Examining The Probabilities Of Spread/Pair Trading

[CoolTraderDude]

Assume that we have two securities that we want to trade using a spread strategy. One will be a buy while the other will be a sell. We will obviously buy the strongest security and sell the security that we think is weak. This will lead to a spread where the strong security will outperform the weak security and allow us to make money off of the spread. Now if the price of the strong security is above the price of the weak security we will have a spread that widens (in pure numerical terms) and if the strong security is below the weak security we will have a narrowing spread. But keep in mind that there are other ways of charting spreads.

If we look at this trade there will be several scenarios that may unfold some will make money and some will lose. Security A will be our strong “stock” and security B will be our weak “stock”. A will be a buy and B will be a sell.


CORRELATED

CONDITION 1

SECURITY A – UP SECURITY B – UP

WIN: SECURITY A RISES FASTER THAN SECURITY B RISES

LOSS: SECURITY A RISES SLOWER THAN SECURITY B RISES

CONDITION 2

SECURITY A – DOWN SECURITY B – DOWN

WIN: SECURITY A FALLS SLOWER THAN SECURITY B

LOSS: SECURITY A FALLS FASTER THAN SECURITY B

CONDITION 3

SECURITY A – UP SECURITY B – DOWN

WIN: NO MATTER WHAT

CONDITION 4

SECURITY A – DOWN SECURITY B – UP

LOSS: NO MATTER WHAT

So we have six outcomes… of which 3 are wins. This means 3/6 or 1/2 or 50 % which is more or less the exact same as trading the regular way.

Now let us examine negative correlation. This means that when A rises B falls and when B rises A falls. To be “hedged” you would have to buy both or sell both depending on the market.


NEGATIVE CORRELATION


CONDITION 1

SECURITY A – UP SECURITY B – DOWN

BUYS ONLY

WIN: SECURITY A RISES MORE THAN B FALLS

LOSS: SECURITY A RISES LESS THAN B FALLS

SELLS ONLY

WIN: SECURITY A FALLS MORE THAN B RISES

LOSS: SECURITY A FALLS LESS THAN B RISES

We have 4 outcomes of which only 2 are wins leaving us once again with only a 50 % probability of getting it right. However this isn’t entirely accurate.

We have three possibilities when we look at correlation.

1. Correlation
2. Negative correlation
3. No correlation whatsoever


We only have a 1/3 chance of getting the correlation right going forward because correlation can also change and in fact does so all the time. Picking the right strategy depends on getting the correlation right first.

This leads us to a joint probability situation in which to get the above results is dependant on getting the correlation right.

Therefore we have 1/3 * 1/2 = 1/6… or only 16 % chance of getting it right. This would seem as a significantly lower outcome than if one just traded a security without a “pair” or “spread” strategy.

To both supporters and opponents of these strategies… Please discuss in a civil manner.

 

[ofthomas]

wait, didnt you "quit" trading?

I will only make one statement... spread/pairs trading is not risk free... it merely carries less risk, which can still be blown out if you abuse size... all I will say with regards to the subject... the style of trading has been around for ages... so not sure why people see it as something so amazingly new...

 

[braincell]

1. If you are assuming you have no information (no model) for entering pairs originally, then your first assumption is true at an approximate 50% win rate. However this would be foolish to begin with.

2. You've only listed 3 cases of "correlation" and assumed that the probabilities of each occuring have a uniform distribution. You need to define what is correlation. If you use a 20 day average and swing trade for 10 days it's different to using a 300 day average and trading for 30 days. Correlations of different periods also have different distributions and skews so if you look at them in 3 dimensions (histogram x period) you get different pictures. Lastly, even when you define your cases they are not uniformly distributed.

3. Your probabilities suffer from what most non-mathematicians tend to do, that is oversimplify in a sense. The entry into a pair depends on correlation, so the probability of choosing a correct correlation assumption depends on what is correct to the previous choice.

That's the bayes theorem and if you plug that in with given distributions of probabilities, you will get about a 50% win rate as well for trades with 0 information (random), not 16% like you say. P(A|B) can mean probability of Negative Correlation (A) given Expecting Positive Correlation (B) = something based on posteriors, etc etc.

With a little bit of math you can actually only trade correlation as if it were a product on the exchange (bar huge transaction costs and inherent lag...).

 

[CoolTraderDude]

Quote from ofthomas:

wait, didnt you "quit" trading?

I will only make one statement... spread/pairs trading is not risk free... it merely carries less risk, which can still be blown out if you abuse size... all I will say with regards to the subject... the style of trading has been around for ages... so not sure why people see it as something so amazingly new...

Yeah I quit... but I still like to talk about it and obviously talk about strategies.

Quote from braincell:

1. If you are assuming you have no information (no model) for entering pairs originally, then your first assumption is true at an approximate 50% win rate. However this would be foolish to begin with.

Just giving a simple model... My hands were getting tired of typing!

