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# Calculate the Forward Rate in Each Currency

Spot market currencies are exchanged for immediate delivery in the forward rate market, whereas contracts are made to sell or buy currencies for future delivery. For example, when a company in the U.S. buys goods from England valued in British Pounds (£), then, the importer owes British Pounds (£) for future delivery, let’s say in 90 days. If, for instance, the current price of British Pounds (£) is $1.71, there is the possibility of the British Pounds (£) rising against the U.S. dollar. This would consequently make the goods to cost more. Negotiating a 90-day forward contract with a bank at a price of, say, £:$ = 1.72, would nevertheless cushion the importer against this risky exchange. In 90 days, the bank will provide the importer with £1 million while the importer gives the bank $1.72. By doing this, the importer can convert a short underlying position in British Pounds (£) to a riskless position, and the bank then takes the risk for a premium. ## Points to Note • The forward profit or loss contract is not related to the current spot rate of £:$ = 1.71.
• The profit or loss on the forward contract approximately offsets the change in the U.S. dollar cost of the good order that is associated with movements in the GBP’s value.
• The forward contract is not optional. Each party is held to pay the price quoted in the agreement.

## Interest Rate Parity (IRP)

According to the IRP theory, the currency of  a nation with a lower interest rate should be at a forward premium compared to the currency of the nation with a higher interest rate. Considering a market with no transaction costs, the interest differential should be close to equal to the forward differential.

For example, at one point in 2018, the spot euro-dollar exchange rate, expressed as USD/EUR, was 1.2775 while the one-year forward rate was 1.27485. This means that the forward rate was trading at a discount with respect to the spot rate. This is because the forward rate was smaller compared to the spot rate. Therefore, the one-year forward points could be quoted as (1.27485 – 1.2775) = -0.00265 = -26.5 pips.

Note that most of the non-yen exchange rates are always quoted to four decimal places (the yen is an exception and is quoted to 2 decimal places for spot rates). In our case, we scale up the answer by four decimal places by multiplying by 10,000 to get -26.5 pips. The answer is then rounded off to the nearest 1 decimal place.

We can also calculate the forward rate consistent with the spot rate and the interest rate in each currency. Since the amount of forward points is proportional to the spread between the foreign and the domestic interest rates $$i_f – i_d$$, we can evaluate this relationship as:

$$F_{f/d}-S_{f/d}=S_{f/d} [\frac{i_f-i_d}{1+i_d τ)}]τ$$

#### Example: Calculating the Forward Rate in Each Currency

If we want to know the 31-day forward exchange rate from a 31-day domestic risk-free interest rate of 2.5% per year, given that the foreign 31-day risk-free interest rate is 3.5% with a spot exchange rate, $$S_{f/d}$$, of 1.5630, then we simply have to substitute these values into the forward rate equation:

$$F_{f/d}=S_{f/d}(\frac{1 + i_f τ}{1+i_d τ})$$

$$F_{f/d}=1.5630 (\frac{1+0.035×\frac{31}{360}}{1+0.025×\frac{31}{360}})=1.5643$$

$$F_{f/d} – S_{f/d}= 1.5643 – 1.5630 = 0.0013$$

Since forward premiums or discounts are usually quoted in pips or points (1/100 of 1%), multiplying the result by 10,000 will give us $$0.0013×10,000 = 13$$ pips, which is the forward trading premium quoted in pips or points.

We can alternatively use the above formula as:

$$F_{f/d}-S_{f/d}=1.5630[\frac{0.035-0.025}{1+0.025\times \frac{31}{360}}] \times \frac{31}{360}=0.001343$$

### Question

When is a base currency at a forward discount?

1. At a time when the interest parity holds.
2. When the forward rate is below the spot rate.
3. When the forward rate is above the spot rate.

Solution

The base currency is at a forward discount if the forward rate is below the spot rate.

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