Alternate title: Is October Really So Bad?
For investors, October has often been the month of doom. It has amassed a rather considerable list of market crashes including:
And probably a few others I forgot. The history is well established, but whether it means anything is a more difficult question to answer1. In the interest of exploring this question, I decided to look at the distribution of S&P 500 returns (daily) for each month between 1950 and today and see if there are differences in the distributions of the returns between months2. (you can check my results yourself if you like, here is the raw data: SPX Data, I didn’t use Excel for the analysis but I did export the results to this spreadsheet: Monthly Return Data – SPX)
The results are, if nothing else, interesting. As I hope to make clear later, I don’t think the data is saying anything useful for investors, but it is interesting. However, the bigger point I want to make is that even when you have data, it is not always straightforward to interpret the data. In this case, depending on how you want to look at the data, October can be seen as either a more volatile, risky month for the stock market or no different from any other month.
The most popular measure of risk is volatility, or statistically speaking, the standard deviation of the returns. Over the past 64 years3, October has, in fact, been more volatile than any other month.
To get these results I separated all of the data for each month and looked at the distribution of the daily returns (so, for example, there were 1,407 trading days in the time period that were in October, 1,280 for November, and so on…in total there were 16,290 days in the time period).
Methodology, and Excel’s annoying unwillingness to let me put the months in a different order, it’s clear that November, September, and October stand out as being more volatile than the other months. October really stands out here, even compared with the next two most volatile months. October also includes both the largest one-day market loss and the largest one-day market gain in the data set. Black Monday (1987) was the largest one-loss, the largest one day gain was on 10/13/2008, so I doubt there was much happiness at the time. Clearly, it doesn’t seem to be much of a stretch to say that the data suggests October is a bad month. Numbers don’t lie, right?
Well, they may not lie, but nor do they tell the truth. Setting aside the countless problems with using volatility as a proxy for risk (that’ll be another post), there are other numbers to consider here. I next looked at the average daily return and the median return for each month.
First, for those who can’t find the energy to enlarge the picture, the orange bar is the mean and the blue is the median. This tells a different story about October entirely. The average trading day in October has a positive return. The median for October is positive. Every month has a positive median return, that’s not too surprising all things considered. It’s more interesting that four months have negative average returns: August, February, June, and September. Of those, only September had an above average volatility.
We can interpret this in lots of ways. I could argue that, given what we’ve seen so far, October is still a good month for investors because it has a positive average return. Or that it is bad because it has historically been more volatile. Really, the data can say what I want it to say depending on what I chose to present and what I don’t present. More to the point, I’d argue that October isn’t really unusual and that a number of very extreme outliers have taken place in October by coincidence and the deviations between the months is mostly noise. I get there by using what I’ve neglected to share so far.
I can’t know how much readers remember from their elementary school classes on applied statistical analysis. So, you may not be familiar with the, slightly obscure, statistical measures called skewness and kurtosis (I’ve talked about this a bit on Seeking Alpha if you’re interested). I’m a bit lazy, so I’ll give a 2 min. explanation here, see link above for better explanation. Skewness tells you, roughly, how asymmetric a distribution is and kurtosis tells you how heavy the distribution’s tail is (very roughly). So a high kurtosis (normal distribution has kurtosis of 0) tells you that extreme events occur much more often than a normal distribution would predict. A strong positive or negative skewness (say below -1 or above +1, again normal distribution has skewness=0) tells you that the left or right tail of the distribution is heavier. With lecture now over, let’s see the data.
How do I interpret that? Let me first say that I’ve seen no evidence of the following:
- There were historical reasons why extreme events happened in October that were not random chance.
- If there was a reason so many crashes happened in October, and the reason was not simply random chance, that the causal link is still meaningful today.
Given that, I’d say that it incorrect to make a judgement about months having different risk profiles. So, does that mean I wasted my time? No, a negative result is still a result.
1. That usually is the hard part, not the math. We have computers for the math.
2. A quick note about the methodology. I used the daily log returns of the adjusted close in all calculations. If is the stock price on day and is the price the day before the log return is given by:
3. Technically 64 years for months through September and 63 years for the rest of the year.