Quote from braincell:

2. You've only listed 3 cases of "correlation" and assumed that the probabilities of each occuring have a uniform distribution. You need to define what is correlation. If you use a 20 day average and swing trade for 10 days it's different to using a 300 day average and trading for 30 days. Correlations of different periods also have different distributions and skews so if you look at them in 3 dimensions (histogram x period) you get different pictures. Lastly, even when you define your cases they are not uniformly distributed.

You're right about them not having a uniform distribution... in the past... But the choices for the future seem to remain the same or am I missing something...? I doubt anyone would share a model for future projections of correlations.

Quote from braincell:

3. Your probabilities suffer from what most non-mathematicians tend to do, that is oversimplify in a sense. The entry into a pair depends on correlation, so the probability of choosing a correct correlation assumption depends on what is correct to the previous choice.

That's the bayes theorem and if you plug that in with given distributions of probabilities, you will get about a 50% win rate as well for trades with 0 information (random), not 16% like you say. P(A|B) can mean probability of Negative Correlation (A) given Expecting Positive Correlation (B) = something based on posteriors, etc etc.

With a little bit of math you can actually only trade correlation as if it were a product on the exchange (bar huge transaction costs and inherent lag...).

Well you might be right here if you use Bayes' Theorem... But I'm not convinced...

First you pick the correlation and then you pick the strategy... Your strategy should be dependant on getting the correlation right.

I look at the third option "no correlation" as an option... An example of "no correlation" being... one security does something the other security does nothing over a period significant to your strategy. The right play being staying out. If you don't get that right... then you play and are wrong. BTW don't take "negative correlation" to mean "no correlation". Negative correlation is a kind of correlation.

We have a small difference in perception.

 

[Bob111]

i stopped on correlated condition 3-win no matter what
what makes you think that if A is up and B is down -you have winner?
you long A and short B and your are saying that this whole thing can't reverse? i can assure you-they can do this just fine. there is far more variables involved besides A is up and B is down. and one more thing to think off: when you plot your spread-you got same trend-up or down. now-how is this different than just trade trend of 1 security?

 

[CoolTraderDude]

Quote from Bob111:

i stopped on correlated condition 3-win no matter what
what makes you think that if A is up and B is down -you have winner?
you long A and short B and your are saying that this whole thing can't reverse? i can assure you-they can do this just fine. there is far more variables involved besides A is up and B is down.

You're absolutely right... The outcomes can easily grow exponentially given your choices and then the market changes that happen after those choices ...

Quote from Bob111:

and one more thing to think off: when you plot your spread-you got same trend-up or down. now-how is this different than just trade trend of 1 security?

Well one security will usually move faster than the other... The idea is to be market neutral, "spread trading" is supposed to be like a coin flip where "heads I win, tails you lose" in practice but they don't work out like that in reality. So you don't have to pick market direction, all you have to do is pick the stronger "horse" of the two. It's like looking at two horses, one is malnourished and the other is all muscle... Now you don't have to pick which way they will run just that one will outrun the other. The idea is that in a falling market the stronger security won't fall as much as the weak security... And in a rising market the weak security won't rise as much as the strong security always giving you the difference between them as profit.

 

[Bob111]

i would love to hear the criteria or some simple algo for finding stronger horse. let say for intraday trading.
this whole thread is sounds pure academic. show us some real stuff.
i'll tell you my little secret-not matter what i tried in past few years(or maybe decade or so)- i was unable to find the method that would work stable enough and produce reliable every day results(in pair stocks trading). i'm too lazy,but i can find table here,on ET back in 2002 with my pair trading of semiconductors stocks. i did good back then. but that was 2002 or 03

 

[CoolTraderDude]

Quote from Bob111:

i would love to hear the criteria or some simple algo for finding stronger horse. let say for intraday trading.
this whole thread is sounds pure academic. show us some real stuff.
i'll tell you my little secret-not matter what i tried in past few years(or maybe decade or so)- i was unable to find the method that would work stable enough and produce reliable every day results(in pair stocks trading). i'm too lazy,but i can find table here,on ET back in 2002 with my pair trading of semiconductors stocks. i did good back then. but that was 2002 or 03

Well... For intraday trading... I'm not sure that these strategies were ever meant for that. They're generally more for macro events... A good example would be going long F (Ford) and shorting GM (General Motors) back when GM went bust... They're both auto companies so they should correlate. But that would have been a fundamental play based on the crisis and GM's debt.

I would guess that if you wanted to go intraday... The following may work... Pick stocks in the same industry and sector with a news event on that day. You don't need both stocks to have news for that day just one in the pair will be enough. Use RSI indicator to determine strength between the two. You would be looking at the absolute number value and not worry if it is at the 70 or 30 mark (or however you want to set it up). One will have a higher reading than the other and that will be the stronger stock for that day. Now if the news is bad in the weak stock you should be good to go long A, short B. If the news is good in the strong stock again good to go long A, short B. Otherwise stay out… Something like this may work ok…