Question

Write an equation that describes interest rate parity and explain the equation.

Short answer

Answer: The interest rate parity equation is given by F/S = (1 + r_d) / (1 + r_f), where F represents the forward exchange rate, S is the spot exchange rate, r_d is the domestic interest rate, and r_f is the foreign interest rate. This equation demonstrates the connection between the spot and forward exchange rates of two currencies and their respective interest rates. If interest rate parity holds, the forward exchange rate will equal the spot exchange rate adjusted for the difference in interest rates between the two countries. This concept is crucial for investors to make informed decisions regarding global investment allocations, considering potential returns and exchange rate risks.

Step-by-step solution

Understand the components of the interest rate parity equation

Interest rate parity equation consists of the following components: 1. Spot exchange rate (S) 2. Forward exchange rate (F) 3. Domestic interest rate (r_d) 4. Foreign interest rate (r_f)

Write the interest rate parity equation

The equation to describe the interest rate parity is given by: F/S = (1 + r_d) / (1 + r_f)

Explain the interest rate parity equation

The interest rate parity equation states the connection between the spot and forward exchange rates of two currencies and their respective interest rates: 1. The spot exchange rate (S) refers to the current rate at which one currency can be exchanged for another. 2. The forward exchange rate (F) is the rate at which a currency can be exchanged for another currency on a specified future date. 3. The domestic interest rate (r_d) is the interest rate paid on domestic deposits or bonds. 4. The foreign interest rate (r_f) is the interest rate paid on foreign deposits or bonds. The equation shows that if interest rate parity holds, the forward exchange rate will equal the spot exchange rate adjusted for the difference in interest rates between the two countries. In other words, if a domestic currency has a higher interest rate than the foreign currency, it is expected to devalue in the future, and the forward exchange rate should reflect this devaluation to maintain interest rate parity. This concept is essential for investors, as it helps them make informed decisions regarding where to allocate their investments globally, factoring in both potential returns and exchange rate risks.

Key concepts

Spot Exchange Rate

The spot exchange rate represents the current price to directly exchange one currency for another. It is the rate you would receive if you were to exchange a currency on the spot, or 'right now', without any delay. Think of it as the price tag for buying a foreign currency with your domestic one, very much like buying a coffee at your local cafe and paying right away. It's set by foreign exchange markets which take into account supply and demand, economic indicators, geopolitical stability, and other factors that might affect the value of a currency.

For example, if you want to buy Euros using US dollars and the spot exchange rate is 1.20, it means that 1 Euro costs 1.20 US dollars. When you travel and exchange money at a currency exchange booth, you're dealing with the spot exchange rates (although they may add commissions or fees).

In the context of interest rate parity, the spot exchange rate is crucial as it serves as a baseline for comparing the present and future value of currencies.

Forward Exchange Rate

Unlike the spot exchange rate, the forward exchange rate is used for transactions that will occur at a future date. It is the agreed-upon rate at which one currency will be exchanged for another in the future. This helps businesses and investors to hedge against potential fluctuations in currency value over time.

Consider the forward exchange rate as a form of a 'reservation' of a currency exchange rate. If you enter into a forward contract today to exchange dollars for euros in six months at a rate of 1.25, it means you have locked in the price of 1.25 dollars per euro, regardless of where the spot rate moves in that six-month period.

In terms of interest rate parity, the forward exchange rate is influenced by the difference in interest rates between two countries. If you expect one currency to yield less interest over time compared to another, the forward exchange rate will generally reflect this by making the lower-interest currency cheaper in the future.

Domestic Interest Rate

The domestic interest rate is the rate of return that investors can expect to earn on investments within their home country. It can come from saving accounts, government bonds, or other financial instruments. Central banks such as the Federal Reserve in the US or the European Central Bank in the Eurozone often set benchmark interest rates that influence these domestic rates.

For instance, if the domestic interest rate in the US increases, it typically makes US financial assets more attractive, because they yield higher returns. This can strengthen demand for the US dollar, affecting the spot and forward exchange rates. Higher interest rates can lead to a stronger currency because foreign investors need to buy more of that currency to invest at higher returns.

In relation to interest rate parity, a higher domestic interest rate can indicate an expectation for the domestic currency to depreciate in the future, which would be captured by a higher forward rate compared to the spot rate. It's like saying that money today will be worth more than the same amount in the future due to interest earned.

Foreign Interest Rate

The foreign interest rate, in contrast, is the rate of return on investments in an external country. Just like the domestic interest rate, it can be influenced by the external country’s central bank and economic policies. Investments might include foreign bonds, savings accounts, or any other financial product available to international investors.

When comparing two countries, if the foreign interest rate is higher than the domestic rate, investors might be attracted to invest in the foreign country to gain higher returns. Yet, they also have to consider the risk of currency fluctuations which could nullify their additional earnings. This is where the forward exchange rates become vital as they provide insight into how the currency might perform in the future.

The interplay between the foreign interest rate and the domestic interest rate is central to the concept of interest rate parity. If foreign interest rates are expected to be higher, the domestic currency is anticipated to appreciate in the forward exchange market to balance the potential extra returns from investing abroad.