FPI - Fractional Product Inefficiency: The Impeccable Hedge

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michal.kreslik
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Postby michal.kreslik » Tue Oct 31, 2006 3:10 pm

makosgu wrote:The actual item being traded is the spread between the equivalence. This balance can be traded ad naseum on very wide variety of instruments. Rather than specify how this can be done and what the driving variables are, I will provide an illustration and then specifically point out what is that you ALWAYS want to do. If one is asking whether to SBB or BSS, then it is not understood as to what they are trading and what it is they are looking to capture.

So let's look a bit closer at what the "Impeccable Hedge Is". What has been stated is that (a/b)*(b/c)*(c/a) = 1. Michal's statement of this equivalence is so simple and yet so valuable especially when considering the imbalance (ie. where the product is <> 1). By rearranging the equation, we can view the equivalence as (a/b)*(b/c) = (1)/(c/a) =(a/c). As a result, we wind up with the actual equation that folks are trading (ie. BBS vs SSB). So taking our classic pair (EUR/USD)*(USD/CHF) = (EUR/CHF), what is it that you want to trade. The answer is the differential between this equivalence equation, or to put in SIMPLY, it is the spread between the two sides. So when your indicator is indicating >1, what it is really saying is that the left hand side of the rewritten equation is 1.001x greater than the right hand side. Let's work out the math so everyone can be crystal clear...

ORIGINAL FORM: (EUR/USD)*(USD/CHF)*(CHF/EUR) = 1
REARRANGE VIA SIMPLE MATH: (EUR/USD)*(USD/CHF) = 1/(CHF/EUR) = (EUR/CHF)
TRADEABLE FORM: (EUR/USD)*(USD/CHF) = (EUR/CHF)*(1)

*NOTE VERY WELL HERE HOW THERE IS ACTUALLY AN EXPLICIT 1 ON THE RIGHT HAND SIDE OF THIS EQUIVALENCE EQUATION*

That 1 is the indicator value some of you have programmed. The key is that when it is not 1, you want to be taking this easy money. A value that is different than ONE is telling you that the variables of the equation are unblanced and more precisely, which direction the imbalance is occuring among the variables. As for the equation, the EQUATION is ALWAYS balanced. Think about this really hard. THIS EQUATION IS ALWAYS BALANCED...

So let's look at the 3 scenarios folks are aware of. x<1, x=1, x>1.

Assuming an indicator value that is less then 1 (ie. .99), the equivalence equation informs you that the product pair (EUR/USD)*(USD/CHF) is .99 the size of (EUR/CHF). Hence, the pair (EUR/USD)*(USD/CHF) is smaller than (EUR/CHF). What trade is one to take? To answer this, one has to know what it is that they are actually trading. The answer of course is the SPREAD between the variables of the BALANCED equation. As a result, the indicator is actually a REALTIME COEFFICIENT that indicates what COEFFICIENT VALUE BALANCES the variables of the equation. So now, what trade is one to put on? The answer is straight forward... If the COEFFICIENT is .99, we know that the left side is smaller than the right side. By thinking of a SEE SAW, this coefficient is saying what needs to occur between the variables in order to balance the SEE SAW. So we know that the pair (EUR/USD)*(USD/CHF) is .99x the size of (EUR/CHF). In other words (EUR/CHF) is numerically higher (think see saw) than (EUR/USD)*(USD/CHF), numerically lower. In order for the variables to be balanced, either (EUR/CHF) must move lower by (1-.99)*(EUR/CHF) pips, or (EUR/USD)*(USD/CHF) must move higher... Since (EUR/USD)*(USD/CHF) must either stay the same or go higher to balance out the variables, then one must Buy (EUR/USD) and Buy (USD/CHF). Since (EUR/CHF) must either stay the same or move lower to balance the variables of the equation, then one looks to Sell (EUR/CHF).

Understanding this explanation, it is then easy to full understand the x>1 case. As a result, we now have a complete understanding of the entire trading paradigm from math, to coefficient, to execution (ie. B or S).

