# Currency triplets - arbitrage opportunity?

I have three currency pairs - USDEUR - 0.88, USDINR - 67.13 and EURINR - 75.88 , so simple math tells me that EURINR should be USDINR/USDEUR = 76.28 ...this is a fairly significant deviation from an exact conversion and i am sure i am forgetting something basic here.

Take the yen now and when i do a similar calculation USDJPY - 100.21 and USDINR - 67.13 and JPYINR - 0.67 ..result of USDINR/USDJPY gives me 0.6698 which is extremely close to the exchange rate.

Questions

a) what explains the difference in the first case? Is it because the factors impacting exchange rate between the pairs of countries are different ? (for e.g. US invests a lot more in India than Europe as a whole hence INR should be very reactive to changes in USD but not so for EUR ? )

b) How come there's a difference in the two cases shown? JPY seems to fit the equation rather nicely.

Apologies if this sounds confusing, I regret not paying attention to these classes in B school :(

## 1 Answer

Think currency rate as simply the price, on the currencies market, of one currency in terms of another. But this is not a perfect market, so to answer your question with some concrete cases:

• even if you want to purchase at time T(price) a certain amount of currency at price P, it's not guaranteed that at the time T(transaction) the price is still P; market is open 24/7 with several transactions every minute that modify the price with rapid changes in supply/demand;
• currency market is not like a grocery store where there are two actors, a price, a transaction, and calculations can be done on the back of the envelope. To sell / buy currencies you need to involve external agents like banks and third-party agencies, all contributing to the final real price;
• risk is not 0: as per first bullet, events can cause currencies fall several points, and the losses should be considered in the real-rates model.