### The State of Short-Term Mean-Reversion: July, 2009

**This is the first in what will be a monthly health check of short-term mean-reversion in the US market.**

Short-term mean-reversion (by “short-term”, think for example RSI(2)) is so important to what we swing-traders are doing right now because at this moment in history, it’s the most effective (directional) trade.

But here’s the kicker: around the turn of the century short-term MR radically evolved, and it’s only a matter of time before everything is turned on its head again (read more and more). This monthly report aims to foresee that next evolution.

There are infinite ways traders are playing short-term MR: RSI(2), stochastics, fast MAs, DV(2), etc. so we need a single gauge of short-term MR that can serve as a proxy for all. I think that proxy should be daily mean-reversion in the S&P 500, or put another way, *the tendency of up days to be followed by down days, and vice-versa.*

We’ve talked about daily MR ad infinitum. It’s not appropriate for actual trading (it’s too volatile, drawdown prone, and weak relative to trading frictions), but its evolution from being momentum-driven in the last century to MR-driven in this century, is a near perfect match with the evolution we see in all other very short-term indicators, because conceptually, this tendency for the market to retrace very recent gains is exactly why all of these short-term indicators work the way they do.

**Report Format**

The report will consist of three charts, each showing the monthly results of trading a daily MR strategy, in terms of (a) average daily return, (b) return versus volatility, and (c) win percentage.

*The proxy strategy will be: go long the S&P 500 at today’s close if the index closed down today and short if it closed up.*

The first chart shows the strategy’s (frictionless) average daily return from 2004 by month. I’ve also included 1-year (red) and 5-year (blue) averages for perspective, and highlighted the most recent month in dark grey.

Daily MR appears to have become considerably stronger in early 2007, but that’s a little misleading, because a good bit of that bump is a result of increased volatility in the market (rather than an increase in the effectiveness of the strategy), so of all three charts, I think this one is the *least* useful.

The second chart attempts to compensate for that increase in market volatility by dividing the average daily return each month, by the standard deviation of daily returns (a simple risk-adjusted measure).

Here daily MR still tests stronger over the last year and a half, but not to the same degree it did when we just looked at pure return.

Finally, the third chart shows strategy results in terms of win percentage, and is trying to capture to what degree daily MR is binary and to what degree it’s a function of winning days being larger than losing ones. The former would benefit strategies like daily MR or unbounded DV(2), while the latter might benefit strategies that took advantage of “stretched” markets like extreme RSI(2).

**So what is the current state of short-term mean-reversion?**

Alive and well.

Across all three metrics 1-year averages (red) trounce 5-year averages (blue), July outperformed the averages for the two most important metrics (return vs volatility and win %), and no significant downtrend is afoot.

I sincerely hope that every report is as clear cut as this one, but when it isn’t (and one day it won’t be), I hope that we’re all a bit more prepared.

Happy Trading,

ms

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Filed under: State of Short-term MR | 27 Comments

brilliant !

dv

Another great post

Michael, this is excellent. Really, can’t thank you enough.

Would be useful to see what the charts look like for a period where MR was not “in effect”. Secondly, how would you anticipate “seeing” that MR is not working any longer? Simply look at the crossover of the MAs?

RE: “charts from pre-MR periods” – good point – will put some long-term charts up for comparison.

RE: “how to anticipate MR failure” – good question – I would start to get concerned if we saw a string of months below averages or a strong downtrend in monthly returns or averages. I would have been raising very big red flags in late 2006 when short-term MR looked to be completely breaking down.

michae

A very sincere thank you from me too. I recently wrote an article that describes an approach for taking advantage of ‘daily follow through’. Hopefully, you will find it interesting. The URL is http://adaptivetradingsystems.com/blog/?p=1359 I use swarms, but the same thing can be done without them. I don’t know how you calculate your confidence metric, maybe what I have done is similar.

James

James,

That’s a nice piece of work, and I think it shows a lot of promise. I like the idea of combining Dakota with some of Michael’s ideas — I’ve been doing it for a while, and had some good luck.

If you do any further work, please post about it. I don’t read your blog religiously, so a post here or over in the Dakota forum would be great.

Thanks,

=Carlos=

I’m surprised that MR seems to work reasonably well in the second half of 2008. Even the months when it fails do not show very large losses. I would have thought that large MR losses were responsible for the problem YK has last fall. If not that, then why did it do so poorly?

RE to Russ: stating the obvious here but it’s because it’s not a follow-through strategy – the strategy bet hard on days that didn’t reverse and weak on days that did. michael

I had the same question, and I don’t understand this response. Could you try to explain it another way?

