What is Interest Rate Parity?

Interest rate parity is a phenomenon in which the appreciation (depreciation) of one currency against another is offset by changes in interest rate differences. According to the interest rate parity relationship, investors will achieve the same domestic rate of return regardless of whether they invest domestically or abroad by hedging in the forward foreign exchange market. ^[1]

Interest parity

The condition that the expected return on any two currency deposits measured in the same currency is equal is called the interest rate parity condition. Such as:

Se / S = (1 + r) / (1 + re)

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

We assume that we are an investor in Country A, and we have a freely disposable fund in our hands, which can freely enter and exit the financial markets of our country and Country B. It is also assumed that there are no restrictions and transaction costs for funds moving internationally. Then the existence of this fund is the choice of the financial market in which country to invest. When making other choices, if other conditions remain unchanged, it is obviously to see which country has the higher returns. Assume that the one-year interest rate of country A is i, the interest rate of country B is i ^ *, and the spot exchange rate is e (direct price method).
If you invest in the domestic financial market, the value added per unit of domestic currency at maturity: 1 × (1 + i) = 1 + i. If investing in the financial market of country B, it can be divided into three steps: exchange into the currency of country B in the domestic foreign exchange market, make a one-year deposit in the financial market of country B, and exchange it into the national currency after the deposit expires. 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 settled one year later, and this forward exchange rate is recorded as f. At that time, the value added of 1 unit of national currency can be: f (1 + i ^ *) / e. Obviously, which investment method we choose depends on the return rate of these two methods. If 1 + i> f (1 + i ^ *) / e, we will invest in the domestic financial market; if 1 + i <f (1 + i ^ *) / e, we will invest in the financial market of country B ; If 1 + i = f (1 + i ^ *) / e, invest in the financial markets of both countries at this time. Other investors in the market also face the same decision choices. Therefore, if 1 + i <f (1 + i ^ *) / e, many investors will put funds into the financial market of Country B, which will cause the immediate purchase of Country B s currency and the future sale of B in the foreign exchange market. China s currency behavior has devalued the domestic currency (e has increased) and long-term appreciation (f has decreased), and the return on investment in the financial market of country B has declined. Only when the return of these two investment methods are the same, the market is in equilibrium. Therefore, when an investor trades in the form of a cover holding forward contract, the market will eventually cause the following relationship between interest rates and exchange rates:
1 + i = f (1 + i ^ *) / e

Sorted out:
f / e = (1 + i) / (1 + i ^ *)
We note that the premium (discount) rate between the spot exchange rate and the forward exchange rate is , that is, = (fe) / e
Combine the two formulas above:
= (fe) / e = (1 + i- (1 + i ^ *)) / (1 + i ^ *) = (ii ^ *) / (1 + i ^ *)
That is: + i ^ * = ii ^ *
Since and i ^ * are small values, their quadrature i ^ * can be omitted, that is:
= ii ^ *
The above formula is the general form of interest rate parity. Its economic meaning is that the forward 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 period; if the domestic interest rate is lower than the foreign interest rate, the local currency will appreciate in the forward period. In other words, changes in the exchange rate will offset the difference in interest rates between the two countries, thereby putting the financial market in equilibrium.

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There are some flaws in this theory, which are mainly manifested in:

1. The interest rate parity theory does not consider transaction costs. However, transaction costs are an important factor. If the various transactions are too high, it will affect the arbitrage income, and thus affect the relationship between exchange rates and interest rates. If transaction costs are taken into account, international covering arbitrage activities will cease before interest rate parity is reached.

2. The theory of interest rate parity assumes that there are no obstacles to capital flows, and it is assumed that funds can flow smoothly and unrestrictedly across the world. But in fact, the flow of funds internationally will be hindered by factors such as foreign exchange controls and underdeveloped foreign exchange markets. Currently, only a few international financial centers have perfect futures exchange markets, and there are fewer restrictions on capital flows.

3. The theory of interest rate parity also assumes that the size of arbitrage funds is infinite, so arbitrageurs can continue to make up arbitrage until interest rate parity is established.