Tuesday, August 9, 2011

Big down days on the DJIA

CXO Advisory wrote about what happens after big down days on the S&P 500. Their study dates from January 1950 and they defined "a big down day as a decline of at least four standard deviations of the daily returns over the preceding four years (1,008 trading days)." They found 45 observations and concluded that:
  • The average next-day return is 0.59% (but variability is high).
  • 60% of next-day returns  (27 of 45) are positive.
  • The average next-day return is fairly consistent for subsamples when the index is above and below its 200-day SMA.
CXO went on to warn that the results were very volatile and 45 days is a relative small sample upon which to reliably draw conclusions. So I repeated the study using data for the Dow Jones Industrials Average, pulled from Yahoo Finance. That data goes back to October 1, 1928 - though if you average four years' worth of data, you missed the Crash of 1929. Here are the results:

DJIA 4-Std Dev Big Down Days

Markets rallied the next day but fell back in a week
I found similar results, though the sample size was slightly larger at 59 (instead of 45). The next day return averaged 0.36%, which beat the average daily Dow daily return of 0.03% by 0.33%. There was an outlier of -22.6% during the Crash of 1987 which pulled down the average return. If we were to look at the median return, which is less sensitve to outliers, the median daily return on big down days was 0.43%, which was substantially ahead of the Dow daily return of 0.04%. 62.7% of the subsequent daily returns were up, ahead of the 52.2% figure for all Dow days from 1928. Next day returns were highly volatile and the standard deviation of daily returns after big down days was nearly four times the standard deviation of daily Dow returns for the entire sample.

CXO Advisory warned against looking at averages of subsequent one-week returns because of overlapping instances of big down days. The table reflects the first instance of a big down day in a five day period and subsequent big down day weekly returns were ignored.

Interestingly, while the markets rose for the next day for big down days, the one-week return was not so encouraging. In all cases, the average and median returns, as well as percentage of positive weeks, underperformed our control sample of the Dow returns for our entire study period.

Monday was not a 4-standard deviation day
Despite the market carnage yesterday, Monday did not qualify as a 4-standard deviation day. The measure actually came in at -3.48. So I repeated the exercise by defining big down days as 3-standard deviations under the 1008-trading day average:
DJIA 3-Std Dev Big Down Days
Here the sample size grew to 170 from 59. The results were similar but not as strong. The one day return outperformed but the one-week returns were mixed.


Sion said...

To me the charts look distinctly 2008ish. The weird thing is this collapse just like the flash crash came with very little warning. I guess whats most likely is a pretty substancial bounce. But I would not trust it further than I could kick it. And I think I'm not alone. What's to trust with a financially engineered financial assets recovery? Main street has not recovered. Everyone knows that. Unless you belong to the species homofinancious you are worse off by far now than you were in 2008. This is unsustainable.

Michele said...

Excellent analysis. I did a much more subjective check of the Dow by just scrolling back through the daily chart - of the VIX. I found that after big gap up days in the VIX that take it over its upper Bollinger band, the next day the Dow rallies (just as it did today). But there's no follow-through a week later. Nice to see some numerical confirmation.