Relative Value: The Triangle Principle using Gold and Currency

Take a moment to think about the measures we use to price anything. If you happen to live in the United States, the price of any good or service is denominated by US Dollars. If you live in Europe then you're using Euros. Mexico? You're working with Mexican Pesos.

Consider the following:

• One is liable for taxes or is owed taxes each year, payable in Dollars
• If exchanging one's time to provide a good/service to someone else (a job, self employed contractor, business, etc), this is likely exchanged in Dollars instead of anything else.
• Our checking/savings/retirement accounts are all denominated Dollars.
• The principal and interest on debts one either owns as an asset, such as a bond, or owes such as a mortgage are all also denominated in Dollars.

Some more common examples:

• The price of crude oil is Dollars per barrel.
• The price of gold/silver/platinum is Dollars per troy oz, or copper is Dollars per pound.
• At the pump, regardless of octane content, Diesel or not, we see Dollars per Gallon.

I can keep going on and on, but you get the point.

The Triangle Principle and its Application in Relative Value

W have 3 items (A, B, and C) that we assume are:

• Liquid – Investors trade these assets often, exchanging one for the other.
• There's a liquid marketplace for the “crosses” of A, B, and C – ie A/B, B/C, A/C (notation similar to Forex, USD/JPY, AUD/CAD, etc).
• We can only see the current “cross” rate, or exchange rate, between A—>B (A/B) and C–>B (C/B), but don't have “quotes” or a reliable way to know the exchange rate between A—>B (A/C)

Assume this is the data we can access.

It takes 2 A's to get 1 B – this means the **A/B cross would be 1/2 or 0.5
reversed: **B/A cross would be 2/1 or 2.0**
It takes 5 C's to get 1 B – this means the **C/B cross would be 1/5 or 0.2**
reversed: **B/C cross would be 5/1 or 5.0**

Given this info above, how can one determine the “cross” between A and C? Is it even possible?

Assuming that the price discovery mechanism of the market is working and that there will always be firms looking to make money arbitraging away discrepancies, using the number of A's it takes for 1 C and the number of B's it takes for 1 C gives us the relationship.

This is called a triangle since both crosses we are examining share a common element – B. Therefore, we can remove B from the picture, and directly compare A to C based on the amount of A and C it took to get B's. This leaves us with the fair value cross of A/C.

Learn The Math Behind the Triangle Principle

The math is actually pretty good to know, and not complicated – its just division.

* It takes 2 A's to get 5 B's -> 2/5 = 0.4
* It takes 0.4 A's to get 1 B
* It takes 5 B's to get 2 A's -> 5/2 = 2.5
* It takes 2.5 B's to get 1 A

0.4 is the reciprocal of 2.5 -> 1.0/0.4 == 2.5

2.5 is the reciprocal of 0.4 -> 1.0/2.5 == 0.4

Important Note

We can get to this same result by using the original crosses – A/B cross would be 1/2 or 0.5 and C/B cross would be 1/5 or 0.2. If we simply do cross the rates 0.5/0.2 we get 2.5!

It works in reverse as well, B/A cross would be 2/1 or 2.0 and B/C cross would be 5/1 or 5.0, thus crossing 2.0/5.0 which gives us 0.4.

One can make the statement that B is “strong” in comparison to A and C, as it takes much less of B to acquire goods and services denominated in A or C.

Now assume some other item, a cup of coffee, used to cost you 0.5 B's and out of nowhere the cost per cup of coffee starts rising, to 0.75, then 1.00 then 1.50. This means it now takes 3 times as many B's to get the same cup of coffee. B has “weakening” purchasing power for cups of coffee.

Your friends that have more A's than they do B's have reported to you that for them the cup of coffee started out at 1.0 A per cup, and then went to 2.0, 3.0, and finally 5.0 (B started at 0.5, 0.75, 1.00, and finally 1.50). This means it now takes 5 times as many A's to get the same cup of coffee. A has “weakening” purchasing power for cups of coffee too, but a much greater decrease to that of B.

Before this event took place, the cup of coffee was priced the same in both A and B. It started at 0.5 A's and 1.0 B's per cup – and recall the cross between A/B was 0.5. So for someone wanting cups of coffee, using A's or B's should have posed no difference.

However, after this move, cups of coffee are now cheaper in B's than they are in A's, since the change was 3x fold increase for B and 5x fold increase for A's.

1) Did the cross between A and B stay the same?

> If the cross between As and Bs stayed the same – someone in the business of buying and selling cups of coffee that uses A's to transact just got a huge boost to his/her business! They would have an incentive to trade any of their As for Bs to purchase the coffee at a cheaper price.

2) Did the cross between A and B move in proportion to the move in coffee?

> If the cross moved in proportion, the new cross between A/B is 3/5 or 0.6 (reverse: 5/3 = 1.66). A is now “stronger” than it was before when compared to B – and likewise, B is now “weaker” when compared to A.

1) did the cross between A and B move in disproportion to the move in coffee?

> Use your imagination to think of the different scenarios…

Back to the Topic: The Dollar

When the price of global commodities move, which are actively priced in several currencies daily, such as gold and oil – analyzing the difference between the move of the commodity priced in Dollars vs Euros can speak volumes to us about the cause/effect. The move could be strictly due to supply/demand of the commodity, as in one of the examples above, but it can also be caused by a dislocation of the triangle pricing model, where gold or oil in Dollars moved less (or more) than gold or Oil in Chinese Yuan for example.

The Gold Rally

The rally in gold that started in October 2018 has been one that can be measured in any other currency since Gold is traded worldwide and has a “monetary” component to it.

Gold **made new all-time highs** when crossed against 71 different currencies this past September 2019, including EUR, GBP, JPY, etc. So how come Gold priced in Dollars did not, too, make a new all-time high?

Based on our triangle principle, 1 unit of Gold will always be 1 unit of Gold, just like 1 cup of coffee will always be 1 cup of coffee…and 1 barrel of crude will always be 1 barrel of crude. It's the currency used to procure the items that can change in purchasing power (the value of A, B, and C – relative to each other, and relative to gold in this case).

The fact that Gold has NOT made new all-time highs in Dollars but it has when priced in 71 other currencies can be viewed as a loss of purchasing power in those 71 currencies when compared against the Dollar. However, at the same time, the fact that Gold is rising simply means the Dollar, too, is losing purchasing power. Just not as much as the other global currencies.

Some food for thought on relative value and price dislocations.