Triangular Arbitrage

The following are spot rate quotes in the interbank market:

USD/EUR 1.4559/1.4561

JPY/USD 81.87/81.89

CAD/USD .9544/0.9546

SEK/USD 6.8739/6.8741

In a previous question we calculated that JPY/CAD cross rate was 85.76/85.80

If a dealer quoted a bid–offer rate of 85.73/85.75 in JPY/CAD, then a triangular arbitrage would involve buying:

answer: CAD from the dealer and selling it in the interbank market, for a profit of JPY 0.01 per CAD.

Initially, I assumed that triangular arbitrage meant we had to go through 3 currencies to come back to where we started, but in this case, we are only working with two. Or did we need to use the given rates to calculate the answer.

I see three: USD, CAD, JPY.

Yes, but the answer provided by the book just said buy CAD from the dealer and sell it in the market. It didn’t refer to any of the other currencies.

You got JPY/CAD rate through USD in prior calculation. Those questions may be linked since this is vignette style questionnaire.

The answer assumes that you understand that selling it in the market involves two other currencies. It would be much better if they were clearer in their explanation.

I’m just confused on the route to take.

The easy way I see it is I buy it from the dealer at 85.75 JPY and then sell it at the market at 85.76 JPY

But if I have to use the arbitrage way, which way do I go?

Buy CAD from dealer for JPY, sell JPY to buy dollars, sell dollars for CAD? 85.75* (1/81.89)* 0.9544= 0.999387.

or do I revert back to JPY?