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concurrent uncorrelated positions

  • #1
  • First Post: Edited Apr 18, 2009 11:24pm Jan 3, 2007 1:10pm | Edited Apr 18, 2009 11:24pm
Double or triple your return without increasing risk: sound too good to be true?

The answer is to trade concurrent (or overlapping) uncorrelated positions.
Let me try to explain the underlying mathematical principles, by using a casino based analogy.

Let’s assume that a casino operates one Roulette table, which provides N trials (spins of the wheel) per hour, and that this results, on average, an hourly profit to the casino of X% of its capital base. It should be obvious that, if the casino adds a second table, so that both are operating concurrently, the number of trials per hour will increase to 2N, and hence the profit to 2X%.

From a money management angle, the big question is: does the casino now need to double its capital reserve, in order to maintain the same risk of drawdown?

The answer is “no”, because the risk of drawdown remains unchanged, no matter how many tables are added. Here’s why.

The probability of gain or loss on each individual trial is (of course) the same. Moreover, the distribution curve of outcomes over N trials is unchanged, regardless of the time frame over which the trials are held. As an example, if 100 trials are executed, it doesn’t matter whether we run 1 trial per day, 1 per hour, 1 per minute, or 1 per second, the probability of obtaining a certain outcome (e.g. 10 successive losses) is identical, except that at 1 per second we’re going to reach any given outcome 86,400 times as quickly as 1 per day. Extrapolating, if the 100 trials were executed concurrently, the risk of drawdown still remains the same, while profit or loss will occur 100 times as quickly than if the trials were consecutive. We are simply leveraging time.

Hopefully it is apparent that we can apply the same rationale to trading. By trading two uncorrelated positions concurrently, we (assuming positive expectancy) double return without increasing risk. By trading three positions, we triple return, and so on. However, the key is this: the trials must be completely independent of each other, i.e. the outcome of one trial must in no way influence on the outcome of another. In other words, 0% correlation.

-- Trading ten simultaneous positions that are 100% correlated, with 2% risk per position, results in a total net exposure of 20%.

-- Trading ten simultaneous positions that are 0% correlated, with 2% risk per position, results in a total net exposure of 2%.

This whole discussion again further highlights the fact that money management does not alter expectancy; it simply accelerates or decelerates the rate at which one attains financial freedom, or total ruin. Expert money management on its own is not enough. Like the Roulette game where the casino sets the odds so that it invariably has an edge, one must somehow employ a system of entries and exits that delivers positive expectancy. However, in an activity like FX where price movements are the result of complex “intangibles” like economics and sentiment, then unlike Roulette, the probabilities of each trial outcome can never be precisely calculated.

For more information, read Chapter 8 of Dr Ryan Jones' book The Trading Game: Playing by the Numbers to Make Millions.
  • #2
  • Jan 3, 2007 1:22pm Jan 3, 2007 1:22pm
I've been thinking the same thing. That is why I am going back to the "daily range strategy" thread. The strategy does seem to give a positive profit in the long run over gbp/usd although it may not be the most efficient. What I'm like about it though is that it is dead simple. This way it would be easy for me to monitor the strategy over many pairs. So long as my account can handle having many positions open over several pairs my account should grow faster than just trading one pair.

The question I have is that for each pair you're going to have different expectencies though. One pair will be 70% successful and another maybe only 45%. Do you gain any edge by trading the 45% successful pair or would you be better putting all the money into the 70% successful pair? Are we only looking to increase the number of trades executed without affecting our success rate; assuming that by trying to increase our trade frequency on one currency drops the success of the trade? I'm wondering. Matt
  • #3
  • Jan 3, 2007 1:32pm Jan 3, 2007 1:32pm
This is something that Ed Thorp talks about in his book The Mathematics of Gambling...

