Foreign Exchange Arithmetic – Rate Computations

Foreign exchange rate computations involve a number of calculations which can be best understood by examples. The following example explains the calculations required to arrive at specific foreign exchange rates.

Example 1: Understanding two way quotes

Suppose a quotation is given as USD/CHF 0.9340 / 42:

a) The two currencies involved are: US dollars and Swiss Franc. In the above case, USD is the base currency and CHF is variable currency. Concept of base currency is very important in foreign exchange market since all quotes are for base currency.

b) The rate is being stated as CHF per USD or CHF price of 1 USD.

c) A bank will buy 1 USD for 0.9340 CHF.

d) A bank will sell 1 USD for 0.9342 CHF.

e) The bid-offer spread is 2 points or .0002 CHF.

Example 2: Arriving at two way cross currency rates The market quotes:

GBP/USD Spot: 1.6180 / 90 USD/JPY Spot: 81.45 / 50 USD/INR Spot: 45.80 / 85

Please calculate two-way, cross currency Spot rates for the following pairs.

a. JPY / INR b. GBP / INR

a) JPY / INR: This quote is derived from USD/JPY and USD/INR quotes. In both

these cases, the base currency is USD. Hence, the rule is to divide one quote by another while arriving at a cross currency rate. We assume JPY / INR, JPY is the base currency in a cross currency quote. Hence, USD/JPY becomes the denominator and USD / INR the numerator.

b) Cross currency bid rate = USD/INR bid / USD/JPY ask = 45.80/81.50 = 0.5620 c) Cross currency ask rate = USD/INR ask / USD/JPY bid = 45.85 / 81.45 =

0.5629

d) GBP / INR: This quote is derived from GBP/USD (base currency GBP) and USD/INR quotes (base currency USD). Since base currencies are different, cross currency calculations are straightforward. Multiply both bid rates and ask rates to arrive at cross currency bid and ask rates respectively.

Cross currency bid rate = GBP/USD bid * USD/INR bid = 1.6180 * 45.80 = 74.10

Cross currency ask rate = GBP/USD ask * USD/INR ask = 1.6190 * 45.85 = 74.23

Forward Market

This segment of the market is an important part, which makes the foreign exchange market vibrant. In this market, contracts are bought and sold at forward exchange rates and hence cash flow happens at a future date (agreed on the date of entering the transaction). Hedging and speculation are main activities, which pertain to forward markets. For example, an exporter who is expecting USD 1mn after 3 months can book a three-month forward ( sell expected USD , where actual cash flow will happen after three months ,once the dollars are received) and know the exchange rate of his/her receivables well in advance and mitigate exchange risks.

Swap Margins and Quotations

While banks quote and do outright forward deals with their non-bank customers, in the interbank market, forwards are done in the form of swaps. Thus, suppose a bank buys pounds one-month forward against dollars from a customer, it has created a long position in pounds (short in dollars) for one-month forward. If it wants to square this in the interbank market, it will do so as follows:

 A swap in which it buys pounds spot and sells one month forward, thus creating

an offsetting short pound position one month forward.

 Coupled with a spot sale of pounds to offset the long pound position in spot created in the above swap.

This is because it is difficult to find counterparties with matching opposite needs to cover the original position by an opposite outright forward whereas accumulation of various customer transactions in a bank‟s books can be easily managed by squaring the spot and swap positions separately or can be easily offset by dealing in the euro deposit markets.

FX Swap can be structured in two ways. If a currency is bought in the spot and simultaneously sold in a forward market, it is called Buy–Sell swap. In the reverse case it will be a Sell–Buy swap.

Receipt and Payment of Swap Points

If the currency is in Discount in Future then a swap where the currency is bought is spot and sold in forward will result in gain of the swap points. This is simply because the currency is being sold costly and bought cheap. Further, in a currency pair, the currency

with a lesser interest rate is at premium and hence the currency having higher interest rate is at discount. We can summarize the rule as given below:

1. A Sell / Buy Swap in Discount currency results in Gain of Swap Points. And it logically follows that.

2. A Buy / Sell swap in Discount currency results in Loss of Swap Points.

3. A Buy / Sell swap in Premium currency results in Gain of Swap Points.

4. A Sell / Buy swap in Premium currency results in Loss of Swap Points.

Some Applications of Swaps

Banks use swaps among themselves to offset positions created in outright forwards done with customers. You may have noticed that swap deals alter the timings of cash flows.

For instance, suppose a firm bought CHF against dollar three-month forward on August 30.The delivery date is December 1. By late November, it realizes that it does not need the CHF on December 1 but on December 14. On November 29, it can do a swap, selling CHF spot and buying it for delivery on December 14. The CHF received from the original forward contract is used to deliver against the spot leg of the swap.

Another variant of swaps is in so called “Roll-over Forward contracts‟. Forward quotes may not exist or lack liquidity beyond certain maturities. Consider the case of a firm in India that has contracted a foreign currency loan of $1,000,000. The principal has to be repaid in 10 six-monthly installments starting six months from today. Ignoring the interest payments (which can be easily figured into the calculation), the firm has definite outflows of $10,000 every six months for the next five years. The firm would like to know the

rupee value of its entire liability at all times. Assume that forward markets are not liquid beyond six months.

The firm can use swaps as follows:

 Buy USD 1,000,000 six-month forward at a rate known today.

 Six months later, take delivery, use USD 100,000 to repay the first installment.

For the remaining USD 900,000 do a six-month swap i.e., sell in the spot market, and buy six months forward. Rupee outflow six months later is again known with certainty.

 Repeat this operation every six months until till the loan is repaid.