Statistical Arb/Pairs trading strategy!

I think that subjectivity is the core of this sytem and this is the only way it can work: not fixing the scales and taking whatever profit or loss you have when charts visually touch. Because if you start looking at charts objectively (set the same fixed range), they just never actually touch.

I donā€™t think the range is larger, ADR for EU and GU is pretty much about the same.

As for trading different lot sizes, you shouldnā€™t really be doing that, otherwise you are basically saying that you know which currency is likely to move more (or less) than the other. This whole strategy is based around being market neutral and in order to do that, you need to have the same position size (in dollar value) for each instrument.

You do touch on the point about when to close the trade. What we are trying to do is pick up small movements where the currencies move in opposite directions, and then wait for them to come back together. So, when to close the trade should be when the currencies come back together. However, if we are not careful, what we will actually do is pick up genuine divergences between the currency pairs. This is when they donā€™t actually come back together, and this is when we start asking ourselves when should the trade be closed.

Hi, I would agree with you for the most part, but if you did not adjust your lot size, I belive you would not be in a market neutral position,

Please check this image:



06:31 EST
Green line is EURUSD
Blue line is GBPUSD

When measuring the pip difference from EURUSD, the difference is 21pips, if you meassure the GBP range, the difference is 30 pips.[EDIT] I am measuring the ā€˜spreadā€™ on the close/current price of each pairā€¦

If the market should go against you here, (dvs North) withouth touching, the GBPUSD would go move longer in the same ā€˜visualā€™ distance than EURUSD, and with equal lot size, GBPUSD would be more in the negative side than EURUSD would be positive at the same ā€˜visualā€™ distance, and if the met at the top, instead of retracing back to middle ground, you would be at a loss.

Please tell me if I am wrong, because then I seriusly would need to reconsider my math :open_mouth:

ok, I be honest and say I canā€™t quite get my head round this overlaying of two different charts, and how you are comparing the movements between those two different charts. The only way overlaying two physically different charts on top of each other would work was if both charts had identical scales, and movements on one chart equated to exactly the same movements on the other charts.

If the scales are different, it just wonā€™t work. I guess this is why you are equating movement with differing lot sizes. What I do know is that normally, to compare two different instruments, you have to equate the movements of one instrument in terms of the other.

As an example imagine your two charts were not financial instruments, but were in fact the speed of two cars. One chart is in miles per hour and the other is in feet per minute. You can see the first car is travelling at 100 mph, and the 2nd is moving at 10,000 fpm. Which is moving quicker? Given no other information, there is simply know way to tell. You could overlay these charts as much as you want, there would be no way to know which car was moving quicker.

Further, if the chart on the first car moves to 110 mph and the other chart moves to 10,500 fpm, which speed has increased the most? It is simply impossible to knowā€¦ However, if I tell you that 100mph = 8800 feet per minute, we can easily rescale the movements of one, into the other. 10,000 feet per minute = 113 mph.

Same comparison with these charts. The only accurate way to do this is to have one chart that shows both instruments. To do that you would take one chart/instrument and then re-scale the 2nd instrument so that it uses the scale of the first instrument.

Some charting packages do this for you. A good example is Yahoo which allows you to overlay one instrument onto another. All it is doing is rescaling the instrument. MT4 doesnā€™t do it out of the box, but you can add an indicator to do the same thing.

Once everything is rescaled, then you can directly compare the movements in the two instruments. If you traded both, you would trade identical lots sizes and behind the scenes, the instruments are moving the ā€œcorrectā€ amount for your lot sizes to balance out.

Hope that helpsā€¦

Hi, after your example, my point, to get both cars driving at different speed, to cross the finnish line simultanisly, you would need to handicap the fastest car(lower lot size), so they would be even. In your example it is possible to know the exact handicap you need to use, but in trading, since this is not possible, Im going to use the latest possible messurment, so, in my example, I would need to adjust the lot size aproxmetly 3:2, and hope the scale does not shift until the trade is closed :slight_smile:

Something I will implement in my final strategy, would be take the latest meassurment and even it out to the average ā€˜scaleā€™ after some period, to get the highest chance of a successful trade :slight_smile:

[EDIT]
What Iā€™m also wondering is if I should take my 2% and have 1% on each trade, or have a full 2% on each?