What really could make this exciting is if one employed a Kelly type risk calculation to the process. Knowing that as the return inceases the risk does not . So, one should be able to proportion the risk over several un-correlated
trades. Thereby allowing the maximum to be risked to perform at the maximum level and never reach the level of ruin. What do you think?
  • #4
  • Jan 3, 2007 1:55pm Jan 3, 2007 1:55pm
Lots of folks go here for correlation data:



http://www.mataf.net/en/analysis-correlation.htm
  • #5
  • Jan 3, 2007 1:56pm Jan 3, 2007 1:56pm
The beauty of employing a Kelly like approach is that if the expectancy is not positive, Kelly formula says do not bet, by showing a negative % of risk. The reason I say like kelly, is because one would have have balls of steel to stand the draw downs that can occur with this type of formula... But, a modified version of say 1/2 kelly, could produce very optimal results.
  • #6
  • Jan 3, 2007 2:19pm Jan 3, 2007 2:19pm
Unfortunately, when it comes to currencies, there is no true independence. It may seem that some pairs may be more independent than others, but in the end, all currencies are interrelated. If one currency moves extremely far, it affects the value of every other currency in the world. Look at when the coup for Thailand went down recently for example. Its change reverberated throughout the forex market. You have to remember, barring spread costs, the exchange rate for all currencies is balanced. If you buy euros with usd, then buy yen with euros, then buy mexican pesos with those yen, then buy canadian dollars with those pesos, then buy usd back with those canadian dollars, you will have exactly the same amount you started with (barring the market didn't change during all those transactions). What effects one effects all, but in different ways. When we buy/sell on the forex market, we are essentially only trying to gain on the change in value for one currency pair.

So, the statistical method of using concurrent casino strategies here I believe would be invalid as there is no true independent currency pairs. If the eur/usd changed value and didn't effect the value of the usd/jpy or the nzd/jpy or whatever pair because they weren't tied together, then you would have true independence, but its not the case.

Remember, the currency markets must balance across the board. Otherwise, people could make instant money by buying mismatched currencies. Trust me, the banks would never allow this.

GirlFlyer
  • #7
  • Jan 3, 2007 2:24pm Jan 3, 2007 2:24pm
Yes I see your point here and of course it is correct, but I wonder if there is a way to create a net neutral position using other instruments, besides spot currencies... Hmm I'll have to think about that.



Quoting GirlFlyer
Unfortunately, when it comes to currencies, there is no true independence. It may seem that some pairs may be more independent than others, but in the end, all currencies are interrelated. If one currency moves extremely far, it affects the value of every other currency in the world. Look at when the coup for Thailand went down recently for example. Its change reverberated throughout the forex market. You have to remember, barring spread costs, the exchange rate for all currencies is balanced. If you buy euros with usd, then buy yen with euros, then buy mexican pesos with those yen, then buy canadian dollars with those pesos, then buy usd back with those canadian dollars, you will have exactly the same amount you started with (barring the market didn't change during all those transactions). What effects one effects all, but in different ways. When we buy/sell on the forex market, we are essentially only trying to gain on the change in value for one currency pair.

So, the statistical method of using concurrent casino strategies here I believe would be invalid as there is no true independent currency pairs. If the eur/usd changed value and didn't effect the value of the usd/jpy or the nzd/jpy or whatever pair because they weren't tied together, then you would have true independence, but its not the case.

Remember, the currency markets must balance across the board. Otherwise, people could make instant money by buying mismatched currencies. Trust me, the banks would never allow this.

GirlFlyer
  • #8
  • Jan 3, 2007 2:24pm Jan 3, 2007 2:24pm
I've got a question.

When you trade two different pairs, you may select different entery times and different exit strategies. Why correlation is so important then?
  • #9
  • Jan 3, 2007 3:32pm Jan 3, 2007 3:32pm
Quoting GirlFlyer
Look at when the coup for Thailand went down recently for example. Its change reverberated throughout the forex market.
With all due respect, and I do enjoy your posts, there are no obvious signs of any market reaction surrounding the coup in Thailand.
  • #10
  • Jan 3, 2007 7:20pm Jan 3, 2007 7:20pm
Quoting aparsai
I've got a question.

When you trade two different pairs, you may select different entery times and different exit strategies. Why correlation is so important then?
If you're using the same strategy for both pairs then if they're correlated pairs they will very often give you the same entry times. Even if they give you different entry times, they will tend to end trades very similar, both winners or both losers. So it doesn't make sense to trade two pairs that are very correlated. You won't get many more trades. It'll be the same as trading one pair, but with twice the number of lots than your standard trade.

