About Big Up / Down Days Within Bearish / Bullish Cycles

This is a follow up to my earlier post that looked at the likelihood of big up or down days in bullish and bearish markets.

Recall the conclusion from that post: big up and big down days (like this past Monday) have been more likely to occur on any given day in a bear market than bull market.

This post will dig a little deeper and look at where these big up/down days tend to fall in bull and bear markets: at the beginning, the middle, or the end. Warning: this will be a thinker.

[click to enlarge]

I’m going to use the same zig-zag approach (pictured above) to define bullish and bearish trends that I described in my previous post. Big up/down days will be defined as X times the standard deviation (SD) of the previous five years. For example, at this moment, 1 SD is about +/- 1.4%, so a 2 SD change is about +/- 2.8%.

Note that this study covers the period from 1960 to 03/10/2009 on the S&P 500.

Analysis

The table below shows the percentage of big up/down days by bullish/bearish trend that occurred during the first, middle, or final one third of the trend. Note that when I say first, middle or final third, I mean in terms of time, not % change.

I’ve defined big up/down days here as greater than +/- 2 SD. And I’ve color-coded the cells using a heat map to help better understand the data.

How to read this table: Using the first column of data as an example, 37% of all big up days during bullish trends occurred during the first one third of the bull trend. 12% occurred during the middle third, and 51% occurred during the final third.

The table shows that in bull markets, 2 SD up and down days have more often than not come towards the end of bullish trends. Bear markets have exhibited a similar tendency, but not to the same extreme; big days have been more evenly distributed over the entire trend.

I would consider a 2 SD day to be a pretty big event (there have been only 843 over this nearly 50 year test), but some of the daily changes we’ve seen over the last six months have been many, many times larger. The next table uses the same approach, but looks at +/- 4 SD days (that’s +/- 5.7% in today’s market).

A word of caution, at +/- 4 SD, we’re looking at very few observations (a total of 88 over the period tested), so treat these results with care.

Looking at just these very big up/down days leads to an even more extreme conclusion. Big up/down days have clustered around the beginning and end of bullish trends, and clearly towards the end of bearish trends.

Conclusion

I’m changing my tune a bit from my previous post. Yes, big up/down days are much more likely to occur in bear markets than others, and no, they don’t in and of themselves signal a change in trend. However, they do tend to (note I say “tend to” and not “always”) increase in frequency as the bullish or bearish trend is waning.

What does that say about this week’s volatile performance? Well Monday’s close took us more than 20% off the low, so technically by the zig-zag methodology above we’re in a new bull trend. Looking just at data column one in the second table, the huge up day we saw on Monday (based on this very limited view) could indicate the start of a protracted run up, but more likely a pull back and another leg down in the markets.

Comments

[CautiousInv...:]

Thanks for the time invested to produce a thoughtful analysis.

Mark Hulber undertok a similar study of the first days of the past 34 bull markets. I quote him below:

"To come up with a list of those bull markets, I followed the lead of Ned Davis Research, the institutional research firm. For them, a bull market requires one of three conditions to hold: (1) at least a 30% rise in the Dow Jones Industrial Average in 50 calendar days, (2) at least a 13% rise in the Dow in 155 calendar days, or (3) at least a 30% reversal in the Value Line Geometric index.

Since the beginning of 1900, according to the research firm, there have been by this set of criteria no fewer than 34 bull markets.
It turns out that the recent rally has been markedly more powerful than the average beginning of prior bull markets.

Over the last two weeks, for example, the Dow has gained 18.8%. The Dow's average gain over the first two weeks of past bull markets, in contrast, has been 8.4%, or less than half as much.
In fact, of the 34 bull markets identified by Ned Davis Research, only one of them produced a greater gain in its first two weeks than in the recent rally.

That was the one that began on November 13, 1929, and is hardly one that the bulls would want to brag about. That bull market lasted just five months and led to an increase of just 48% in the Dow -- making it one of the most modest of bull markets in the sample, despite have one of the most impressive returns in its first two weeks."

Mar 25 07:33 AM

[John Lounsbury:]

Michael - - -

I am puzzled by what you said with respect to the 2 SD markets"

<<<The table shows that in bull markets, 2 SD up and down days have more often than not come towards the end of bullish trends. Bear markets have exhibited a similar tendency, but not to the same extreme; big days have been more evenly distributed over the entire trend.>>>

Could you explain "Bear markets have exhibited a similar tendency,..."? This does not make sense to me. What am I missing?

I am also feeling thick regarding your statements:

<<<Looking just at data column one in the second table, the huge up day we saw on Monday (based on this very limited view) could indicate the start of a protracted run up, but more likely a pull back and another leg down in the markets.>>

Are you suggesting that we are in a bull trend so the first column is an appropriate reference? Since I don't know your definition of a bull trend, that may be what I'm missing here. My definition is that we are still in a bear trend (with a counter-trend rally) so the third column in the 4 SD table would be the appropriate reference. That would indicate a significant (but not overwhelming) probability (55%) that we are in the last third of the bear trend.

I am feeling uncertain about interpretation here so your comment would be appreciated.

Mar 25 03:22 PM

[Michael S:]

RE to John: good questions...re: "a similar tendency" - in both down trends and up trends a large number of 2 SD days (positive and negative) have come towards the end of the trend. In up trends, this has been more pronounced (a lot of big days towards the end, some towards the beginning, but very few in the middle). In down trends, it has been more evenly balanced - still more towards the end, but quite a few in beginning and the middle. Not sure if that answered your question (but I hope it did).

RE is the bull trend an appropriate reference? - that would be for the reader to decide. Based on the cutoffs that the study used, this current leg up would technically be categorized as a "bull market" (20% off the low), but it just barely made the cut and I think it would be perfectly reasonable to lean towards the bull market column.

P.S. you're a frequent constructive commenter here at SA (which I appreciate). Feel free in the future to take a look at the post on the actual blog - there is a lot more reader discussion there expanding on ideas and often a question asked at SA has already been treated.

All the best,
michael

Mar 26 03:41 AM