Pairs Trading: Reversion to the Mean

What is pairs trading?

Take any highly correlated pair, for example AUDUSD/NZDUSD, when they decouple, short the higher one, buy the lower one, in anticipation that they will revert to the mean, at which time positions are closed.

Virtually all threads/forums that discuss FX pairs trading start and end in confusion. Traders seem to like the idea of pairs trading FX but I’ve not seen a strategy conceptualised very well, let alone traded well.

This thread will attempt to reverse this trend.

Pairs Trading Strategy:

I’ve come across an interesting MT4 indicator that nicely conceptualises FX pairs trading, giving me a good starting point. The picture attached shows a bollinger band looking indicator, however the difference here is that the oscillator represents the price difference between 2 pairs. When the oscillator moves to either extreme the 2 pairs are indicating a decoupling; buy the lower pair/ short the higher pair, TP at reversion to the mean.

However, just like bollinger band trading, price contacting the standard deviation band does not always represent a buy or sell. These signals need to be intelligently filtered.

Note: Because the indicator I refer to is a commercial one, and I don’t want this thread moved to the commercial section, I wont mention names nor provide a link here. My hope is that either there is already a good free version of this indicator floating around or someone tech savvy can whip one up for us.

The purpose of this thread:

[1] thrash out the pros and cons of pairs trading
[2] if we can get through that, build a strategy


Let the games begin.

.

Although I will agree that AUDUSD and NZDUSD are correlated, I think that basing a strategy on reverting to a mean is risky.
If the 2 pairs tend to revert to a mean value, then you would see the AUDNZD chart oscillate around a pivot and this is not the case.
Of course, looking at the chart, you will probably be able to identify places where this happens, but in real time, not so easy.

You cannot just buy Aussie and sell Kiwi. Doing so you end up with a long position on AUD/NZD. You must balance the positions size depending on the current cointegration factor of the two pairs.

If not already done I suggest you read
http://www.forexfactory.com/showthread.php?t=265350
http://www.forexfactory.com/showthread.php?t=262827
7bit wrote a EA which does almost everything for you.

The filter you need is a unit root test like theAugmented Dickey–Fuller test
Be aware that those tests
- need a lot of samples to give a valid reading (=lag)
- perform bad on market data (fractionally integrated time series)

Wasn't 7bit's EA for co-integration, not correlation, which is what PeterE is talking about?

The OP wants to trade the mean reversion of the spread between two instruments. He needs the two price series to not wander off in opposite directions for very long time without coming back together. I think what he calls correlation actually is cointegration. Correlation doesn't guarantee the mean reversion. For instance after a permanent shock, like a news that would have more effect on one than the other, the two prices may stay perfectly correlated at their new level. Two majors will always be correlated through the USD. The statistical arbitrage comes from the cointegration.

well thank you for the replies PipMeUp and Gumrai

pairs trading seems much more complex than i'd realised in terms of indicator/system development

........let alone application

Great idea Pete

Totally agree.
Long back, was quite interested into this & searched about it (not detailed though) . Ended up reading HIGHLY contrasting views and stuff

Subscribed and looking to read something of worth this time(in free time)
Co-relations always interest me

Peter,

I'm aware of two main schools of thought regarding pairs trading. Both involve mean reversion. Both have plusses and minuses.

1) Empirical or model-free (correlation)
The empirical school calculates a spread on two (or more) highly correlated pairs and trades deviations in that spread back to the mean or some other point. The calculation can be something like:

spread = A * coef1 - B * coef2

Where A and B are two correlated pairs and coef1 and coef2 represent weights / coefficients / betas / constants that help to normalize / make the spread more stationary for easier mean reversion.

I know 3 methods for calculating coefficients:
a) volatility, such as ATR1 / ATR2 (where 1 and 2 are correlated currency pairs)
b) betas such as betaA = cov(A, B) / var(B) to get a beta for symbol A in terms of symbol B
c) cointegration to calculate the betas / eigenvectors to use as weights.

Pro: model-free pairs trading is exceptionally easy to understand and fairly easy to trade. Once you set upon some weights you simply apply rules to a spread for mean reversion. Assuming pair A and B stay correlated, you will eventually get mean reversion. It is worth noting that correlations based on market data are notoriously unreliable.

Con: If a shock occurs where A / B decouple, the spread will trend and a mean reversion strategy will lead to losses.

2) Model based (cointegration)
The model based cointegration method typically uses either the Engle-Granger two step method or the Johansen method which test for long-term co-movement among pairs. Co-movement is different from correlation in that the pairs don't have to move together all the time (as in correlation), they simply need to revert (rather than drift) and stay within a certain distance apart.

