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# Testing Pairs for mean-reversion

Discussion in 'Strategy Development' started by chs245, Feb 12, 2003.

1. ### chs245

I have been trading Pairs using entry and exit rules based on a standard deviation band around an average spread.
This seems to work fine, but I have heard that you can improve the performance of the system if you choose an additional mean reversion test for the pairs, called "cointegration".
It seems pretty complicated to do , and I'm wondering whether anyone here has tried implementing such a test to his pair trades. As far as I understand, cointegration is similar to examing visually a chart to check how often the spread of a pair crosses its mean. If it crosses its mean more than 5% of the time, than the spread is considered mean-reverting.
The trouble with some pairs is that they seem highly correlated, but don't revert back often to their means, ie you have to wait for a long time to realize your profits....

Anyone done cointegartion studies ???

Oliver

2. ### man

cointegration is a less strict concept than correlation, yet it requires some programming with matrices. we experimented with it mainly to define baskets of several stocks which move together. in contrast to correlation you can use the concept for more than two stocks.

anyways we are trading pairs but do not use cointegration at the moment. to define our pairs we are now using kind of least square methodology, but we think it would not matter to much of we used correlation or cointegration.

peace

3. ### chs245

What is the advantage of using lest square methodology over normal standard deviation bands ?
As fas as I understand, least squares are not "symetric", ie you would get different signals whether you regress FNM vs FRE or FRE vs FNM.

Oliver

4. ### man

we use a variation of least square, but it is not because we think it's superior but we just had it at hand. if you are really interested in it i have to come back after having looked it up in more detail.
what I am trying to say is that we find it not so difficult to find highly "correlated" (whatever measure you take) pairs but to trade this correlation. try to trade FNM-FRE, correlated between 0.8 and 0.8 on daily data. on daily data it is rather tough. thus correlation does not tell too much about tradeability IMO.

what could be interesting for you is that cointegration allows you to find triplets or quadruples instead of pairs. thus you trade on mean reversion to an equilibrium of n stocks rather than two. there are a couple of papers out there on cointegration where you should find useful information. we did not succeed in bringing a cointegration model above a sharpe ratio of 1.0, which is our absolute minium requirement for trading a strategy. but we might look it up again.

peace

6. ### sshakhshir

I have never known this as a tool to measure frequency or tendency towards mean reversion but I too focus on exactly this issue!

If you guys could provide any web links or book references, I'd greatly appreciate it.

It is very weird, I have simply "thought" my way into my methods for pairs trading from just brute force effort but have ended up doing things similarly to the institutional quant desks and hedge funds... affirmation feels good.

Regarding entry/exit times, I have been focusing almost exclusively on entries at the end of day with exits late on the following afternoon and, occasionally, holds for another night or two. Do others find other timeframes adequate for stat-arb type pairs trading?

8. ### chs245

That would indeed be intersting, but I don't have enough math background, nor the necessary software packages to do that. Currently I'm studying pair spreads only in the context of a 60 day st dev band and enter the trades at the close of each day. Average holding period can be quite long (30 days or more). It is pretty low risk if you have enough pairs, but the payoffs are moderate, but still big enough to do it.
I'm still looking to improve the performance, by setting max holding period and stop loss limits, comparing 60d st dev to 200d st dev etc, but it seems difficult to significantly improve the performance significantly.

Oliver

ten days.

10. ### chs245

I calculate my spread as (SharePrice(2)/SharePrice(1))*SharePrice(1) - SharePrice(2)