Fixing cross-currency rates

B. Venkatesh

THIS week's article is in response to a reader's query.

The query is how cross-currency rates in the foreign exchange (forex) market are fixed.

To understand the mechanics of cross-currency rates, we need to first look at the forex market, where various currencies are bought and sold.

Typically, the US dollar (USD), the UK pound, the euro and the Japanese yen are actively traded in the forex market. In India, however, the forex market actively trades only the USD. So, what do you do if you want a quote for, say, the Hong Kong dollar (HKD)? You need to ``move'' to the HKD via the USD quote.

Let us take an example. Suppose the rupee-dollar bid-ask in the forex market is 47.50-47.55. This means you buy one USD for Rs 47.55 and sell one USD for Rs 47.50. Remember, you always pay the higher quote to buy the foreign currency and receive the lower quote when you sell the currency.

Next consider HKD, which trades at, say, 7.70-7.75, meaning you can buy one USD for HKD 7.75 and sell one USD for HKD 7.70. You, thus, have two currencies -- the rupee and HKD -- in terms of the USD. You have to use these two quotes to arrive at the cross-currency rate between HKD and the rupee. How do you do that?

Picture yourself buying USD in the forex market. A bid-ask of 47.50-47.55 means you will have to pay Rs 47.55 to buy one USD. Now, if you use this USD to buy HKD, you will receive 7.70 HKD.

In short, you paid Rs 47.55 to buy one USD and used that to buy 7.70 HKD. With this information, we can now calculate the cross-currency ask rate, which is 6.17 (47.55/7.70). Similarly, the cross-currency bid rate will be 6.12 (47.50/7.75).

You, thus, have the rupee-HKD cross currency bid-ask rate of 6.12-6.17, which means you can buy one HKD at Rs 6.17 and sell one HKD at Rs 6.12. The principle is the same for calculating any cross-currency rate.