There are other tests such as the Phillips-Ouliaris test which attempt to account for structural breaks in the data.

In the case of the Engle-Granger two step method, the betas of the regression provide the trade sizes for the pairs. With Johansen, the eigenvectors are used to size the spread trade.

Con: Structural breaks (as in the empirical school) can't easily be identified before they happen and as a result trends can occur in actual trading that don't occur in testing. In addition, regression is an optimization method and as a result there may be a natural tendency for the spread calculation to be overfit.

Pro: Additional statistical tests such as the ADF (augmented dickey fuller) can be used to validate or gain some measure of confidence regarding whether a cointegrating relationship actually exists in the first place. But, it is worth noting that like all statistical tests, passing the ADF doesn't guarantee that the spread will remain cointegrated on new unseen data.

Summary
Perhaps the first question should actually be: should I use a mean reversion method in financial markets? Markets have fat tailed distributions and thus a mean reversion strategy starts off at a disadvantage vs. market structure. This basically means that pairs, and spread_s calculated from those pairs will have a natural tendency to not remain stationary and thus spread_s may not mean revert over the long term.

I had started writing a big post but it is obvious, not that related to pairs trading and a waste of space so deleted it. OP's points are more relevant than your question. Markets do have fat tails but ALSO have a tendency to revert to the mean (some more than others) and do it most of the time. When fat tails happen are predictable a lot of the time (major news announcements, market opens/closes etc). You are misinformed to think mean reversion strategies have a disadvantage.

Edit: not disputing your correlation and cointegration stuff, good information

Something you might want to look at that will get a lot of the retail crowd off side when I say it is averaging in. A lot of people who trade spreads and pair trade stocks, rather than say enter in their full position a one point, might enter half at one point, then another half at another point (if it gets there), or do it in thirds etc. You need to be flexible depending on the volatility of the pair and market conditions.

Personally, I would look at pair trading stocks or spreading other instruments rather than pair trading forex as you are effectively just outright trading a cross pair. Or maybe spreading a currency with another instrument rather than another currency.

If I could go back to the beginning of my trading journey or was recommending to someone how to get started in trading, I think pairs trading/spreading is a great way to go.

For those who are interested in understanding a bit more about the nature of the mean reversion disadvantage I mention:

http://www.quantifiedstrategies.com/...ng-strategies/

http://glynholton.com/wp-content/upl.../10/Skewed.PDF

This thread here http://www.forexfactory.com/showthread.php?t=262827 was the best attempt so far in FF. 7Bit was the most wicked coder to ever set foot on FF, he was light years ahead of anyone here.

yet he and all his followers were taken to the cleaners.There have been many attempts at basket trading with all the 'perpetrators' disappearing shortly afterwards.

here is one indicator what you guys can use
http://www.forexfactory.com/showthre...82#post6674382

it is like to know when one currency is strong or weak or confused, like trend or range
you can easily modify indicator to whatever currency you want or how you want to see things

i have for example for yen, everypair opposite by itself, so when everyone is same side, it is a possible trade,
yen is strong/weak

for example usdjpy mirror 12 in M5, and all other like same

like this, gbpjpy<->jpygbp 12, and when all other yen pairs looks like same, then it is a go

*bump

Another 1?

^Bump

bump


PS: I am more interested in #2

Hello everyone,

I had done extended researches on pairs trading, and there are some methods in the literature. Keep in mind that pairs trading is a own recipe in order to succeed, depending upon the markets you trade with pairs trading.

The methods are:

1. Statistical approch like the article of Gatev and Al 2006
2. The cointegration approch of Vidyamurthy from his book "Pairs trading: Quantitative methods and analysis" and the like
3. Stochastic spread approch (very few in the scholars talk about it)
4. Fundamental approch and TA approch
5. Fundamental approch
6. TA approch

I put some articles on the subject. The two first approches are more simple in term of calculation in comparison with the last one. In summary, the pairs trading strategy have to rely upon statistical evidence in order to be a winning strategy. After that, the methodology you use to find the pairs trading is your own recipe.

You could use correlation, cointegration or a mix or whatever, as soon as you are profitable!

Hello everyone,

Here is a simple pairs trading strategy on the eurobund/bobl futures. The two assets are very correlated.

The resultas are pretty good. I think the same strategy could be applied on the US bond futures market and the UK bond futures market as well.

Tell me more about it on this thread!