Understanding Discounts and Premiums in Exchange Rates with Excel Formulas

Discounts and premiums exchange rates are terms that describe the difference between the spot exchange rate and the forward exchange rate of two currencies. The spot exchange rate is the current price of one currency in terms of another currency. The forward exchange rate is the agreed-upon price of one currency in terms of another currency for a future transaction.

A forward premium occurs when the forward exchange rate is higher than the spot exchange rate. This means that the market expects the first currency to appreciate or increase in value relative to the second currency in the future. A forward discount occurs when the forward exchange rate is lower than the spot exchange rate. This means that the market expects the first currency to depreciate or decrease in value relative to the second currency in the future.

For example, let’s say the current spot exchange rate between the US dollar and the Japanese yen is 109.38 yen per dollar. This means that one US dollar can buy 109.38 Japanese yen at the present time. Now, let’s say the 90-day forward exchange rate between the US dollar and the Japanese yen is 109.50 yen per dollar. This means that one US dollar can buy 109.50 Japanese yen in 90 days.

In this case, the US dollar is trading at a forward premium relative to the Japanese yen, because the forward exchange rate is higher than the spot exchange rate. This implies that the market expects the US dollar to appreciate or become more valuable compared to the Japanese yen in 90 days. Conversely, the Japanese yen is trading at a forward discount relative to the US dollar, because the forward exchange rate is lower than the spot exchange rate. This implies that the market expects the Japanese yen to depreciate or become less valuable compared to the US dollar in 90 days.

One of the main factors that influence the forward exchange rate is the difference in interest rates between the two countries. Generally, the currency with the higher interest rate will trade at a forward discount, and the currency with the lower interest rate will trade at a forward premium. This is because investors will demand a higher return for holding the currency with the higher interest rate, and will accept a lower return for holding the currency with the lower interest rate.

Basic Theory:

Exchange rates are influenced by various factors, including interest rates, inflation, economic indicators, and market sentiment. The concept of discounts and premiums arises when the exchange rate for a currency differs from its nominal or official rate. A discount occurs when the exchange rate is lower than the official rate, while a premium occurs when the exchange rate is higher.

Procedures:

To calculate the discount or premium percentage, you can use the following formula:

Now, let’s proceed with a scenario to illustrate these concepts.

Scenario:

Imagine you are a financial analyst dealing with the USD to EUR exchange rate. The official exchange rate is 1 USD = 0.85 EUR. The market exchange rate is currently 1 USD = 0.80 EUR.

Excel Calculation:

1. Create an Excel Table: Set up a table with the following columns: Date, Official Rate (0.85 EUR), Market Rate (0.80 EUR), and Discount/Premium (%).
2. Apply the Formula: In the Discount/Premium column, use the formula:

      

3. Interpret the Results: The calculated discount or premium percentage will help you understand how the market rate compares to the official rate on each date.

Results:

For our scenario:

This negative percentage indicates a 5.88% discount in the exchange rate, suggesting that the market rate is lower than the official rate.

Other Approaches:

1. Historical Analysis: Track and analyze historical data to identify trends in discounts or premiums over time.
2. Forward Rates: Consider using forward rates to estimate future exchange rates and potential discounts or premiums.
3. Volatility Measures: Incorporate measures like standard deviation to assess the volatility of exchange rate movements.