RE to Kraig: simplest way I can:

“because it’s not a daily mean-reversion strategy”

YK is influenced by short-term MR, but is not interpreting it the specific way we are in this report.

michael

I hear the McDonald’s marketing jingle in my head. Ba da ba bup baaaah… ;-) Jeff

A very simple way to verify “implied” reversion is to count the number of up days and the number of down days for any period. Studies over very long periods show the number very close to 50/50. Whether or not next day reversion is more or less significant during some period, there will be some short period, 2, 3, or 4 days, where it will be observable.

The random walk produced by repeated coin flips has the property that over a long period the number of heads and tails will approach 50/50. But that doesn’t imply that a mean reversion strategy will work. After all it’s random; so on any give flip mean reversion and follow-through are equally likely to work. The long-term results for each strategy should approach each other — and each should approach 0.

On the other hand, if you were guaranteed that every time the sequence switched from heads to tails or vice versa (call it an inversion), the subsequent flip would be a follow through, then follow through would be a champ and mean reversion would be a dog. Yet the same 50/50 overall statistics would hold. (That’s because after each change from heads to tails or vice versa, the next flip is the same but the flip after that is still random.)

One could make lots of money by betting follow-through only on the flips after inversions. One would be guaranteed to win each of those. But even if one bet on each flip, the non-inversion flips would split 50/50 between winners and loser. So they would wash out.

Similarly if each single inversion were guaranteed always followed by a second inversion (but two inversions in a row were followed by a random flip, the opposite of the previous case), the opposite results would hold. MR would be a champ but follow through would be a dog. Yet long-term 50/50 would still be the case.

So MR and Follow Through depend crucially on next-flip results and not on longer-term overall statistics.

Unfortunately, I’m not mathematician enough to take this further. But it’s interesting to note that these two examples are something like a random walk with local structure. Is there a mathematical/probabilistic theory that can be applied to that? I don’t know.

Sorry for going on so long, but consider this. Suppose one had a collection of flip sequences from which results were constructed. E.g., you constructed a sequence of “flips” from hth, tht, hhtt, tthh but after each sequence a new one were picked at random. then after the first two flips in each sequence you would know what the third and possibly fourth was and could make lots of money betting on those. Betting on the first two would be random but would neither help nor hurt. Overall one would have a 50/50 sequence.

Now this suggests looking at the up-down sequence and asking whether any sub-sequences are good predictors of the following flip. If it’s random, the answer should be “no.” But if there is some structure in the system, there should be some reasonably prediction possibilities — even though the overall results are still 50/50. This is the sort of thing that Frank’s Trading the Odds Looks for.

RE to Russ: I’ve tested more or less what you’re discussing. I think these sequences exist, but from a risk-adjusted perspective are difficult to capitalize one. The farther removed we are from a simple comparison of today versus the day before, the less binary the market becomes. Put another way, I think for understanding short-term mean-reversion beyond daily follow-through, I think an indicator like RSI(2) or RSI(3) (that accounts for magnitude and not just direction) is more appropriate. michael

Interesting that you’ve tested it. What do you make of Trading the Odds (http://www.tradingtheodds.com/)? It seems to do fairly well — even though no performance statistics (audited or not) are ever given.

RE to Russ: similar to my thoughts on rob hanna’s quantifiable edges. Love both of those blogs, but they take a very different path than I do. They are analyzing very specific characteristics of today and drawing analogies with similar past days (often based on a very low number of historical occurrences). My approach is different in that I’m trying to find systems that are appropriate for all markets at any time. Not saying one is any better than the other…just different. michael

MR vs follow-through is such an important aspect of the markets to monitor.

Are your three charts based on close-to-close returns? What position would be taken on a gap-up day that closed lower (ie, close > close[1] AND close < open)?

(Just read your post on overnight vs trading hours returns. ;-)

Thank you,

Ruth

RE to Ruth: I don’t do a lot of gap analysis (not an intraday guy) but two folks who do and you should definitely tap into are quantifiableedges.blogspot.com and http://www.tradingtheodds.com. Hope that helps. michael

I’m not wondering how to analyze gaps. I am asking for clarification on what data you are using.

Let me repeat my question:

Are your three charts based on close-to-close returns?

And reword it:

Are the daily returns that you are using open-to-close returns or close-to-close returns?

Thanks,

Ruth

RE to Ruth: sorry about that – skipped straight to your second question. Yes, I’m using close-to-close changes. michael

As far as predicting or finding when the MR is shifting, I could supplement this with some statistical or control chart type methods and calculations. Also I wonder about a forecasting model for the MR measure that would forecast where it is headed or something.

RE to Caveman – would love to see anything you can add re: supplementing the data (let me know if you need me to send you the raw data). michael

I seem to have problems doing the embedded reply on a reply thing.

But yes, if you can, send me the data to my email.

when you impled mean reversion was still alive and well 3 years prior, did you ever expect it to continue to perform as well as it has done this year? I’ve personally been reverting to the mean since 2007 =) Great way to trade.