So its beneficial to trade uncorrelated pairs, because if they don't have the same trading pattern then while one could be in a bad trading pattern, the other does not follow the pattern and could be trading well. If they were correlated they would both be trading poorly. When we assume that our trading system is profitable then it is a given that even uncorrelated pairs will both be trading well more often than not. We will experience massive drawdown if all the pairs start losing at the same time, which is what would happen when we trade correlated pairs. Thus, trade uncorrelated pairs for just as much/more profit, but not as much drawdown. Adding uncorrelated pairs to your trading almost acts as a hedge since when one pair is losing there is a very good chance the others are winning or helping to alleviate the losses. Matt
  • #11
  • Jan 4, 2007 10:40am Jan 4, 2007 10:40am
Quoting permanentjaun
If you're using the same strategy for both pairs then if they're correlated pairs they will very often give you the same entry times. Even if they give you different entry times, they will tend to end trades very similar, both winners or both losers. So it doesn't make sense to trade two pairs that are very correlated. You won't get many more trades. It'll be the same as trading one pair, but with twice the number of lots than your standard trade.

So its beneficial to trade uncorrelated pairs, because if they don't have the same trading pattern then while one could be in a bad trading pattern, the other does not follow the pattern and could be trading well. If they were correlated they would both be trading poorly. When we assume that our trading system is profitable then it is a given that even uncorrelated pairs will both be trading well more often than not. We will experience massive drawdown if all the pairs start losing at the same time, which is what would happen when we trade correlated pairs. Thus, trade uncorrelated pairs for just as much/more profit, but not as much drawdown. Adding uncorrelated pairs to your trading almost acts as a hedge since when one pair is losing there is a very good chance the others are winning or helping to alleviate the losses. Matt
Let me be specific and then based on that we can probably continue this discussion. I've heard a lot of times that GBPUSD and EURUSD are almost fully correlated (i.e. they move 98% of the time in the same direction).

I use a MetaTrader Expert Advisor to trade both pairs. The system is the same. It's basically a breakout system with some adjustments. However, it analyzes the EURUSD movements around 10:00pm EST and GBPUSD next morning around 6:00 am EST. So it never enters the EURUSD and GBPUSD trades at the same time.

When it enters the GBPUSD trade the market conditions are usually different from the time it entered the previous night EURUSD trade. That's why sometimes it enters EURUSD long and GBPUSD short and both end up either in loss and/or profit. It also uses different TP and SL levels.

Although the price movements of both pairs at a specific time are very similar but depending on the following factors the outcome of your strategy to trade these pairs can be near to indepent:

  1. Time of entry
  2. Exit strategy

Most people see one side of the story which is the currency pair correlation but the other side which is your system of trade can make trading corrolated pairs almost independant of each other.

I believe even if you trade both pairs at the same time, depending on the "exit strategy" you might see some level of independency. The same is true if you use different entry times but similar exit strategies.

  • #12
  • Jan 4, 2007 11:27am Jan 4, 2007 11:27am
Whats the point in doing that? If they trade so similar to one another why not just trade gbp/usd in both time frames? It wouldn't make a difference since they trade so similar to one another. You may be trading gbp/usd and eur/usd, but really you're just trading one currency since they trade so similar. IN your definition then gbp/usd could be two pairs itself. The gbp/usd in the morning is different from the gbp/usd at noon. It's still just gbp/usd, but the signals have changed.

If you trade uncorrelated pairs then it makes a difference because at almost any point in time you could get signals different from correlated pairs. eur/usd will almost always give you a buy signal when gbp/usd would. There is no divergence. So when gbp/usd is ranging, most likely eur/usd is as well. That can be bad. I think it is better to look at uncorrelated pairs so you're experiencing your prime market conditions more consistently than all of your pairs giving you profit or loss. Your account will be much more volitile and experience larger drawdown. Matt
  • #13
  • Jan 4, 2007 12:22pm Jan 4, 2007 12:22pm
Quoting aparsai
Let me be specific and then based on that we can probably continue this discussion. I've heard a lot of times that GBPUSD and EURUSD are almost fully correlated (i.e. they move 98% of the time in the same direction).

I use a MetaTrader Expert Advisor to trade both pairs. The system is the same. It's basically a breakout system with some adjustments. However, it analyzes the EURUSD movements around 10:00pm EST and GBPUSD next morning around 6:00 am EST. So it never enters the EURUSD and GBPUSD trades at the same time.

