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