, Working Paper, October 2014.
6. Jacobson, B. and Zhang, C.Y., “Are Monthly Seasonals Real? A Three Century Perspective”, Review of Finance, Vol. 17, No. 5, 2013, pp 1743-1785.
7. Andrade, S.C., Chhaochharia, V., Fuerst, M.E., “”Sell in May and Go Away” Just Won’t Go Away”, Working Paper, July 2012.
8. Home page of Robert J. Shiller, Sterling Professor of Economics, Yale University. http://www.econ.yale.edu/~shiller/data.htm.
9. Zhan, G. “The Tournament Behavior in Hedge Funds: A Reexamination”, Working Paper, October 2010.
10. Taylor, J.D., “A Role for the Theory of Tournaments in Studies of Mutual Fund Behavior”, Working Paper, February 2000.
11. Doeswijk, R.Q., “The Optimism Cycle: Sell in May”, Working Paper, November 2005.

 

Disclosure for Backtested Studies

1. Trend-following models applied to S&P 500 total return index with monthly data.
2. No transaction fees applied to either the seasonality trading model or the trend-following models.
3. Trades initiated at the close of the month using the month-end buy/sell signal.
4. T-bill data from http://www.federalreserve.gov/releases/H15/data.htm. Used three-month T-bill (secondary market) daily yield to calculate cash returns.

 

Disclosure

The content contained within this blog reflects the personal views and opinions of Dennis Tilley, and not necessarily those of Merriman Wealth Management, LLC. This website is for educational and/or entertainment purposes only. Use this information at your own risk, and the content should not be considered legal, tax or investment advice. The views contained in this blog may change at any time without notice, and may be inappropriate for an individual’s investment portfolio. There is no guarantee that securities and/or the techniques mentioned in this blog will make money or enhance risk-adjusted returns. The information contained in this blog may use views, estimates, assumptions, facts and information from other sources that are believed to be accurate and reliable as of the date of each blog entry. The content provided within this blog is the property of Dennis Tilley & Merriman Wealth Management, LLC (“Merriman”). For more details, see the Important Disclosure.