# Forward Premium and Discount – Meaning, Calculation, and Example

## Forward Premium and Discount: Meaning

We use forward premium and discount terminologies for forward contract transactions in the foreign exchange markets. In the currency market, it is a situation where the spot rate of the currency, under trade, is less than its forward’s exchange rate. In other words for buying a forward contract if one has to pay more than the prevailing sport rate, the differential is the Premium and is also known as Forward Premium. It acts as an indicator for traders and sends a signal that the exchange rate is possibly going to rise shortly against another currency. Conversely, this also means that the currency will probably experience a decrease in value trading with a forward premium.

Similarly, the forward discount is the exact opposite of the forward premium. To elaborate, a forward discount will mean that the forward exchange rate of the currency is lower than its spot exchange rate in the forex market. The traders can take a cue and enter into positions accordingly. The currency in question is probably going to appreciate soon about another currency, in it carries a forward discount.

Forward premium and discount are based on speculations and market conditions. They do not provide a surety that the currency will move in the direction of the predictions. Various indicators and technical analyses can help traders and investors to make much more accurate predictions and improve the probabilities of a positive trade. But nothing can guarantee the happenings or currency movement exactly as per the predictions all the time.

## Calculation of Forward Premium and Discount

We calculate the forward premium by deducting the spot exchange rate from the forward exchange rate. Then we adjust it with the duration of the forward contract to get the annualized forward premium. The formula for the same is:

Annualized forward premium= {(Forward exchange rate – Spot exchange rate)/ Spot exchange rate} * (360/ Actual duration of the forward contract) * 100

#### Example

Let us go through an example to understand this. Suppose the ninety-day forward exchange rate of the Indian National Rupee(INR) to the US Dollar is 80.50. The spot rate for INR/ USD is 80.25.

Therefore, the annualized forward premium= {(80.50 -80.25)/80.25}* (360/90)*100

= 0.25/80.25 * 4* 100

=1.25%.

In the above example, we need to pay 0.25 INR more after ninety days to get the same \$1. Therefore, the value of INR is depreciating, and that of US\$ is appreciating.

### Forward Discount

As we discussed above, Forward Discount is the opposite of Forward Premium. Therefore, to calculate the Forward Discount Rate, we will have to deduct the forward rate from the current spot exchange rate. And as we did for Forward Premium, we need to adjust this answer with the duration of the forward contract to arrive at the annualized forward discount rate.

The formula for annualized forward discount is:

{(Spot exchange rate – forward exchange rate)/ Spot exchange rate} * (360/ Actual duration of the forward contract) * 100

Continuing with the above example, the US\$ to INR forward exchange rate is 1/80.5= 0.01242236, and the spot exchange rate for the same is 1/80.25= 0.01246106

Therefore, the annualized forward discount = {(0.01246106-0.01242236/0.01246106}* (360/90)*100

= 0.000039/0.01246106*4*100

= 1.25%.

### Calculation of Forward Exchange Rate

In the above example, we already know the forward exchange rate. However, in case the forward exchange rates are not available then also it is possible to calculate the Forward Exchange Rate. This calculation can be attempted with the help of prevailing interest rates for both the countries, domestic and foreign. The formula for the same is:

Forward exchange rate= Spot rate x {(1 + Domestic interest rate)/ (1 + Foreign interest rate)}

Let us assume that the spot exchange rate for INR to USD is 80.25. The domestic rate of interest is 4%, and the foreign rate of interest is 3%. We have to calculate the six months forward exchange rate from today.

Now we will substitute the given values in the above formula.

Forward exchange rate= 80.25 * {(1 + 0.04)/ (1+0.03)}

= 80.25* 1.0097

=81.03

Hence, we can see that a forward premium exists. Now we can calculate the annualized forward premium as:

Annualized forward premium= {(81.03-80.25)/80.25} * 360/180*100

= 0.0097 *2*100

=1.94%

### Arbitrage Opportunity

Suppose the interest rate in India is 5% while it is 4% in the United States. So can one borrow from the United States, invest in India, and easily make a profit of 1%?

On the face, it looks positive. But practically due to the impact of the “interest rate parity” theory, this may not be possible. This arbitrage opportunity is not possible because of the existence of forward premium when the interest rate is higher than in other countries. An example will throw better light on this concept.

Let us assume the spot exchange rate of INR to USD is 1.5. Mr. X decides to borrow 100 units of currency from the United States and invest it in India. He will get 100*1.5= 150 INR. Let us assume that the time under consideration is one year for the sake of simplicity.

Now we will calculate the forward exchange rate as follows:

1.5 * {(1+.05)/(1+.04)}

= 1.5 * 1.0096

=1.5144

At the end of one year, Mr.X will receive 157.5 units of INR at the interest rate of 5% (150 units x 1.05)

Now he decides to convert it back to USD. The new exchange rate is 1.5144.

Therefore, he will get (157.5/ 1.5144)= 104 USD.

The interest rate in the United States was 4% p.a. Interest on the 100 USD that he borrowed initially. Hence, the interest amount for one year = 100 * 4%= 4 USD.

Therefore, the amount that he will get at the end of the year is \$ 104 – \$4= \$100. Thus, he ends up making no arbitrage profits.

Moreover, even if due to market inefficiency such a trade may be possible, however, such an arbitrage opportunity will be extremely short-lived. This is considering the kind of volume and dynamic trading happening in currency all over the world where rates are changing very fast. For swift trading traders and investors are using the software rather than trying their hands.

## Summary

A forward foreign exchange contract is simply the price that we are willing to pay for a currency today to get it in the future. The forward premium and discount help investors to gauge the likely price movement of currencies, trade accordingly, and make profits or minimize adverse impacts in the process.

However, traders should do appropriate technical analysis before entering into any position based on forward premium or discount. Because though the terminologies and concept are exactly opposite of each other, however, both the parameters do not guarantee a likewise movement in the value of the currencies in question. Hence, the element of risk does exist and can also result in a loss. This fact and risk management, therefore, need to be planned meticulously. 