One of the unfortunate realities that we know as retail traders is that we can’t practically access arbitrage.

Algos are so much faster in balancing triangular arbitrage. So, unless we make an investment in the hundreds of thousands of dollars, being an arbitrageur is likely not in the cards.

But, that doesn’t mean we can’t use it to analyze cross relationships to optimize hedging in basket trading.

Fair warning: math ahead

Reviewing the Underlying Logic

For the purpose of this article, let’s consider a simple basket of the three majors: USDJPY, EURJPY, and EURUSD.

Generally, we’d ignore the arbitrage aspect, because the algos are going to keep the three currency pairs’ relative values in line. In this case, though, we want to remember that arbitrage exists because the currency pair values are all relative.

If the EURUSD goes up, it could mean that either the euro got stronger, or the dollar got weaker. The move in the pair is determined by the relative value of each currency with respect to the other.

This then translates into fluctuations in the cross pairs. How much those other pairs move, however, is relative to the relative value of the base currencies.

The Moves Aren’t Always Consistent

In this example, you could say that if the euro got stronger, then the arbitrageurs are going to make the EURJPY also go up. The assumption might be that it will be the same number of pips, but because the currencies’ values are relative, it doesn’t always translate directly.

This is because the dollar and the euro have different relative values to the yen. So, in order to balance the exchange rates between the three pairs, one of the pairs has to move more or less than the other. This can be expressed mathematically.

Splitting the Pairs Into their Parts

If we use the notation EUR/USD, we can compose it into a recognizable algebraic formula: EUR/USD = 1.2000. What this means is that we can operate with the currencies as numerator, denominator, and factors in equations. That allows us to substitute currencies and calculate their cross values:

EUR/USD = 1.2000; EUR/JPY = 120; USD/JPY = 100

Is not all that different from: A/B = 1.2; A/C = 120; B/C = 100.

You can then use the currency pairs in the same way you’d use any other equation, with the currency names being used as variables instead of arbitrary letters.

If EUR/USD = 1.2000 then EUR = 1.2USD so EUR/JPY = 120 can also be written as 1.2USD/JPY = 120.

If you resolve that equation and don’t come to the same answer as the trading in the market (USDJPY at 100), then there is a difference.

That’s the arbitrage amount!

Leveraging Arbitrage Into your Basket Strategy

Of course, the algos are going to wipe out that difference before you can take advantage of it. That’s not the point: the idea is that by using this principle, you can calculate where the other pairs in your basket will be once certain levels (such as take profit and stop loss) are achieved.

This makes it easier for you to know precisely where to place your hedging stops and take profits.

So, if in our example basket, the EUR/USD went to 1.3000; we have two alternatives. Either the euro got stronger or the dollar got weaker. In the former case, the EURJPY would have gone up. In the latter case, the USDJPY would have gone down. But, the question is, how much?

Euro Strength v Dollar Weakness

To find out what happens to the EUR/JPY when the EUR/USD goes up 100 pips, we have to do the substitutions in the equations above, with USD/JPY staying consistent. The result is that EUR/JPY goes to 130.

We can do the same substitution in the equations to find out what happens to the USD/JPY if the EUR/USD goes up 100 pips (this time assuming that the dollar weakened, in other words, the EUR/JPY stays consistent). The result is that the USDJPY drops to 92.3.

The Differences Aren’t the Same

Note that if the EUR/USD moves 100 pips because of euro strength, then the EUR/JPY moves up 100 pips as well. But if the EUR/USD moves 100 pips because of USD weakness, then the USD/JPY moves down only 77 pips. This is because the values of the currencies are relative only to each other.

The practical application of this is that you can calculate much more precise levels, so you don’t have unnecessarily large stops. It also shows the size of your hedging position needs to be different depending on which direction and currency you are hedging against.