It's All Relative

Over the previous period of bear market action I had been continually dismayed by statistics used in the mainstream media. Statements like “…the Dow had its largest one day decline in history” may sound fair enough, but when we are talking about absolute changes in price they are really quite useless.

Take the 778 point move on 29 September 2008; this was the largest points decline on the Dow ever. However, this is completely irrelevant considering the Dow was trading at less than 400 before the 1929 decline. Of course 778 points is going to be more than any day in that period! The only value of statements like that is selling more news papers and generally scaring the uninitiated.

So with this in mind, I decided to take a look at just when the biggest relative moves have occurred. Most, including myself, naturally gravitate towards the assumption that the 1929 saw the biggest single day declines, but is this really the case? Let’s have a look.

For this process I have used the Dow Jones Industrial Average back to January 1929. The reason for choosing this market is due to the ease with which I can access its data going back to before 1929. If you have the data for the All Ordinaries Index back this far, the same analysis could be performed with what I assume (wrongly or rightly) would be similar results.

The first step in this analysis was to identify how I would define up and down days. Open to close, close to previous close, high/low to previous high/low? For simplicity and because of the data available, I used the current close compared to the previous close as the measure of the move and its direction.

Next I calculated the biggest price moves in absolute terms as a reference point. These can be seen under the column ‘Close to Close’ in Table 1. As expected, the vast majority of the biggest absolute moves have occurred within the last decade and 7 out of 10 within the current decline. Nothing earth shattering there! The shading also highlights that 7 out of the 10 biggest price moves were down days.

Table 1

Now for the interesting part… How do we measure moves on relative terms? The simplest method is to convert the price moves into percentages. Table 2 shows the biggest percentage moves and straight away we see a very different picture. First, the biggest move is a down day rather than an up day. Second, only two days from the current period factor in the top 10 and these were both up days! So in percentage terms the October 19 1987 fall counts as the single biggest move on the Dow, with the October 28 1929 coming in fourth. So much for the 1929 theory!

Table 2

Chart 1

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But hold on, is the percentage move the best measure? Certainly it is better than just the price change, but what about the fact that volatility fluctuates over time? With this in mind, I added a third measure that compared the day’s move to the current standard deviation level of the last 252 days – one trading year. This tells us how much bigger these days were than the norm at the time. Or in other words, just how big a shock they would have been.

The Standard Deviation method also ranks the October 19 1987 as the biggest day on the Dow at 2.01 standard deviations. The September 17 2001 – shortly after September 11 – ranking second also makes sense. The most interesting point to note is that the current decline does not rate a mention at all (in the top ten) by this measure. The 1929 date comes in at 8th which dispels the idea that the biggest relative down days occurred during that period.

Table 3

Chart 2

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The picture that is painted by Table 3 shows just how misleading some market statistics on the nightly news or in business section of the paper can be. After all, at some point in the future we may see 5000 point moves in day and no doubt someone will be there to tell us it was the biggest in history!

Happy Trading

Jordan Craw