The elusive market drop we have been waiting for all
year. Each month, from May through
August, we anticipated what would finally be a large market
correction. Or an outright fearful crash, given
the likely tapering later this year of the Federal Reserve quantitative easing. In this note we examine the worst 1% of
market crashes through history.
Soon we will approach the autumnal season, and we all suspect
that these are some of the riskiest months in the market. After all, most of the 10 worst, one-day market panics on the Dow, have infamously occurred near October. But a ranked listing of only 10 is a
freakishly small sample of extreme events, from which to draw any statistical
significance.
The history of the Dow goes back to the late 19th
century. And with enough data we
can better understand the frequency of when severe market drops occur. We know that Mark Twain said back
at about the same time the Dow started, “It is not worth while to try to keep
history from repeating itself, for man's character will always make the
preventing of the repetitions impossible.”
And here in this note we will show that there is a
statistically strong historical repetition of market crashes, occurring in the
months near October (e.g., September through November). But so too do
crashes more often occur on Mondays, for any month of the year. Of the nearly 29 thousand trading days in the
history of the Dow, which follows a downward skew pattern, we looked at the worst 294 (or 1%) of them. In order to qualify for this club of
the worst 1% days, a daily price drop of at least 3.2% was needed. And while this works out to a pace of five of these worst
1% days biennially, the most recent one we have had was November 2011.
Here is the distribution of those 294 days by month, in red on the chart. As a statistical alternate, we also show in light green the distribution of 294 days evenly spread across 12 months. In addition to the distribution test being significant at less than 1%, at the same degree of statistical significance is a combinatorics analysis of seeing four straight months of above-typical number of worst-1% days. We have three blog pieces (May 9, May 14, and June 12) exploring combinatorics in financial markets.
Next we show the distribution of these worst 1% trading
days, by the weekday when they occurred.
The statistical strength of Mondays is very powerful, and it does not
transfer over generally to either the trading day before or after (e.g., Fridays or
Tuesdays). We can see this with a
simple binomial kernalized technique, with a width of plus or minus one
day. This smoothed distribution essentially matches the
uniform distribution in light green, so we fail to appreciate that the
Mondays results is a product of luck inside the five-weekdays cycle. This weekday signal also equally applies, for any given week of the month.
On the contrary, a similar smoothing exercise in the monthly
distribution data above wouldn’t have changed the monthly seasonal pattern we
see. Additionally, we know that
there are two weekend, non-trading days, breaking the psychological rhythm between
Friday and Monday. There is no similar
large break, of any non-trading months, in the monthly distribution.
It is worth noting that the combinations of the weekday and
monthly data are also statistically significant. Again, here we use a Chi-square non-parametric test, to
measure possible differences from expectations. With the 294 worst trading days, spread over 60 (12*5) weekday and
month combinations, we have designed a statistically large enough sample to see
significance within the weekday and month combination.
We see this 60 weekday and month combination distribution
above. October is represented in yellow;
Monday is represented by blue.
We see that the riskiest time for the markets, shown about the green data, have been on or about October, with a large bias towards Mondays.
None of the above analysis is statistically significant for
the average severity of these worst-1% market drops. But as we have
shown in this note, it is important to also pay attention to the frequency of
highly risky market times when thinking about the choppy, year-ending months before us.
Nice work.
ReplyDeleteWould love to see the flip side of this analysis: The top 1% days by month.
Thanks much Anonymous. It is important to note that the research conclusions, about choppiness between now and year end, reflect some contextual information that is not included in simply the distribution of the worst-1% risks. Despite the general reduction in volatility over the past 100+ years, the broad underlying tail events are fairly consistent in their seasonal rhythm, regardless of whether one looks at the worst-1% days, or best-1% days. The weekday effect however only holds for the worst-1% risks; and not for the best-1% risks.
DeleteNow staying with the seasonal months effect, it is important to not overlook that the market tends to have a high general positive drift associated with it, which also constricts the risk-neutral probability of an up-move for asset valuations. These returns are also asymmetrical, so a less impressive one-day change of 2.9% is needed to be in the best-1%. While a larger emotional surprise of being down -3.2% is what's in store to be in the worst-1%. Leaving aside these percent changes, which will scale on both sides, through lengthy economic cycles, the distribution patterns here are otherwise essentially the same. With a critical level generally of less than 1%, across time, and regardless of whether it is the worst-1% or best-1% being looked at. To be clear, the distribution changes slightly when one examines this across time, however these changes are not significant. But if one chooses to examine these differences then this would also imply using a smaller set of data in one's marginal distribution. A broader point of this analysis is to educate that there is a trade-off in finding the optimal settings for an analysis such as this. Here the trade-off is having a lower confidence interval on the this outer-1% analysis, or instead maybe looking at say an outer-2% returns in order to maintain the same confidence interval.
For more on applied confidence intervals, one may enjoy the "⅕ chance of rate firming, prior to 2015" note here: http://statisticalideas.blogspot.com/2013/06/a-20-chance-of-rate-firming-prior-to.html.