Most investors have heard the adage "Sell in May and go away" which reflects the common wisdom that markets perform less well during the summer months than during the winter. This anomaly is well described here.
Many widely held beliefs go away, precisely because they're widely held and get priced into the market. I am testing the "sell in May" myth to see how well it has held up in modern markets.
This is also a great case example to illustrate seasonality analysis - something which I believe gets too little attention because it seems "too simple" to work. Not nearly enough MACD-stochastic-crossover-descending triangles involved!
Month of Year
I'll begin by simply plotting the average log-returns by month for SPY since inception in Feb. of 1993. Note that these are total returns - I've used prices adjusted for dividends and splits (source: Yahoo Finance).
Surprisingly - to me, anyway - there is indeed a great deal of truth to this myth. The below chart shows that the months of June thru September are notably worse than the rest of the year.
Most commonly, "Sell in May and go away" is interpreted as May 1st and re-entering the market on November 1st. However, it appears that a more apt interpretation would shorten this period of avoidance to June to September.
The below chart shows just how significant this difference is. Virtually all returns generated in the 25-year period came from the "winter" period of October to May.
But a lot has changed over the past 25 years. Have the quants and vampire squids taken all of this anomaly out of the markets as theory would predict? Below is a chart comparing the groups of months for each year over the 25-year period.
Since this data is a bit noisy, I've also taken a four-year rolling average. Why four year? Some have asserted that this anomaly may be related to presidential election cycles, so a four-year average will neutralize that effect.
Day of Month
Now that we've validated our first pattern, I'd like to test for other calendar patterns, starting with monthly cycle.
It seems pretty clear that there are some parts of the month which, on average, have much better/worse returns. By my eye, it appears that the change of month (from about the 28th to the 5th) as well as the early/mid-part of month (say 11th thru 18th) are the "good" days and the rest are not.
I'll follow the same approach and group the data into the "good days" (28-5, 11-18) and the "other days":
Wowza! If you had purchased at the close on the 27th, sold at the close on the 5th, purchased again at the close of the 10th, and sold on the 18th, your compound annual return would have increased from 8.1% to 11.9% - even though you were only in the market slightly more than half the time.
Again, let's check the time stability:
Clearly, the markets have become somewhat more efficient in the past 7 years, but the anomaly is remarkably persistent and significant. Of course, with the "other days" return becoming positive since 2012, we'd make less money by timing the markets than by sticking with them but would have higher Sharpe ratios, return-on-capital-employed, etc...
Day of Week
Finally, I'd like to test for weekly cycles. The below chart shows that Monday through Wednesday appear to be notably more favorable than Thursday and Friday!
Following the same approach, I'll aggregate the daily average return for these days of week, and then plot this over time (again using a moving average).
On the time dimension, it seems that the day-of-week anomaly was strongest in the 2004-2011 period and has somewhat evaporated in the past 7 years. Given that it seems to be fickle - and that I've never heard of this anomaly - I'm particularly skeptical of this one but would not dismiss it outright.
And yes, from a practical point of view, trading in and out of the markets each week would probably not make sense. Interesting nonetheless.
Why, in a world of low trading costs and arbitrage trading, would these effects persist on the most liquid of stock indices? There are many potentially market-moving factors that occur with daily, weekly, monthly, and annual frequency. Consider the following questions:
- Weekly - Are investors likely to be more upbeat on Fridays than Mondays? Does more bad news get "dumped" late Friday or over the weekend?
- Monthly - Do contributions and redemptions of cash tend to occur at certain times of the month? Is there a net inflow during periods of the month where paychecks are issued, driven by monthly direct deposits to 401(K) plans? Do fund managers engage in end of month "window dressing"? Do futures & options expiry dates, which often occur around the 18th of the month, distort prices?
- Annually - Does investor mood differ by month, (e.g., the Santa Claus rally)? Do tax strategies (tax loss selling, end of year contributions) cause net inflows and outflows? Do summer vacation plans cause institutional investors to "take their foot off the gas" for a few months? Are markets weighed down by uncertainty prior to US elections in early November?
It is impossible to say with certainty which, if any, of these factors are at work. However, observing that patterns do exist and that several factors do repeat on calendar cycles should open our minds to the possibility that seasonality trends are likely to continue.
So, what to do with this information? First, if you don't believe that the anomaly is likely to persist, do nothing. Skepticism is a good null hypothesis.
However, certain of these patterns, especially the month-of-year and the days-of-month, appear relatively robust and persistent, so I believe they merit consideration.
Probably the most sensible way to incorporate this anomaly into your portfolio is as a "nudge factor", meaning one that may nudge you to make a trade you're already inclined to make a bit earlier or later than you otherwise might.
For sake of analysis, however, I've simulated five different market timing strategies for the 25+ year period since SPY inception.
- Buy and Hold - what it says on the tin
- Good months - hold from Oct. 1st to May 31st
- Good days of month - hold from 28th to 5th, 11th to 18th of each month
- Good days of week - hold only on Mon, Tues, and Weds
- Good days of month, good months - hold only 28th-5th, 11th-18th of Oct. thru May
Since each strategy is exposed to markets for very different fractions of time, Sharpe ratio (returns / standard deviation of returns) is a useful way to compare performance.
Further, since the more active strategies could imply lots of trading and commissions, I've adjusted returns by transaction costs using 1 basis point of trade value.
The below table gives the results. Both the "good months" and "good days of month" strategies beat the buy-and-hold handily, even after commissions are included. Somewhat surprisingly, combining both of these individually useful strategies yields a slightly lower Sharpe ratio, though does considerably boost the return on capital deployed.
The winner, in my view, is "good days of month" which increases annualized returns by 3.0% and nearly doubles Sharpe ratio vs. buy and hold.
A practical usage of this pattern may be as follows: become more choosy about stocks, perhaps raise your percentage in cash/cash-like, in late April and become more aggressively allocated in late September. When implementing trades, consider using the 27th and the 10th (or earlier) as "buy days" and the 5th and 18th (or earlier) as "sell days".
As I've already implied elsewhere in this article, I would not advocate this pattern as a standalone strategy but can work nicely in concert with other analyses and opportunities.
Seasonality does indeed appear to persist - the widely known "sell in May and go away" myth appears to remain in effect.
However, stronger and more consistent than this anomaly is a pattern within days of month, favoring the end/beginning of each month (28th to 5th) as well as the early middle days (11th to 18th).
Most investors will not seek to trade solely on the basis of seasonality cycles, but all investors can benefit from listening to history when considering future trade timing decisions.
Note: this article has been adapted from this blog post on alphascientst.com* further explains methodology and provides full python code for those wishing to replicate results.
* The author's blog focused on applying data science methods to investing.
Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.