Lets try and bring this back to finance :slight_smile:

Visually, your lot sizing has been taken care of by the rescaling. Lets talk about the Dow and the S&P as an example. If you rescale the S&P up to the dow level (by multiplying everything by 10), then a 1 point move in the S&P equates to a 10 point move in the Dow.

Now lets say we get a 30 point gap in our new scale, we must trade equal lots. You wouldnā€™t trade 10 lots in the S&P and 1 in the dow because the S&P only needs to move 3 points in actual terms. If you change the lot size for the S&P, you would need it to move more (or less) than the 3 points, but hte poiint is, we don;t know which way the S&P is going to go, we only knowthere is an imbalance.

There is another way to work it out based around buying or selling in a ā€œperfectā€ hedge. ignore spreads and everything hereā€¦
So with the 3 currencies GU, EU and EG if you trade 1 lot :

buy 1 GU
Sell 1 EU
you are net USD flat, and effectively traded short 1 EG

However if you
buy 1 GU
sell 0.7 EU
Not only do you have a short position of 0.7 EG, but you also have exposure to the USD as you are still short 0.3 USD!

And that is most definitely not market neutralā€¦

Perhaps Iā€™m not explaining it well enough, but trust me, lot sizes must remain the same in both positions, otherwise the trade doesnā€™t balance out. I have an article about this somewhere, let me see if I can dig it outā€¦

Just saw your edit. The 2% operates slightly differently when trading this strategy. If 2% is your risk then you need to work out at entry, how far apart you anticipate the spread widening by. Lets say some pair has widened by 40 pips. It then closes to 30 and you think this is a good time to enter. Your analysis shows that in the last month the most it has widened to is 80 pips. 80-30 = 50, so you work out the lot size based upon a 50 pip ā€œstop lossā€. You then buy/sell each trade at half the calculated lot size.

However, note that you canā€™t set a SL (or TP) on the trades, you have to monitor and close the trades manually. This is because, both trades will ebb and flow together and might move say 100 pips up (because they are so tightly correlated), before the gap finally closes.

Hi, I will read this many times, and try to understand, I dont know if this is off topic or what :confused:

Shouldnt you be EG neutral? I didnt get that part, and then I didnt get the other part at all :frowning:

If GU moves say 1.5 times farther then EU on the same visual scale(10$profit target), if it would meet in the middle you would get 6.6 dollar in profit from GU Sell, and 3.3$ in EU Buy.

But if price meet above GU entry say 50%, then GU would be down (i dont know how much) and EU would not reach up in profits, so you would be down some amount

If price meets below EU entry say 50% you would be highly in plusā€¦

This is ofcourse if the ratio dosnt change, and GU moves more between highs and lows than EU.

If you find that article you have written about this, I would really appreciat to read more about this :slight_smile:

I like thatā€¦ :slight_smile:

All currencies are pairs, so you are always buying something and selling something else. There are always 3 currencies involved in the "currency triangle"
So
Buy 1 GU means you are long 1 GBP and short 1 USD
Sell 1 EU means you are short 1 EUR and are long 1 USD

This means you are 1 USD short and 1 USD long, so are net USD flat, and thus have no exposure to the USD.

That leaves you with the 1 GBP that you bought and the 1 EUR that you sold, so you are net short 1 EURGBP (or net long 1 GBPEUR).

Now, the EUR, GBP and USD can do what ever they want, they can go up, they can go down, what ever. Ultimately, you will only make money when the EUR weakens against the GBP, i.e. the EURGBP actually moves down. Given that this trade is taken on the theoretical imbalance between the GU and EU, a small move down in the EURGBP is likely, hence why the trade was taken.

So now you know what net position you have, lets take a look what happens if the markets moves.

If the GU goes up and the EU stays flat, and all other things are equal, you make money. This is because if GU is up and EU is flat, EG has to be net down and you have a net short EG position.

Correspondingly, if the GU goes down and the EU stays flat, the EG is net up, so you lose money.

If the GU goes down a little and the EU goes up a little (the same amount), the GU / EU pair are diverging further, so you lose money.

Finally, if the GU goes up, and the EU goes down, you rake in the cashā€¦ :wink:

I did find the article, but it is not how I remember it. It talks mostly about trading the correlation with options. However, if you are interested:

http://mediaserver.thinkorswim.com/articles/TPPairsTradingArticle.pdf

Trading correlation with options is how the big boys do it. If the position moves against you (i.e. there is a genuine divergence in the price), all you have lost is the cost of the options. Trading forex correlation is more like trading straight equities in that, if the price moves against you (the gap widens), you lose money all the way until you close your position.

