Just a short post today. Jack Damn has been tweeting about consecutive up/down days lately, which inspired me to go looking for a potential edge. The NASDAQ 100 has posted 6 consecutive up days as of yesterday’s close. Is this a signal of over-extension? Unfortunately there are very few instances of such a high number of consecutive up days, so it’s impossible to speak with certainty about any of the numbers. Let’s take a look at QQQ returns (including dividends) after X consecutive up or down days:

There’s no edge on the short side here if you’re looking for a mean reversion trade. Looking out over longer horizons, it seems like many consecutive up days tend to be followed by above-average returns. Another argument in favor of the idea that the bottom of the current pullback has been reached, but nothing really useful in terms of actual trading.

Finally, a look at the probability of positive returns following X consecutive up or down days:

**UPDATE: **Here’s the spreadsheet.

**UPDATE**: read *The IBS Eﬀect: Mean Reversion in Equity ETFs* instead of this post, it features more recent data and deeper analysis.

The location of the closing price within the day’s range is a surprisingly powerful predictor of next-day returns for equity indices. The closing price in relation to the day’s range (or CRTDR [**UPDATE: **as reader Jan mentioned in the comments, there is already a name for this: Internal Bar Strength or IBS] if you’re a fan of unpronounceable acronyms) is simply calculated as such:

It takes values between 0 and 1 and simply indicates at which point along the day’s range the closing price is located. In this post I will take a look not only at returns forecasting, but also how to use this value in conjunction with other indicators. You may be skeptical about the value of something so extremely simplistic, but I think you’ll be pleasantly surprised.

### The basics: QQQ and SPY

First, a quick look at QQQ and SPY next-day returns depending on today’s CRTDR:

A very promising start. Now the equity curves for each quartile:

That’s quite good; consistency through time and across assets is important and we’ve got both in this case. The magnitude of the out-performance of the bottom quartile is very large; I think we can do something useful with it.

There are several potential improvements to this basic approach: using the range of several days instead of only the last one, adjusting for the day’s close-to-close return, and averaging over several days are a few of the more obvious routes to explore. However, for the purposes of this post I will simply continue to use the simplest version.

### CRTDR Internationally

A quick look across a larger array of assets, which is always an important test (here I also incorporate a bit of shorting):

Long when CRTDR < 45%, short when CRTDR > 95%. $10k per trade. Including commissions of $0.005 per share, excluding dividends.

One question that comes up when looking at ETFs of foreign indices is about the effect of non-overlapping trading hours. Would we be better off using the ETF trading hours or the local trading hours to determine the range and out predictions? Let’s take a look at the EWU ETF (iShares MSCI United Kingdom Index Fund) vs the FTSE 100 index, with the following strategy:

- Go long on close if CRTDR < 45%
- Go short on close if CRTDR > 95%

FTSE vs EWU CRTDR strategy, 1996-2012. $1m per trade (the number was a technical necessity due to the price of the FTSE 100 index).

Fascinating! This result left me completely stumped. I would love to hear your ideas about this…I have a feeling that there must be some sort of explanation, but I’m afraid I can’t come up with anything realistic.

### Trading Signal or Filter?

It should be noted that I don’t actually use the CRTRD as a signal to take trades at all. Given the above results you may find this surprising, but all the positive returns are already captured by other, similar (and better), indicators (especially short-term price-based indicators such as RSI(3)). Instead I use it in reverse: as a filter to exclude potential trades. To demonstrate, let’s have a look at a very simplistic mean reversion system:

- Buy QQQ at close when RSI(3) < 10
- Sell QQQ at close when RSI(3) > 50

On average, this will result in a daily return of **0.212%**. So we have two approaches in our hands that both have positive expectancy, what happens if we combine them?

- Go long either on the RSI(3) criteria above OR CRTDR < 50%

RSI(3) and RSI(3) w/ CRTDR strategy applied to QQQ. Commissions not included.

This is a bit surprising: putting together two systems, both of which have positive expectancy, results in significantly lower returns. At this point some may say “there’s no value to be gained here”. But fear not, there are significant returns to be wrung out of the CRTDR! Instead of using it as a signal, what if we use it in reverse as a filter? Let’s investigate further: what happens if we split these days up by CRTDR?

Now that’s quite interesting. Combining them has very bad results, but instead we have an excellent method to filter out bad RSI(3) trades. Let’s have a closer look at the interplay between RSI(3) signals and CRTDR:

Next-day QQQ returns.

And now the equity curves with and without the CRTDR < 50% filter:

RSI(3) and RSI(3) w/ CRTDR < 50% filter applied to QQQ. Commissions not included.

That’s pretty good. Consistent performance and out-performance relative to the vanilla RSI(3) strategy. Not only that, but we have filtered out over 35% of trades which not only means far less money spent on commissions, but also frees up capital for other trades.

**UPDATE: **I neglected to mention that I use Cutler’s RSI and not the “normal” one, the difference being the use of simple moving averages instead of exponential moving averages. I have also uploaded an excel sheet and Multicharts .net signal code that replicate most of the results in the post.

Tuesday saw QQQ drop somewhat heavily, and for the third day in a row. These three drops took us back to mid-August levels, blowing through a ton of support levels… My mean reversion senses are tingling!

So, let’s take a look at what happens in these situations by formulating a simple rule to capture them, that will then exit after the mean reversion has (hopefully) happened:

- If QQQ is down at least 3 days in a row, and it closes below the 10-day intraday low, go long.
- Close the position one day after QQQ closes above its 5-day SMA.

A simple rule, designed to capture big drops in hope for a bounce. The usual issues associated with catching falling knives come up.

Sometimes it works great…

April 2012

And others not so much…

September 2001

But over time there is remarkable consistency:

Run-up & drawdown, assuming $100k per trade, including $0.005 per contract in commissions

Here are the stats:

Note: dot-com bubble not included in these stats because they would look better than they really are over the long run.

Downside skew is never nice of course, is there something we can do to soften the biggest losses? As it happens in most cases with swing systems, adding a stop loss is generally a bad idea. Indeed adding a simple 3% stop loss would decrease returns, lead to a much more uneven equity curve, and also result in deeper and longer drawdowns. Getting fancier and adding various special rules to the stop (such as a period after getting stopped out during which trading is not allowed) does not significantly improve the results. The solution here is simply proper position sizing so that you can take the losses you have to take and still be comfortable.

Finally, is this just an accidental feature of the NASDAQ 100, or could we use it in other markets as well? Let’s have a look at a broad array of equity index ETFs:

Trades start at each ETF’s inception; dividends are included, commissions are not.

Well, there you have it…

**Disclosure:** Net long U.S., U.K., Singaporean equities.