Question

A US importer of German cars wants to arrange a forward contract to buy euros in half a year. The interest rates for investments in US dollars and euros are \(r_{\mathrm{USD}}=4 \%\) and \(r_{\mathrm{EUR}}=3 \%\), respectively, the current exchange rate being \(0.9834\) euros to a dollar. What is the forward price of euros expressed in dollars (that is, the forward exchange rate)?

Short answer

The forward exchange rate is approximately 0.9784 euros per dollar.

Step-by-step solution

Identify the Given Values

Let's identify the values provided in the exercise: \(r_{\text{USD}} = 4\text{\%}\), \(r_{\text{EUR}} = 3\text{\%}\), current exchange rate \(S_0 = 0.9834\) euros per dollar.

Calculate the Forward Exchange Rate Formula

The forward exchange rate can be calculated using the following formula:\[ F = S_0 \times \frac{(1 + r_{\text{EUR}})^t}{(1 + r_{\text{USD}})^t}\] where \(t\) is the time period in years. In this problem, \(t = 0.5\).

Substitute the Values

Substituting the identified values into the formula, we get:\[ F = 0.9834 \times \frac{(1 + 0.03)^{0.5}}{(1 + 0.04)^{0.5}} \]

Calculate the Exponents

Calculate the exponents for both the numerator and the denominator:\( (1 + 0.03)^{0.5} \approx 1.01489 \) and \( (1 + 0.04)^{0.5} \approx 1.01980 \)

Divide the Values

Divide the numerator by the denominator:\[ \frac{1.01489}{1.01980} \approx 0.99519 \]

Multiply by the Initial Exchange Rate

Finally, multiply the result by the initial exchange rate:\[ F = 0.9834 \times 0.99519 \approx 0.9784 \]

Key concepts

foreign exchange

Foreign exchange (forex) refers to the global marketplace for trading national currencies against one another. It is the largest and most liquid financial market in the world. Transactions in foreign exchange often involve currency conversion and are used by businesses, governments, investors, and tourists. In this exercise, the US importer needs euros to buy German cars, so they are participating in the foreign exchange market to exchange US dollars (USD) for euros (EUR). Forex prices change based on supply and demand, economic factors, and geopolitical events. The current exchange rate given is 0.9834 euros per dollar, which means that 1 USD can be exchanged for 0.9834 EUR.

interest rate parity

Interest rate parity is a fundamental theory in foreign exchange markets that connects interest rates, spot exchange rates, and forward exchange rates. It asserts that the difference in interest rates between two countries equals the differential between the forward exchange rate and the spot exchange rate. This theory ensures that investors cannot arbitrage between differing interest rates in different countries without risking exposure to currency fluctuations. In our example, the US interest rate is 4% and the Eurozone interest rate is 3%. We use these rates to calculate the forward exchange rate, as the difference in these rates will affect how the currencies exchange value over time.

forward contracts

A forward contract is a customized financial agreement between two parties to buy or sell an asset at a specified future date for a price agreed upon today. In the context of foreign exchange, forward contracts are used to hedge currency risk. For the US importer mentioned in the exercise, a forward contract helps lock in the exchange rate for euros in half a year, mitigating risks related to potential unfavorable movements in the exchange rate. The forward price is calculated by adjusting the spot rate by the interest rate differential between the two currencies over the contract period. This ensures the importer can adequately budget and avoid financial uncertainty.

currency risk management

Currency risk management involves strategies to protect against potential losses due to unfavourable changes in exchange rates. One effective method is using financial instruments like forward contracts, options, and swaps. In this exercise, the US importer uses a forward contract to manage currency risk, thereby locking in the price for future euro purchases to eliminate the uncertainty of fluctuating exchange rates. Such proactive measures are critical for businesses involved in international trade to stabilize financial forecasts, budgets, and operational costs. By hedging against currency risks, companies can focus on their core operations without worrying about adverse currency movements.