# 4. Forward Calculations

## e. convert forward quotations expressed on a points basis or in percentage terms into an outright forward quotation;

## f. explain the arbitrage relationship between spot rates, forward rates, and interest rates;

## g. calculate and interpret a forward discount or premium;

## h. calculate and interpret the forward rate consistent with the spot rate and the interest rate in each currency;

What is the difference between the spot market (spot rate) and the forward market (forward exchange rate)?

In the spot market, currencies are traded for immediate delivery. In the forward market, contracts are made to buy or sell currencies for future delivery.

Explain a typical forward transaction where a US company buys textiles from England with a payment of £1 million due in 90 days. The present price of £ is $1.71.

Since the price of pounds may go up in the next 90 days the importer can guard against exchange risk by immediately negotiating a 90-day forward contract with a bank at a price, say, £:$ = 1.72. In 90 days the bank will give the importer £1 million and the importer will give the bank 1.72 million U.S. dollars. By going long in the forward market, the importer is able to convert a short underlying position in £ to a zero net exposed position.

What is a forward discount and a forward premium?

Forward exchange rates are often quoted as a premium, or discount, to the spot exchange rate. A base currency is at a forward discount if the forward rate is below the spot rate, whereas a forward premium exists if the forward rate is above the spot rate.

What is the interest rate parity (IRP) theory? What is the calculation?

- The currency of the country with a lower interest rate should be at a forward premium in terms of the currency of the country with the higher rate.

- $$\frac{F - S}{S} - \frac{i_f - i_d}{1 + i_d}$$

- The exchange rate is d:f = S for the spot rate and F for the forward rate.

- Both id and if are periodic interest rates, which should be computed as `i = annual interest rate x number of days till the forward contract expires / 360`

What is covered interest differential?

It is when the difference between the domestic interest rate and the hedged foreign rate is zero.

What is covered interest arbitrage? Explain the arbitrage steps given the following:

- Interest rate on GBP (£) is 12% in London

- Pound spot rate £:$ = 1.75

- One year forward rate is £:$ = 1.68

1. Borrow $1,000,000 in New York at 7%;

2. Convert the $1,000,000 to £571,428.57 at £1 = $1.75;

3. Invest the £571,428.57 in London at 12% for one year, and sell £640,000 forward at a rate of £1 = $1.68 for delivery in one year.

4. At the end of the year, collect £640,000 from the investment in London, deliver it to the bank's foreign exchange department in return for $1,075,200, and use $1,070,000 to repay the loan in New York. The arbitrageur will earn $5,200 on this set of transactions with no investment at all.

##### Source:

- CFA