Thanks for the in-depth explanation, Ill keep re-reading this :slight_smile:

No problemā€¦ :slight_smile:

Actually, as I was looking into the various ways of pairs trading, I was reading a few articles that suggest that it is very hard to pick up the short term fluctuations in the correlation. Rather than trying to quickly trade these correlation changes, we should be looking for longer term divergences.

It certainly looks like a safer way of doing it as it is less likely that the position will move against you. It is the same strategy in principle, you wait until two well correlated instruments have diverged by 2 standard deviations, and then place the buy/sell trades.

It is longer though, typically days/weeks, so if doing it by trading CFDā€™s (or spreadbetting in the UK) you would probably also want to look at the financing charges and make sure the trades were also in the same direction as the interest rates (i.e. just like carry trades, etc).

Iā€™ll look into it next weekā€¦

Thanks Jedster, for your explanation.

Iā€™m then making this rules to have a more mathematical way to trade this.

Choose 2 pairs that are highly correlated, with 90 % or more on W1, D1, H4, H1 and M15 (this for the first time)

Then, everytime the H1 and M15 are above 90 % you configure the MT4 charts on Scale fix, placing the max and min based on current price +/- 1 daily ATR or about 10 times the standard deviation (of 1 day of minutes, in 1 minute time frame, or 1440 minutes) of trading time frame (1 minute view for me). That should keep the price inside the chart for at least that day.

Because the price is very well correlated at the time of picking the scale fix, you will see very correlated lines at the center of the charts.

When the prices diverge for about 1 or two standard deviations (in EU/GU 1 deviation on 1 minute view is about 20 pips), you follow Keltonā€™s indications.

Because the scale donā€™t change over time, when price converge again, you will be winning.

For lot size, I use a percent of my account. If I want to win 2 % of my account on a spread of 20 pips, I calculate the lot size to win that percent if it moves 20 pips, on both pairs. If I had 1000 USD, and want to win 2 % of the account on a move of 20 pips (20 USD), then I size my trade so each pip is 1 dollar. That is about 0.1 full lots on EU and GU. So, if the spread between EU/GU is 20 pips, I place a trade like Kelton says, and when they touches again, I will win 20 pips, maybe 10 on EU and 10 on GU, maybe another combination.

After that, I go again to move the scale fix when the correlation on m15 and h1 is above 90 %. I need to wait until this to start with a highly correlated chart.

So far, this is working good. This generated about 4 trades tonight, all winners, winning about 2 % on each one, on a demo account.

Yes, I definitely agree that there should be a clear way to determine when a pair is correlated and when it moves away from the correlation so that it can be traded.

There is another way to measure correlation divergence and that is to work on the ratio from one instrument to another. That is, you simply divide one instrument value by the other and this gives the ratio beween them. This was what I was talking about in previous posts. If this ratio was plotted on a chart, it would show how much variance there has been in the correlation between 2 instruments. Using this as a meausre it is relatively easy to see when the correlation has diverged and thus when to trade.

Again, agreed, we are looking for some statistical measure of how much 2 instruments have diverged. Any consistent method should be sufficient. Interestingly, it turns out another good way to do this is to look at the standard deviation of this ratio that I mentioned above.

That is a clear way to set a profit target, which is good, but if your profit level based around 2% what and how are you setting your stop loss/exit strategy ? This leads onto a second part/questionā€¦

You are opening trades when the pair diverge by 2 standard deviations, which you say is about 20 pips, but if the pair regularly diverge by (say) 50 pips, then you could potentially be setting yourself up for a loss (or certainly a period where your positions are sitting at a lossā€¦) It would appear to me that the GU and EU regularly diverge by this amount, so we need to make sure we are not over exposedā€¦

So far I have only have a few trades and they have all been profitible, but that is because I basically left them open until the prices came back together. I donā€™t know yet if that is a viable long term strategy.