Earlier someone mentioned the hedges going against you. This is impossible due to programmed arbitrage. But, let's look at what this means!!! Say the COEFFICIENT went to 1.5. This would mean that (EUR/CHF) is trading at a higher price then (EUR/USD)*(USD/CHF). It would be exactly like buying a $1 and then immediately selling the $1 elsewhere for $1.50. In otherwords, FREE MONEY. NO MARKETS allow for such gross arbitrage opportunities.

The principle behind the equation is that whether you exchange your EURO directly for CHF or indirectly by first converting to to USD and then converting USD to CHF, you should always end up with the same amount. Otherwise, one could arbitrage the opportunity.

The coefficient explicitly says their is a small opportunity to sieze. We have just described exactly why the opportunity is really and bound to being small and not large...

So what to do to create more opportunities? Personally, I like to play with a variable that is there but has been removed from the equations (ie. t=TIME). Folks have mentioned how they have to pull the trigger quickly on all 3 simultaneously. I on the other hand, don't mind varying the individual time component of each variable...

Let's see how much of this folks are chewing before we can crank the discussion up several notches... Also, the 17 point or 67 point move is not in the space of possible outcomes of this type of SPREAD trading. In other words, the individual movement without regard to the other variables has nothing to do with this type of framework...

Regards...


Well stated, makosgu! We may express the FPI as a ratio between the value of arbitrary FX pair in ring and the value of the rest of the ring.

I disagree with your "time varying" idea, though. Anytime your overall position is not fully hedged, you are exposed to the fluctuations of the non-hedged parts of the individual positions.

In commonplace trading, we are always exposed to the fluctuactions, that's obvious. But for FPI to work properly, this exposure must be eliminated by opening/closing the individual positions at once if possible.

Michal

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Gert Frobe
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Postby Gert Frobe » Tue Oct 31, 2006 3:19 pm

Michal, again thanks for sharing your FPI.

with the intrest roleover, do you think it might be possable to to interlock two rings by where one of the the pairs of both rings cancel each other out. or is this just a four pair ring. sorry im not able to state it better- i guess i need to think on it more before i ask. LOL

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Postby ryan » Tue Oct 31, 2006 3:41 pm

eagles wrote:The challenge is to figure out if there is a bias to opening and closing positions
from low extremes to high extremes of FPI, or
from high extremes to low extremes of FPI, and
to figure out if there is an advantage for the positions being
buy/sell/sell, or
sell/buy/buy.


1. WHEN TO OPEN/CLOSE TRADES

Eagles brings up a very important point. To maximise the profit of the FPI trade we want to open our FPI trades at the lowest (<1) position practical and close out where FPI>1 again ideally at the highest point possible.

With this in mind I think perhaps we should look at adding a Simple Moving Average-type indicator to complement the FPI indicators.

Where we determine the upper and lower quartiles of the FPI range (for want of a better mathematical expression) over x periods. So for example, where the lowest low is 0% and the highest high is 100% and FPI=1 is 50% we take the 25% and 75% mark as our entry and exit positions respectively.

Ideally we could alter these positions to say 10/90 etc. to lock in more profit.

2. SLIPPAGE

The other interesting parameter I believe would be FPI volatility because where the FPI is not held for say 10 or more ticks we run the risk of slippage (where trades are not simultaneously executed) and our hedge not being hedged at all.

I have seem graphical evidence here which shows both extreme FPI volalitity and more stable behaviour.

Does anyone have any thoughts on how we might predict the duration of FPI<1 or >1 condition?

In thinking about these two parameters I hope we might be able to (a) maximise profit, (b) minimise the effect of slippage effecting profitability.

Ryan
Last edited by ryan on Tue Oct 31, 2006 4:56 pm, edited 2 times in total.

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Postby ryan » Tue Oct 31, 2006 4:11 pm

Thinking out loud ….. to follow Gert’s lead….