When it enters the GBPUSD trade the market conditions are usually different from the time it entered the previous night EURUSD trade. That's why sometimes it enters EURUSD long and GBPUSD short and both end up either in loss and/or profit. It also uses different TP and SL levels.
[...]
I believe even if you trade both pairs at the same time, depending on the "exit strategy" you might see some level of independency. The same is true if you use different entry times but similar exit strategies.


From the teoretical standpoint the corelation between currencies is one thing and the correlation (or not) between the results of two systems on two different pairs in another.



IMHO it should be calculated on individual basis, and under certain conditions I can imagine two systems even on the same pair with uncorrelated results (for example first long term on D1, second scalper on M1).
Quidquid latine dictum sit altum viditur
  • #14
  • Jan 4, 2007 12:42pm Jan 4, 2007 12:42pm
Quoting hanover
From a money management angle, the big question is: does the casino now need to double its capital reserve, in order to maintain the same risk of drawdown?

The answer is “no”, because the risk of drawdown remains unchanged. To those who are in doubt, here’s why.

The probability of gain or loss on each individual trial is (of course) the same. Moreover, the distribution curve of outcomes over N trials is unchanged, regardless of the time frame over which the trials are held. As an example, if 100 trials are executed, it doesn’t matter whether we run 1 trial per day, 1 per hour, 1 per minute, or 1 per second, the probability of obtaining a certain outcome (e.g. 10 successive losses) is identical, except that at 1 per second we’re going to reach any given outcome 86,400 times as quickly as 1 per day. Extrapolating, if the 100 trials were executed concurrently, the risk of drawdown still remains the same, while profit or loss will occur 100 times as quickly than if the trials were consecutive. We are simply leveraging time.
Hi David, here is my [independent] and [uncorrelated] I hope humbleopinion

1. Risk of drawdown actually increases and casino should increase its capital, not necesarily double but increase. Two arguments: imagine real life situation when on both tables casino loses. Is it possible? If yes, then casino should increase capital for operational safety.

Second one - suppose that every 100 days there is one drawdown on average on single table. If for 2 tables risk remains unchanged then the same is true for 100, 101 or arbitrary number of wheels.

But - over 100 wheels we have: one table daily will experience ruin, over 200 - TWO on average experience ruin so in this case we are almost SURE that we should have casino's capital doubled. In fact we shoud for safety actually have capital multiplied by x where x is maximal but reasonable number of drawdowns. we can assess this taking into account probability of one drawdown a day per table and number of tables and also past data.

Quoting hanover
Hopefully it is apparent that we can apply the same rationale to trading. By trading two uncorrelated positions concurrently, we (assuming positive expectancy) double return without increasing risk. By trading three positions, we triple return, and so on. However, the key is this: the trials must be completely independent of each other, i.e. the outcome of one trial must in no way influence on the outcome of another.

David
even if trades are completely uncorrelated probability of two simultaneous losses is greater than zero so in fact you are increasing risk, proof above.
Quidquid latine dictum sit altum viditur
  • #15
  • Jan 4, 2007 12:43pm Jan 4, 2007 12:43pm
The problems I see with this (and I may be stupid) are that there are some very strict rules which it may not be possible to observe in order for such a strategy to work.

First, each event must be completely independent. However, in forex, there is always likely to be some correlation between any two given currency pairs. A crash in a major, for example, would cause ripples to affect every curreny on earth in one way or another, though that effect may not be predicatble.

Secondly, in the roulette analogy, each table has the same set of rules, the same chance of success, and the same method of gaining that success. no external variable affects its chances and the profit and loss are predictable in each individual round.

It is highly unlikely that a single method of forex trading will generate the exact same success rate in two or more currency pairs.

Furthermore, the way you measure that success would also be difficult bearing in mind the external variables of pip spread and slippage
quote of the day: . It's like deja-vu all over again
  • #16
  • Jan 4, 2007 12:49pm Jan 4, 2007 12:49pm
Quoting Gmak
The problems I see with this (and I may be stupid) are that there are some very strict rules which it may not be possible to observe in order for such a strategy to work.

