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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.
Of course with such broad statements there will always be plenty of examples where the saying proved true, but as any student of science will tell you, that hardly constitutes proof. 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 a bit 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 1911 (there is no significance in this date, it’s just the starting point for the data I had available). Between then and now we have seen a total of 1194 months. Of these 506 were negative, 679 were positive and 9 were flat. I then went ahead and calculated the percentage of negative/positive months that occurred in January, February, and 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. More accurately, the observed divergence may be sufficiently explained by chance alone. (Indeed, statistically speaking, the chances of observing a perfect distribution are actually rather low).
However, rather than just arbitrarily decide what is and isn’t statistically significant (as many 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, that there is no significant difference between observed and expected results. As a starting point, we will assume that all months should have an equal chance of providing positive or negative returns, with no month particularly suited to either. In other words, the variation we observe in the frequency of negative and positive months should be explainable by chance alone. Let’s see whether or not this turns out to be valid. (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 September has the highest Chi square value (5.21), 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 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 to scrutiny.
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 “sell in September” cliché, you need to seriously re-evaluate your investment strategy. Of course if you have other good reasons to sell, then so be it, but likewise ensure that they are at least supported by sound reasoning.
Finally, let me emphasise that I am NOT saying that this all means that the market won’t rally this December. What I am saying is that historically, any observed strength we have observed in December is sufficiently explained by chance alone. Happy Christmas.
Make the markets work for you!
Andrew Page
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