I recall from some involvement with the Hedge Hog system (which operated on a simple pair) in a quiet market (like at 0000 GMT) with a standard oscillation the market moves up and down the principal was that you could execute a Hedge on the pair with a TP 10 and SL 50 position and close out both the BUY and SELL trades in profit as the market bobbed around, ie. open a buy and sell trade at 0000GMT with TP10 and SL50 the market will rise and fall to close out both orders profitably.

Historically and through forward testing this methodology had around 75% success which did not make it overly profitable given the SL positions necessary.

HOWEVER, profitability was improved through a ‘third (unhedged) trade’ ‘inside’ the hedged range where the additional trade was also closed out in profit when primary hedge closed profitably.

Does any of this make any sense? I am wondering in guess whether given the correlation of the pairs, and by implication their ‘misalignment’ where FPI<1 whether it is possible to identify the rogue pair and open a trade on that AS WELL AS executing the FPI hedge trade … or indeed is this a lot of baloney to borrow an American term :? Thanks for your forbearance.

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Postby eagles » Tue Oct 31, 2006 9:12 pm

Michal,

Sorry for being lazy, but do you have a code segment that calculates the lot sizes based on the ring & bid-ask prices?

I would like a generic code that the symbols could be entered, and the lot sizes would be calculated.

If you have something like this, it would be great. If not, I will grind it out sometime.

Thanks.

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Postby Nicholishen » Tue Oct 31, 2006 9:22 pm

_______________________________________
Last edited by Nicholishen on Tue Oct 31, 2006 9:51 pm, edited 1 time in total.

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Postby makosgu » Tue Oct 31, 2006 9:39 pm

@Ryan...

1. When to open a trade is anytime there is a reasonable unbalance. So pull in more rigorous stats. Furthurmore, you want to continually cycle between being LONG and SHORT the spread so as to continually pull profits... In other words, when FPI<1, you want to BBS, assuming the ring is (EUR/USD)*(USD/CHF) = (.99)*(EUR/CHF). This is being LONG the spread and/or COEFFICIENT since equillibrium MUST ALWAYS BE ONE! Thus you anticipate FPI to go back up to ONE if not higher. Closing out this BBS anytime that FPI is greater than .99 generates a profit. If it goes to 1.01, again the variables become unbalanced and thus you know for CERTAIN that for equilibrium to be reestablished, 1.01 must go back down to 1.0. To seize this opportunity you close out the initial BBS and simultaneously execute a SSB which SHORTS the spread. Note very carefully that when we say SHORT or LONG, we are really saying that you want to go SHORT the FPI value or go LONG the FPI value. Knowing which side of the equation your FPI COEFFICIENT resides on tells you EXACTLY how the trade is to be taken...

Were I you, I would drop the simple moving average and simply just plot the distribution of FPI values tick by tick. A moving average that uses more than 1 period will lag and kill your results. Instead, you will need appropriately synched tick data to create your own unique distribution of FPI values. I will jump on a limb and predict that the distribution is NORMALLY distributed. As a result, there is roughly an equal number of BBSs and SSBs. From this, you can then optomize to figure out which is the most profitable lower bound and upper bound thresholds for which to cycle trades off of. Given this unbiased assumption about the distribution of FPI, you gain the benefit of optimizing without guessing and with being calibrated to the trading paradigm. It is the same principle casinos use to guarantee their profits. They do not play the every game analysis. They deal with the aggregation of many transactions...

2. Predicting the duration of FPI is not possible. Given the Gaussian assumption of the distribution of FPI, it would imply that roughly equal amounts of time is spent above and below 1. Isolating any particular interval that is above 1 or below 1 is not informative since knowing this information will not improve the trade. The point is that there is ABSOLUTELY ZERO NEED to spend time figuring out whether to get in or get out of a position. You execute as soon as you see it. If you don't get it, then just get out of the position...
Last edited by makosgu on Tue Oct 31, 2006 9:54 pm, edited 1 time in total.

