Interest Rate Parity (IRP), also known as interest rate parity, refers to the equilibrium condition achieved by the foreign exchange market when the expected rates of return of all freely convertible currencies are equal.

Interest rate parity stipulates that the appreciation (devaluation) of one currency against another will be offset by changes in interest rate differences.

For example: Suppose you are an investor in country A with a freely disposable fund in your hand, and you can freely enter and exit the financial markets of your country and country B. At the same time, it is assumed that there are no restrictions and transaction costs for international movement of funds. Then there is a choice of which country’s financial market the funds are invested in. When making a choice, if other conditions remain the same, it is obvious which country has higher returns. Assume that the one-year interest rate of country A is i, the interest rate of country B over the same period is i^*, and the spot exchange rate is e (direct pricing method).

Interest rate parity
If you invest in the domestic financial market, the value of each unit of domestic currency at maturity is: 1 × (1 + i) = 1 + i. If you invest in country B’s financial market, it can be divided into three steps: convert it into country B’s currency in the domestic foreign exchange market, make a one-year deposit in country B’s financial market, and convert the deposit to the country’s currency after maturity. However, there is an exchange rate problem. Since the spot exchange rate ef after one year is uncertain, we can purchase a forward contract that is delivered one year later. This forward exchange rate is recorded as f. At that time, 1 unit of national currency can increase in value as: f(1+i^)/e. Obviously, which investment method we choose depends on the level of return of these two methods. If 1+i>f(1+i^)/e, then we will invest in the domestic financial market; if 1+i<f(1+i^)/e, then we will invest in the country B financial market ; If 1+i=f(1+i^)/e, investment in the financial markets of both countries is fine at this time. Other investors in the market also face the same decision-making choices. Therefore, if 1+i<f(1+i^*)/e, many investors will invest funds into the financial market of Country B, which leads to the spot purchase of Country B’s currency and the forward sale of B’s currency in the foreign exchange market. The country’s currency behavior will depreciate the domestic currency (e increase) and forward appreciation (f decrease), and the rate of return of investing in the financial market of country B will decrease. Only when the return rates of these two investment methods are exactly the same, the market is in equilibrium. Therefore, when investors adopt the arbitrage trading method of holding forward contracts, the market will eventually form the following relationship between interest rates and exchange rates:

1+i=f(1+i^*)/e

f/e=(1+i)/( 1+i^*)

We record the rate of appreciation (discount) between the spot exchange rate and the forward exchange rate ρ, namely

ρ=(f-e)/e

Combine the above two formulas to get:

ρ=(f-e)/e=(1+i-(1+i^))/(1+i^ )=(i-i^)/(1+i^)

That is: ρ+ρi^=i-i^

Since ρ and i^* are both very small values, their product ρi^* can be omitted, namely:

ρ=i-i^*

The above formula is the general form of arbitrage interest rate parity. Its economic meaning is: the forward premium and discount rate of the exchange rate is equal to the difference between the currency interest rates of the two countries. If the domestic interest rate is higher than the foreign interest rate, the local currency will depreciate in the forward; if the domestic interest rate is lower than the foreign interest rate, the local currency will appreciate in the forward. In other words, changes in the exchange rate will offset the difference in interest rates between the two countries, thus keeping the financial market in a state of equilibrium.

Interest rate parity theory
The forward exchange rate determination theory proposed by Keynes and Einziger. They believe that the equilibrium exchange rate is formed by foreign exchange transactions caused by international arbitrage. In the case of differences in interest rates between the two countries, funds will flow from countries with low interest rates to countries with high interest rates to make profits. But when arbitrageurs compare the rate of return of financial assets, they not only consider the rate of return provided by the interest rates of the two assets, but also consider the changes in the returns of the two assets due to changes in exchange rates, that is, foreign exchange risks. Arbitrageurs often combine arbitrage with swaps to avoid exchange rate risks and ensure that there is no risk of loss. The result of a large number of foreign exchange swap transactions is that the spot exchange rate of currencies of low-interest rate countries fluctuates, and the exchange rate of futures floats; the spot exchange rate of currencies of high interest rate countries rises, and the exchange rate of futures fluctuates. The forward price difference is the difference between the future exchange rate and the spot exchange rate. As a result, the currency of the low-interest rate country will have a forward premium, and the currency of the high-interest rate country will have a forward discount. As the cover arbitrage continues, the forward price difference will continue to increase until the return rates provided by the two assets are exactly the same, then the cover arbitrage activity will stop, and the forward price difference is exactly equal to the spread between the two countries. That is, interest rate parity is established. Therefore, we can summarize the basic point of the interest rate evaluation theory: the forward price difference is determined by the difference in interest rates between the two countries, and the currencies of high interest rate countries must be discounted in the foreign exchange market, and currencies of low interest rate countries must be premium in the foreign exchange market.