A cross rate is the currency exchange between two currencies where neither are the official currencies of the country in which exchange rate quote is given.
It means that cross currency rate is when the currency being mentioned do not belong to domicile. Therefore, a finance Journalist in Japan will refer to EUR/GBP as the cross-currency rate. This is because neither Euro nor the GBP are the official currencies in Japan.
Thus, in India, a cross rate is any exchange rate which excludes Rupee (INR). For example,
EUR/GBP, US Dollar/ Fr. Franc, DM/GBP
Therefore, it can be said that cross rate is an exchange rate between the currencies of two countries that are not quoted against each other but are quoted against the common currency.
One morning after their International Finance class, Sagnik looked puzzled while revising exchange rates.
Sagnik:
Mohini, I understand USD/INR and GBP/INR quotes now. But today the professor mentioned something called a cross rate. Why do we need it at all?
Mohini:
Good question. A cross rate is used when two currencies are not quoted directly against each other, but both are quoted against a common third currency.
The situation
Mohini opens her notebook and writes:
- USD/INR = 83
- GBP/USD = 1.25
Mohini:
Suppose an Indian company wants to convert pounds into rupees, but there is no direct GBP/INR quote available. What do we do?
Sagnik:
We use the US dollar as a bridge?
Mohini (smiling):
Exactly! That’s where the cross rate comes in.
Mohini:
To find GBP/INR, multiply the two rates.
GBP/INR=GBP/USD×USD/INR
=1.25×83=103.75
Sagnik:
So one pound is equal to Rs.103.75. But why cross rates matter?
Mohini:
Cross rates are important in international trade, banking, and forex dealing. They ensure consistency in exchange rates.
Sagnik:
So without cross rates, different banks could quote different prices and create confusion.
Mohini:
Exactly. Cross rates connect currencies globally, even when they are not directly traded.
Let’s discuss cross rate using bid and ask rate concepts with two cases of Exporter and Importer.
Assume it’s a Bank’s quotation):
- USD/INR = 83.00 / 83.20
(Bank buys USD at 83.00, sells at 83.20) - GBP/USD = 1.24 / 1.26
(Bank buys GBP at 1.24 USD, sells at 1.26 USD)
Explanation:
Dealing with cross currency two-way quotes
- Bid rate is multiplied by bid rate and
- Ask rate is multiplied by ask rate
Cross rate calculation
Bid price= 83*1.24 =102.92 and Ask price = 83.20*1.26=104.32
Therefore, If GBP is bought then Rs.104.32 (sold by banker) should be the price and, if, GBP is to be sold to the banker (bought by banker) then the price should be Rs. 102.92
Question:
An Indian bank provides the following exchange quotations:
USD/INR = 83.00 / 83.20
GBP/USD = 1.24 / 1.26
An Indian exporter is to receive GBP 40,000, while an Indian importer has to pay GBP 60,000.
You are required to:
Calculate the GBP/INR cross rate from the bank’s point of view.
Determine the rupee amount receivable by the exporter.
Determine the rupee amount payable by the importer.
Briefly explain why bid and ask rates are used differently in cross-rate calculations.
Answer:
Let’s understand the cases of the Importer and the Exporter where the Importer needs to buy GBP 60,000, and the Exporter needs to sell GBP 40,000 but the quotes are not given directly but are quoted against the common currency.
1. GBP/INR cross rate = Bid rate 83*1.24= Rs. 102.92
Ask rate 83.20*1.26= Rs.104.82
2. The exporter will receive GBP 40,000. So he will sell GBP and will receive USD at bid price (Bank is buying) 1.24*40,000= $49,600. Thereafter, he will sell USD at bid price 83*49,600 and will receive= Rs. 41,16,800. Now if we apply cross rate = 102.92*40,000= Rs.41,16,800.
3. So, when the importer needs to buy GBP, he will first buy GBP at $ and at ask price 60000*1.26= $ =$75600. To buy $ 75,600, the INR to be paid = 83.20*75,600= Rs. Rs. 62,89,920. Now if we apply our cross rate (Ask rate is multiplied by Ask rate) = 83.20*1.26= Rs. 104.832*60,000= Rs. 62,89,920. (Importer will buy GBP).
4. Bid and ask rates are used differently to ensure that the bank does not incur losses. The bank buys foreign currency at the bid rate and sells foreign currency at the ask rate. Cross-rate calculation using bid and ask rates requires identifying whether the bank is buying or selling the base currency.