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Postby makosgu » Tue Oct 31, 2006 9:42 pm

@ Nicholishen

There is definitely an EXPLICT way to trade the rings (ie. NO GUESSWORK). Check my earlier post. I went through an explicit logical walkthrough of what is to trade an "IMPECCABLE HEDGE". There shouldn't be any confusion whatsoever at anytime as to what to expect, what to do, how to put on the position, and when to REVERSE the position. Once you understand the 3 asset case, the N asset cases are all the same exact logic...


Looking at your example, you definitely want to go LONG on the FPI at the open as indicated by your calculations (ie. FPI = .9983551). The only questions you have to answer is what does going LONG mean with regard to the assets you have chosen (ie. gbpjpy, gbpusd, usdjpy). Given these assets, the answer is straight forward. Setting up the equivalence equation, we get

(GBP/JPY)*(.9983551) = (GBP/USD)*(USD/JPY)

Thus going LONG FPI means SHORTING (GBP/JPY) and going LONG (GBP/USD) and (USD/JPY), in other words SBB as folks seam to word things.

If the FPI at the open were 1.0012841, the equivalence equation would still be the same but with a different FPI. In other words, once you've identified the layout of the equivalence equation, you then can correctly interpret what to do, when to do what, and how to interpret the FPI COEFFICIENT.

(GBP/JPY)*(1.0012841) = (GBP/USD)*(USD/JPY)

Here we want to go SHORT on the coefficient. In this equation, going SHORT the coefficient dictates that you want to SELL (GBP/USD) and (USD/JPY) and BUY (GBP/JPY)...

Hope this helps...
Last edited by makosgu on Tue Oct 31, 2006 10:14 pm, edited 1 time in total.

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Postby Harm » Tue Oct 31, 2006 9:57 pm

makosgu wrote:@Ryan...

1. When to open a trade is anytime there is a reasonable unbalance. So pull in more rigorous stats. Furthurmore, you want to continually cycle between being LONG and SHORT the spread so as to continually pull profits... In other words, when FPI<1, you want to BBS, assuming the ring is (EUR/USD)*(USD/CHF) = (.99)*(EUR/CHF). This is being LONG the spread and/or COEFFICIENT since equillibrium MUST ALWAYS BE ONE! Thus you anticipate FPI to go back up to ONE if not higher. Closing out this BBS anytime that FPI is greater than .99 generates a profit. If it goes to 1.01, again the variables become unbalanced and thus you know for CERTAIN that for equilibrium to be reestablished, 1.01 must go back down to 1.0. To seize this opportunity you close out the initial BBS and simultaneously execute a SSB which SHORTS the spread. Note carefully that a SHORT and LONG are relative terms that are based on how you are declaring the equation.

Were I you, I would drop the simple moving average and simply just plot the distribution of FPI values tick by tick. A moving average that uses more than 1 period will lag and kill your results. Instead, you will need appropriately synched tick data to create your own unique distribution of FPI values. I will jump on a limb and predict that the distribution is NORMALLY distributed. As a result, there is roughly an equal number of BBSs and SSBs. From this, you can then optomize to figure out which is the most profitable lower bound and upper bound thresholds for which to cycle trades off of. Given this unbiased assumption about the distribution of FPI, you gain the benefit of optimizing without guessing and with being calibrated to the trading paradigm. It is the same principle casinos use to guarantee their profits. They do not play the every game analysis. They deal with the aggregation of many transactions...

2. Predicting the duration of FPI is not possible. Given the Gaussian assumption of the distribution of FPI, it would imply that roughly equal amounts of time is spent above and below 1. Isolating any particular interval that is above 1 or below 1 is not informative since knowing this information will not improve the trade. The point is that there is ABSOLUTELY ZERO NEED to spend time figuring out whether to get in or get out of a position. You execute as soon as you see it. If you don't get it, then just get out of the position...


Here's a interesting read-up adressing the above mentioned FPI distribution (which is indeed gaussian) and some calculations on the timing/slippage factor.

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Postby Harm » Tue Oct 31, 2006 10:04 pm

well, it would have attached if it wasn't too big. I put it in the download section

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