First, each event must be completely independent. However, in forex, there is always likely to be some correlation between any two given currency pairs. A crash in a major, for example, would cause ripples to affect every curreny on earth in one way or another, though that effect may not be predicatble.
in fact small correlation always exists as fx is not the only investment medium and large institutions can whithdraw money simultaneously from 'uncorrelated' pairs hoping for better gains in commodities, bonds, stocks, options, whatever.
Quidquid latine dictum sit altum viditur
  • #17
  • Jan 4, 2007 1:30pm Jan 4, 2007 1:30pm
Quoting dottore
Hi David, here is my [independent] and [uncorrelated] I hope humbleopinion

1. Risk of drawdown actually increases and casino should increase its capital, not necesarily double but increase. Two arguments: imagine real life situation when on both tables casino loses. Is it possible? If yes, then casino should increase capital for operational safety.

Second one - suppose that every 100 days there is one drawdown on average on single table. If for 2 tables risk remains unchanged then the same is true for 100, 101 or arbitrary number of wheels.

But - over 100 wheels we have: one table daily will experience ruin, over 200 - TWO on average experience ruin so in this case we are almost SURE that we should have casino's capital doubled. In fact we shoud for safety actually have capital multiplied by x where x is maximal but reasonable number of drawdowns. we can assess this taking into account probability of one drawdown a day per table and number of tables and also past data.



even if trades are completely uncorrelated probability of two simultaneous losses is greater than zero so in fact you are increasing risk, proof above.
I think this wasn't necessarily where the thread was going. I don't think risk or drawdown is increased. If we trade just one pair then when we lose, we lose. There is no other option. What if you trade 5 pairs though. What are the chances all 5 lose? Not very likely, but still possible.

Imagine a 50 TP, 50 SL system. If you trade 1 standard lot on one pair you lose 50 pips at one lot. In the long run the system is 60% correct. That one loss gives your account a big drawdown. So what if you split that among 5 uncorrelated pairs with 60% success on each pair? 3 out of 5 win for +50 pips. The pairs will rotate which loses on that day, but its the law of large numbers. We're increasing our times of losing in a day, but if our system is more successful than not then we can expect to increase the number of times we win more than the number of times we lose. It smoothes out the drawdown.

Is risk increased? Only if you normally trade 1 standard lot at any given time, but then increase to 5 lots when you trade 5 pairs. If you keep your same lot risk over all the pairs, ie 2 minilots per pair, you are not introducing any more risk into the system. The roulette example isn't that great because each new table would require the same risk on each.

I'm saying that it's more like what if a casino has 1 table playing at a $50,000 max bet, or 5 tables at a $10,000 max bet. We can expect to win while we lose with the 5 tables rather than only playing 1 table and experiencing $50,000 losses at once. It'd be hard to have 5 tables lose all at the same time. Matt
  • #18
  • Jan 4, 2007 1:34pm Jan 4, 2007 1:34pm
Quoting permanentjaun
Imagine a 50 TP, 50 SL system. If you trade 1 standard lot on one pair you lose 50 pips at one lot. In the long run the system is 60% correct. That one loss gives your account a big drawdown. So what if you split that among 5 uncorrelated pairs with 60% success on each pair?
Your point is well made. Unfortunately, you can't list 5 uncorrelated currency pairs.
  • #19
  • Jan 4, 2007 1:39pm Jan 4, 2007 1:39pm
No, but I think we can get uncorrelated enough for it to work. Some pairs obviously trade very similar and others not so much. It can be hard to say if pairs are uncorrelated though. Price either goes up or go down. If we know two pairs are uncorrelated, but still move up in the same time period, does that mean we were wrong about them being uncorrelated? No. It just means by coincidence they moved in the same direction in this period.
  • #20
  • Jan 4, 2007 2:25pm Jan 4, 2007 2:25pm
if you have a system that works at 60% profitability and you see two simultaneous opportunities of entering a trade with it on different currencies. I would expect to enter both trades.

Of course I am only risking 2% of capital on each trade and if the result was negative on both counts it would be just like losing two trades entered over a period of time.

I have no problem with that.

It is unlikely though that these simultaneous possibilities will arise in uncorrelated markets. If they constantly arose, the markets would ergo be correlated.

I don't think you can make a system out of this, without employing more than one system of entering a trade, and those two systems themselves being entirely independent of each other.
so for this to work. You need

1) two or more uncorrelated pairs. where opportunities of entering market occur simultaneously.

2)2 systems of equal probability completely unrelated to each other.

3)not only should the two systems have the same win probability. They must also net the same real profit/loss.
quote of the day: . It's like deja-vu all over again
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