I look at Z-Score : Z(x) = (x-average(x))/stddev(x) Price 1 -> Z1, Price 2 -> Z2 Positively correlated pairs Dislocation Metric = Z(Z1-Z2) Negative correlated pairs Dislocation Metric = Z(Z1+Z2) I know that neither price, nor log price, is really normally distributed, but this corrects the first two moments. it also allows me to plot several things on the same scale. If I size my legs inverse proportionately to volatility (stddev), then the profit/loss of the pair trade is accurately represented by the visual difference in the Z(prices). The Dislocation Metric is then proportional to the profit/loss of the pair trade. It is more useful to scale it this way. Pair Trades between stock indices, for example, have Z(Price1)-Z(Price2) with a very small magnitude. For both highly positively correlated and highly negatively correlated markets, dividing out the standard deviation is essential to even vaguely judge statistically significance. Low Z-scores should have low statistical significance. In practice, small(abs) Dislocation Metric values tend to have little predictability. Much like two houses jockeying for position at the nose. High Z-scores should have high statistical significance. In practice, large(abs) Dislocation Metric values tend to revert. If a value gets too large, say +/- 4, I start to worry that the change has broken the underlying economic model. For example, a pair trade between Microsoft and DEC might have looked good fantastically profit potent until 1998 when Compaq bought it. Initially one could see the trade as two moving average (fast innovative poorly funded vs slow but well funded.) At some point, however, you have to say DEC is just not a competitor for Microsoft. I allow, at various times, for detrending, logging, labeling the cumulative normal distribution, walk-forward calculation, and different ways to back-adjust futures. I haven't found any of these to be terribly helpful. I have setup a crude website on my PC: http://toolkit.entonesoftware.com/Correlation/CorrOvODisplay.aspx Correlation/cointegration is helpful in finding tradables with an economic relationship. The big question, though, is finding valid economic relationships which are being stressed but which are now being restored. (For example, electricity price vs a ceramic manufacturer. If the manufacturer is stressed too much, they will change to a different business.)
As an update, you can also count me in the skeptical camp regarding the Forex EA but I've decided to give it a fair shot on a relatively small new account. ie with money that I could afford to lose. The signals given are not based on typical pairs trading. Rather, its a simple scalping system which runs on three currency pairs and only at a specific time each day. In fairness to Jared, I don't want to give any further details so please don't ask. The backtesting looks pretty good but, as we all know, that counts for squat when real money is on the line. So, its sort of an experiment for me in that I get to watch an automated system in action. I'll report the results in a month or so, assuming that there is some interest here- if I haven't, by then, woken up one morning to discover that the robot has decimated my account and forced me to relocate to a cardboard box under a bridge ;-) As for opening a foreign FX account, short of presenting a blood sample, they do require more documentary proof than the US brokers I'm familiar with. Guess thats to do with all the money laundering that's going on. Another irritation was the process of wiring funds. I had to inform the airhead at BOA ( God bless America - land of the free, home of the geographically challenged) that: 1) Limassol was not in Romania 2) Cyprus was in actual fact a sovereign state and not a new high-protein sports drink. Anyway, we'll see how it goes....
Can you guys pls share how you deal with rogue trades? I am not talking about the ones which diverge more, but more about the ones which do not converge well after diverge. For example, once in every 20 trades I usually have a pair which is loosing more money when it converges from 2.5Z to approx. 2.0Z and then starts to improve PnL again once it moves from 2.0Z towards 1.0Z. Also, how does anyone deal with drawdowns? From my paper trading for one month I've seen a couple of pairs which can loose up to 23% and then go down to -5% when converge around Z=0. This can be pretty dangerous when trading over the margin, however, I still not convinced that killing those at 25% is the right thing to do. I understand that no stop losses is probably a winning strategy for pair trading, however, I do no think that margin-related calculations are always taken into consideration. Finally, what do you think about pair trading penny stocks from time to time? If you guessed with the direction, returns can be huge (the same as losses, obviously). From what I have seen, I believe that it probably makes sense pair trading on them by using less order size and less leverage. Any opinions on this are very appreciated. Thanks and Merry X-mas!
My 2-cents. 1. Rogue trades. If the pair is converging and the trade profit/loss is is losing money, then your position sizing sounds to be incorrect relative to your Dislocation Metric. For example, if you trade $1000 to a side based on share price, and you are measuring the pair's convergence by Z-Score (standard deviation), then I see problems. A little more information about your trading would go a long way to understanding these âRogue Trades.â 2. Drawdown. I am a fan of using regular technical analysis for a Dislocation Metric (or ratio, if you prefer) graph. In my backtesting, a 25-day channel breakout system which waits for the Dislocation Metric to cross the 1.6Z line and a profit target at 0.1Z was profitable for most Futures pairs tested. It was a bit of a rushed job, though, so I am sure that there are more profitable systems possible. I would think that any good technical analysis system could be applied to the pair. There are just three provisos: pairs can take a long time to converge; too great a dislocation may reflect underlying changes which invalidate the pair; and, when the pair converges, don't be surprised if the pair jump around parity rather than sailing through with momentum. 3. Penny Stocks. I haven't traded or studied Penny Stocks with an eye for pair trading, but my opinion is that they would be poorly suited. Penny Stocks, to my understanding, are characterized as companies being restructured in the hopes of becoming profitable some day. So much depends upon the hopes and accounting of each stock, that I wouldn't expect common economic factors to be a significant explanatory factor in its variance. On a more practical note, the volatility of Penny Stocks is expected to be far from constant. This makes correct position sizing about impossible. For example AAA is at 20 cents on Monday and 40 cents on Tuesday. BBB is at 40 cents on Monday and 20 cents on Tuesday. No matter how you sized your position on Monday, and no matter how/whether you rebalanced on Tuesday, I don't see how you could be hedged against common economic factors on Wednesday. Anyone have any actual knowledge of pair-trading Penny Stocks? Best of luck, and Happy Holidays!
Any opinions about the pair DHI: Horton DR Inc vs PHM: Pultegroup Inc ? They have been 80-90% correlated until last year. They are both home construction companies. Starting in 2009, the tracking has been a little off, and especially starting 4th quarter of this year, PHM has been diving against DHI.
How about the pair BTI: British Amer Tobacco ADR , MO: Altria Group ? Two tobacco companies. Both have had new all-time highs (25 year) in 2010 Q4. Historical price correlation is > 90% over all long periods, but yearly correlation, especially daily return, is spotty.
How about the pair SCCO: Southern Copper , BHP: BHP Billiton ADS? Two of the largest copper producers in the world (SCCO 1st, BHP 3rd.) Long term correlation in the 90's and yearly correlation mostly > 50%. Pair started diverging 2010 Q4. For the leader, Southern Copper, I can't find any relevant news. The share prices is out performing copper, silver, gold, and platinum. Recently it is an incredible match for the CRB Index. I really don't understand why it is outperforming. For BHP Billiton, they have alot of press releases. It lost some money in Sept-Oct of 2010 on an Australian gas deal. It got blocked on an iron ore deal. It got blocked on a fertilizer take-over deal in Nov. After committing more money to the iron ore deal, a mining accident suspended a South African mine. This looks like a company with a run of bad luck. The only warning sign is that the stock is tracking copper quite precisely rather than underperforming. The pair is still pulling apart. Opinions? Is this pair worth watching?