[I]"ā€¦What I do is wait untill something upsets the two currency pairs
that makes them fall out of correlation. Then I buy the underperforming currency and short
sell the over performing currency at the same time and the same lot size. Eventually these
currencies will go back to their normal path and touch again. I then close both orders and have
now profited the distance between the two when I opened the ordersā€¦"[/I]

I have two questions. Is it 100% sure that the pairs will go to their normal path and touch again? What if a gap starts off and is maintained forever? The correlation can still be high afterwards and after a while, the chart will make the overlay perfect because the gap will be out of sight.

Also, has anyone tried indicators? On another forum, someone suggested to use Bollinger bands on the resulting pair. For instance, if price on EURGBP touches the upper BB, it would be time to sell EURUSD and buy GBPUSD.

Thanks for answering.

Read more: 301 Moved Permanently

This is a point that is often raised (long GU, short EU = short EG), but when you get down into the nitty gritty of the calculations there remains some residual USD. While it is true that when you trade equal amounts of GU long and EU short, the GBP and EUR positions offset. However, a small exposure to USD remains due to the price differences between EU and GU. If the prices of the two instruments (EU and GU) were identical then yes, the USD component would completely cancel out and long GU short EU would be equal to EG. However as per this example:

Long 10,000 GU @ 1.601
Short 10,000 EU @ 1.334

To calculate the USD portion of the GU position take 10,000 * 1.601 = 16,010 USD short.
For EU the equation is 10,000 * 1.334 = 13,340 USD long. Taking the difference you are still left with a residual USD position of $2670 short. This is true because you must borrow more USD to finance your GBP purchase (due to the higher price) than you must borrow to finance your EUR sale.

The USD portion is smaller so it will have less influence on the P&L than the EUR or the GBP, but there will be some influence from USD moves.

Firstly, what I wa talking about was theoritical to explain the principle. On a practical basis, yes you are correct there are minor exposures, but it shouldnā€™t be anywhere as big as in the example you were using. If it were, then people would be trading it and the broker would be losing money hand over fist.

I wrote down 3 prices a few days ago:
GU 1.5901
EU 1.3297
EG 0.8362

If you do GU * EG = 1.5901 * 0.8362 = 1.32964 which is 0.00006 different from the quoted EU price.
So the three currencies are in (almost) perfect balance. Note that this 0.00006 difference was because the prices were only to 4dp, if I had written down the numbers to 5dp, it would have probably been even closer.

The reason you are seeing that exposure I suspect is due to your brokers pricing/spread. If you do the calculations ignoring spread, the exposure would be literally a few points, relating to how the broker has updated their prices at that time.

If it isnā€™t, it would mean the broker was losing moneyā€¦and that is an entirely separate strategy. If you were quick enough, it would be possible to take advantage of where the broker has been unable to update their price in a quick moving or highly volatile market. However the spreads would have to be very tight for that to work, literally 1 or 2 points (not pips but 1/10th pip). On a practical basis, there are no brokers that quote in the retail market with spreads that tight. Well, not that I know of anywayā€¦ :slight_smile:

Iā€™m designing a strategy to trade this technique.

I think that when placing an order, to be best balanced, i need to check the average moves of both pairs.

Let say, that Iā€™m going to trade EU and GU. I measure the average move on a daily basis on both, having EU move 123 pips and GU 100pips (an example! hehehe)

I want to win 2 % of my account on a spread between EU and GU of 20 pips, but at the same time I want to have a trade that is near to perfect neutral trade.

If I place 1 lot on GU and 1 lot on EU, the trade will be unbalanced, because if I use the average move of both, when GU moves 10 pips, the EU could be moved 12.3 pips, and because the pip value is the same, that means that the trade becomes unbalanced for 2.3 pips. So I need to redistribute the lot size acording to this average move.

Iā€™m going to trade 2 lots, and I know that there is a proportion of EU/GU of 1.23, I then use this formula

1-(ATR pair 1)/((ATR pair1)+(ATR pair2)) to get the percent of that 2 lots for each pair.

I want to get the volume for EU, so I use (1-123/(123+100))=44.84 % of the 2 lots, so the total size for EU should be .8968 lots, and for GU it should be 1.1032 lots, and that should make that a move of 10 pips on GU is equal in price for a move of 12.3 pips on EU, making a more balanced and neutral position.

This is just an idea, and Iā€™m going to test it on this week. What do you think about it?

