gobreeze,

Thanks for your reply. I take exception (slightly) to what you said about the U.S. dollar. Although it’s true that the USD plays a powerful role on the world currency stage, nevertheless, fixed mathematical relationships would apply to all currency pairs even if there were no U.S. dollar. Let me try to explain.

The relationship among ANY three individual currencies is defined by specific mathematical equations. These equations hold, whether the USD is involved or not. And these equations can be violated only momentarily, before market forces will arbitrage the imbalance, and restore the equations.

Here is the general case. Suppose you have three currencies: A, B and C. Those three currencies can be paired three ways: A and B can be paired, either as A/B or B/A; B and C can be paired, either as B/C or C/B; and A and C can be paired, either as A/C or C/A. We don’t get to choose the way they are paired — that’s dictated by some quasi-government organization in Switzerland. Let’s say the gnomes in Switzerland have paired these three currencies as A/B, C/B, and C/A. Immediately, we know the following facts:

A/B = C/B divided by C/A

C/B = A/B times C/A

C/A = C/B divided by A/B …just like in high school algebra class.

Re-writing these three equations in a more algebraic form, we get:

A/B = (C/B) / (C/A)

C/B = (A/B)(C/A)

C/A = (C/B) / (A/B)

At this point, prove to yourself that these algebraic equations are correct.

Next, let’s use real currencies, instead of A, B and C. Let’s say that A = CHF, B = JPY, and C = GBP. Notice that the USD is not involved in this example. Our three equations now read:

CHF/JPY = GBP/JPY divided by GBP/CHF

GBP/JPY = CHF/JPY times GBP/CHF

GBP/CHF = GBP/JPY divided by CHF/JPY

A few minutes ago, I noted the following current market prices for the three currency pairs in this example:

GBP/CHF = 1.63517, GBP/JPY = 139.158, and CHF/JPY = 85.080

I’ll prove the first equation for you: CHF/JPY = GBP/JPY divided by GBP/CHF

substituting actual prices, we get: 85.080 = 139.158 / 1.63517

which resolves to: 85.080 = 85.103 (close enough)

You can prove the other two equations with a pocket calculator. And you can experiment with other combinations of currency pairs to prove the following rule to yourself: Any three individual currencies make up three unique currency pairs, and the market prices of these three pairs are related to one another by specific mathematical formulas. When these formulas are temporarily violated, the market quickly corrects the disequilibrium through arbitrage, and restores the formulas. This rule applies whether or not the USD is one of the currencies involved. In fact, if the USD ceased to exist, this rule would apply to the remaining currencies.

Sorry for the long-winded explanation.

Good trading,

Clint