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There are a number of clichés associated with the various months of the year, and what we tend to observe on the market in those periods. “Sell in May and go away”, “Santa Clause Rally” (December), “Crash Month” (October) and the “September sell off” are perhaps the more common ones, but is there any truth behind these sayings? As is so often the case with investors, we tend to accept things at face value without ever seeking validation, which is amazing considering the importance of our financial decisions.
In the interests of objectivity and empiricism I decided to examine these claims and see if there was indeed any statistical accuracy to them. The process is quite straightforward, and I will first outline this before we examine the results. Don’t be put off by a few statistics and words of jargon, although the method might seem to be slightly complicated, you just need to get the “gist” of it!
To begin with I have used almost 100 years worth of data for the Dow Jones Industrial Average index, going all the way back to March 1910. There is no significance to these dates, it’s just the data I had close to hand. From March 1910 and now we have seen a total of 1194 months. Of these, 506 were negative months, 679 were positive and 9 were flat. I then went ahead and calculated the percentage of negative/positive months that occurred in January, February, March etc.
It turns out that of all the negative months for the Dow Jones, most of them did indeed occur in September. June, May and February also do not fare well.
Figure 1. Frequency of negative months for the Dow Jones since 1910. The blue line represents the expected frequency based on a perfectly random set of data.
click to enlarge
What about the upside? The results show that the best month to be invested over the past 100 years has been December.
Figure 2. Frequency of positive months for the Dow Jones since 1910. The blue line represents the expected frequency based on a perfectly random set of data.
click to enlarge
At first glance it appears that some of the clichés are supported. Certainly the Santa Clause rally appears to be irrefutable, as does the September Sell-off. However, there doesn’t seem to be any significant divergence from the theoretical average (8.33%) for most other months. In other words, although there ‘seems’ to be evidence that some months are good or bad for investors, the difference is so small as to be nearly irrelevant.
However, rather than just arbitrarily deciding what is and isn’t statistically significant (as most investors tend to do), it’s best to employ an established test, such as the chi-square test. Statisticians use this test to verify the null-hypothesis – that is, whether or not the difference between observed and expected results are significant. For our purposes, the null hypothesis is that all negative and positive months are equally divided between the various months i.e., the observed frequency should be 8.33% for each month for both positive and negative months. That might seem a little complicated but it’s a simple idea really. Just think of it like this; all months should have an equal chance of providing positive returns or providing negative returns, with no month particularly suited to either! Seem fair?
(I won’t bore you with the mathematics, but for those so inclined you can find a nice explanation at www.enviroliteracy.org)
Table 1. Chi square values for frequency of negative months.
| Month |
Observed Frequency |
Expected Frequency |
Chi Square Value |
| January |
36 |
42.17 |
0.902 |
| February |
47 |
42.17 |
0.554 |
| March |
40 |
42.17 |
0.111 |
| April |
43 |
42.17 |
0.016 |
| May |
48 |
42.17 |
0.807 |
| June |
51 |
42.17 |
1.850 |
| July |
39 |
42.17 |
0.238 |
| August |
38 |
42.17 |
0.412 |
| September |
57 |
42.17 |
5.218 |
| October |
39 |
42.17 |
0.238 |
| November |
40 |
42.17 |
0.111 |
| December |
28 |
42.17 |
4.760 |
It turns out that December has the highest Chi square value (4.76), but for the difference between the observed and expected frequency to be statistically significant, with 95% confidence, the value needs to be greater than 19.68. Plainly, the chi square value is not even close to this.
The bottom line? The observed frequencies of winning and losing months is NOT significantly statistically different from the frequencies we would expect from an entirely random distribution. That is, we CANNOT reject the null hypothesis. Again, for those not mathematically inclined, although we have indeed observed that September tends to be the worst month for investors, this can be put down to nothing more than natural random variation. There might be lies, damn lies and statistics, but in this case, the numbers are telling us something undeniable. The notion that some months are better or worse than others does just not stand up – don’t ‘myth-take’ sound bites for reality!
So what does this mean for investors in practical terms? Essentially, don’t let important investment decisions be influenced by unsubstantiated myths and half-truths. If the only reason you are choosing not to buy in September is because of the “September sell off” cliché, you need to seriously re-evaluate your investment strategy. Of course, if you have other good reasons, then so be it, but likewise ensure that they are indeed supported by empirical evidence and sound judgement.
Finally, let me emphasise that I am NOT saying that this all means that the market won’t go down this month. What I am saying is that historically, any observed negativity we have observed in September (or any observed strength we have noticed in December) is sufficiently explained by chance alone. Full stop, end of story.
Make the markets work for you
Andrew Page
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