No it is absolutely not 100%. The big question is, when is the change due to a genuine correlation divergence, and when is it due to an actual change in the value between two instruments. All you can do is look at the history of two correlated instruments and see how often they diverge and by how much. You can then decide that when you see a 20 pip divergence, youā€™ll trade it, or that youā€™ll wait because quite often it goes to 40 pips, or 70, or 100ā€¦ Looking at the history is very revealing and very important in order to help you form your plan as to when to enter, and when to exit.

In some respect that does make sense. Bollinger bands show 2 standard deviations away from the mean, and that is often regarded as a good point to enter the market. However, you are not trading one instrument, you are trading the divergence between 2 and I am not sure how you would see that using standard bollinger band I think you would have to write a custom indicator specifically to do thatā€¦

Do you mean you are designing a strategy to trade the imbalance between a brokers prices on a triangle of currencies, such as the GU/EU/EG ?

If so, I am interested in that so I suggest you start a new thread and get a discussion going, separate to this thread. I looked extensively into trying to trade the imbalance. I wrote an EA to automatically detect it and trade it. Theoretically it is possible, and it definitely works, but in practise it can only work if your broker has really tight spreads. If your broker has spreads something like 1 or 2 pips, then that is wide enough that you only get 1 trade every blue moon. You need really tight spreads in order for this to work, so something like 0.5 pip max.

Yes, I agree with that. We need to look historically and see what is a typical move/divergence for the instruments.

Nope.

Iā€™ve been thinking for quite some time how to explain this clearly, and I am obviously struggling. I know what I know, but trying to get it written down is really hardā€¦I was talking with a trader friend this evening in the pub and we were speaking about this very point. I will try to explain and Iā€™ll start by saying, I think the issue gets confusing because the EU and the GU trade very close together.

That is, the EU is trading at 1.30 and the GU at 1.60, so they appear to be comparable. You would think that a 10 pip move in one is the same as a 10 pip move in the other, but that is not true. They are only comparable if you convert one into the terms of the other. I posted earlier about this using the example of cars, but instead of that, try to see each instrument denominated in it own unit. Iā€™ll try to describe this. Lets say the GBPUSD is denominated in units of GU. The EURUSD is denominated in units of EU. EU and GU units are not the same. They look very similar, they are close to each other and they are related to each other, but they are not the same. So, a 10 pip move in GU units is not the same ā€œvalueā€ as a 10 pip move in EU units. However, using your example, a 10 pip move in GU units IS the same value as a 12.3 move in EU units. It is all relativeā€¦

A better pair to explain this with is the Dow and S&P. They are approximately 10 times apart (the dow is 13000 and the S&P is 1400). You canā€™t get mixed up talking about these. A 10 point move in the dow in real terms, approximately equates to a 1 point move in the S&P, but you still trade 1 lot in each. You donā€™t trade 10 lots in the S&P because it is only moving 1 point compared to the 10 point move in the Dow. Same thing with the EU and the GU, it is just that the EU and GU are actually much closer together, so the distinction is harder to see.

Um, ok, youā€™ve got me :slight_smile: I am completely lostā€¦ :15:

The ATR is a measure of volatility, why is it relevent in determining how far two correlated instruments have diverged? All it is telling you is that one instrument is more or less volatile than another, it is not an indication of how they are correlated.

How about you rework your example using the hypothetical dow and S&P:

The dow trades at 14000, the S&P trades at 1400. Lets ignore spreads here as it is hypotheticalā€¦

A typical daily range for the dow is 150 points, and also 150 pips because the precision of the dow is to 1.
A typical daily range for the S&P is 12 points which is around 120 pips because the precision of the S&P is to 0.1.

1 lot for the dow is 10 points (10 pips).
1 lot for the S&P is 1 point (10 pips).

The two are highly correlated, so if the dow moves to 14050, the S&P typically moves to 1405.

Lets say our dow now moves 20 points up, but the S&P stays flat. You see this divergence, what do you trade?

Iā€™ll tell you what I will do. I will sell 1 dow and buy 1 S&P.

If the S&P stays where it is, and the dow moves back to where it was, I close my positions at +20pips.

If the dow stays where it is, and the S&P rises to join the dow, I only need the S&P to rise 2 points and I have also made +20pips.

If the dow drops 10 points and the S&P rise 1 point, again I close my positions as I am +20pips.

I thinks that is all the information needed, so, what would you trade an why?