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We’re not inclined to automatically buy in to perceived wisdom, and you probably aren’t either; but that shouldn’t stop either of us from at least exploring market proverbs to see if there a kernel of truth within them.  With that, several years ago, we found an article that took a stab at return seasonality[1], specifically where stock market performance seems to be better in the winter than in the summer.[2]

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In the spirit of Edward Tufte, the author created an excellent infographic describing the seasonality of stock market returns.  We’ve pasted it in to the right.  It highlights (in dark red) the best six months in any given year – but instead of simply looking at one single year, it analyses the average returns in any given month for the next twenty years.  The conclusions one can immediately draw from the table struck us as almost too good to be true.[3]

Over a ~70 year period (1940-2011), the consistency of returns by month appeared remarkable.  Essentially, the best six months of the year seem to almost always include Jan-March and Nov-Dec, with April and October fighting over the final spot.  The six worst months seem to reliably begin in May (sometimes April) and run through October (sometimes September).  So, perhaps there was some truth to the old adage “sell in May, and go away”?

Curiously, the creator of the table also added a comment “the ‘best’ six month period was chosen based on volatility-adjusted (not absolute) dividend adjusted S&P 500 returns”.  This made us wonder if he perhaps massaged the data to tell his story (perhaps using Sharpe ratios as the proxy?). 

So, wondering if that clouded the analysis, we were curious enough to pull down some data ourselves and play with it.  We pulled an end-of month total return series (thus, including dividends) on the S&P 500 since December of 1939.  Before presenting similar tables of our data, there is one broad point that is worth making.  Since 1940 – which was 78 years ago – every single month has shown an average positive return. 

However, there has been a significant difference in “performance” by each month (if we can call it that) which may or may not be random.  We’re not going to prove the non-randomness of this here, but plenty of papers out there have made this attempt.  In any event, on to our observations: 

 

The average total returns by month of the SPX from December of 1939 through January of 2018 are below:

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Since all of the months are winners, the adage “sell in May and go away” seems like a misnomer at first blush.  But let’s explore it a little bit further.  A great deal of empirical work has been done on seasonality and return anomalies, including some suggesting that the “Sell in May” or “Halloween Effect” has been persistent not just in the US, but in the UK – and for over 300 years.[4]  However, we have not seen any similar infographics accompanying this kind of work – and we think they are fascinating, and perhaps illuminating.  When we rank the months above by colouring the top six performers in green, and inserting the monthly ranking – some seasonality does indeed start to emerge:

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And if we take the returns five years at a time (so, from 1940-1944, 1941-1945….2013-2017):

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And with ten year data:

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And with twenty year data:

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So, a few observations: 

  •  At least in the period from 1940 through 2017, the gains from buying in late-September and selling in late April have exceeded those from May to September.
  • The difference is stark.  In the five months from May to September, the average gain has been 2.7%.  In the seven months from October to April, the average gain has been 9.4%.
  • Cumulatively, over the past 78 years, the S&P 500 has seen May to September gains of 455%.  The October to April period has experienced gains of over 70,000%.

To see how the seasonality really emerges as we go from shorter to longer time horizons, the tables on the following page emulate the infographic from the website.  Our results use actual returns rather than Sharpe ratios (or other volatility-adjusted metrics), and we haven’t done anything special with any factors.   In any event, however, we think it is fair to conclude (as many empirical studies already have) that there may be something to this “selling in May and going away” thing, especially over very long time horizons. 

Not practical, perhaps, but interesting.

Seasonality of Stock Market Returns (S&P 500, Including Dividends):

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Monthly, Average, and Cumulative Data:

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[1] http://marketsci.wordpress.com/2012/05/03/sell-in-may-debunked/

[2] The northern hemisphere winter, that is.  Someone else can compare southern and northern hemisphere returns.

[3] The author implicitly thought the data was too good to be true as well, as it was part of a larger article attempting to debunk the seasonality implicit in the  “Sell in May and go away” trading adage.   As part of this article, he showed an impressive cumulative outperformance of a trading strategy long from November to April and then neutral from May to October – but suggested that it was backward looking – and that if any investor had simply been long the six best months from over the previous ten or twenty years to that date – there was no outperformance as you “walked the test forward”.  Interestingly, however, when he based the investment decision on thirty years of data instead of ten or twenty, the seasonality reared itself again

[4] Are Monthly Seasonals Real?  A Three Country Perspective.  Jacobsen Yang (2010).  Abstract:  Over 300 years of UK stock returns reveal that well-known monthly seasonals are sample specific. For instance, the January effect only emerges around 1830, which coincides with Christmas becoming a public holiday. Most months have had their 50 years of fame, showing the importance of long time series to safeguard against sample selection bias, noise, and data snooping. Only- yet undocumented- monthly July and October effects do persist over three centuries, as does the half yearly Halloween, or Sell-in-May effect. Winter returns – November through April- are consistently higher than (negative) summer returns, indicating predictably negative risk premia. A Sell-in-May trading strategy beats the market more than 80 % of the time over 5 year horizons.



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