## What is the Uncovered Interest Rate Parity (UIRP)?

The Uncovered Interest Rate Parity (UIRP) is a financial theory that postulates that the difference in the nominal interest rates between two countries is equal to the relative changes in the foreign exchange rate over the same time period. It is quite similar to an economic theory called the “Law of One Price (LOOP).” It is similar in the sense that UIRP also claims that the price of an identical commodity, financial security, etc. anywhere around the world should have the same price when currency exchange rates are taken into consideration, regardless of its location in the world.

The uncovered interest rate parity ensures that an investor gains no excess return by relative changes or differences in foreign exchange rates. It does so by assuming that the country with the higher interest rate will experience depreciation in its domestic currency value relative to the foreign currency value with the lower interest rate.

**Summary**

**The Uncovered Interest Rate Parity (UIRP) is a financial theory that postulates that the difference in the nominal interest rates between two countries equals the relative changes in the foreign exchange rate over the same time period.****Without interest rate parity, it would be very easy for banks and investors to exploit differences in currency rates and make profits.****UIRP works by assuming that the country with the higher interest rate will experience depreciation in its domestic currency value relative to the foreign currency value with the lower interest rate.**

### Formula for Uncovered Interest Rate Parity (UIRP)

Where:

**E**is the expected value of the spot exchange rate_{t}[e_{spot}(t + k)]**e**, k periods from now. No arbitrage dictates that this must be equal to the forward exchange rate at time t_{spot}(t + k)**k**is number of periods in the future from time t**e**is the current spot exchange rate_{spot}(t)**i**_{Domestic }is the interest rate in the country/currency under consideration**i**_{Foreign }is the interest rate in another country/ currency under consideration. In the equation of the uncovered interest rate parity mentioned above, the forward exchange rate is the future exchange rate. They are available with banks and foreign-exchange dealers.

### Assumptions of UIRP

**Capital mobility in the marke**t: The uncovered interest rate parity assumes perfect capital mobility in the market.**Non-arbitrage condition**: UIRP follows a no-arbitrage condition in the UIRP equation. If the condition is violated, a risk-free return exists, and an opportunity to make a risk-free profit unfolds.

** **

### Limitations of UIRP

**Expected rate of depreciation**: Empirical evidence concludes that the expected rate of depreciation, which plays a crucial role in uncovered interest rate parity, is often less than the difference that needs to be adjusted. Such a limitation often hampers the efficient working of the uncovered interest rate parity equation.

### Practical Example

Assume the nominal interest rate in the US is 6% per annum, and the nominal interest rate in India is 14% per annum. Since the nominal interest rate in India is higher, the investor will perceive it to be beneficial to borrow in USD and invest that in INR, and then reconvert the investment proceeds to USD to make a profit from the difference.

Say, for example, the investor borrows USD1,800 and converts it in INR at a spot rate of INR70/USD. Hence, he would need to repay USD1,860 after a year. Hence, he invests INR126,000 at a rate of 14% per annum. Hence, by the end of the year, he will receive INR143,640.

Now, when he tries to reconvert the investment proceeds back to USD, the uncovered interest rate parity condition will come into play, and the nominal interest rate difference will rise in order to eliminate the difference. The investor will then neither be better off nor worse off and will not make any profit as the difference in interest rates will be adjusted according to the no-arbitrage condition of UIRP.

### Covered Interest Rate Parity vs. Uncovered Interest Rate Parity

#### 1. Future rates

Covered interest rate parity involves the use of future rates or forward rates when assessing exchange rates, which also makes potential hedging possible. However, uncovered interest rate parity takes into account expected rates, which basically implies forecasting future interest rates. Hence, it involves the use of an estimation of the expected future rate and not the actual forward rate.

#### 2. Difference in exchange rates

According to covered interest rate parity, the difference between interest rates gets adjusted in the forward discount/premium. When investors borrow from a lower interest rate currency and invest in a higher interest rate currency, they are consequently in advantage through a forward cover. The forward cover eliminates any risks associated with their investment.

However, the uncovered interest for parity adjusts the difference between interest rates by equating the difference to the domestic currency’s expected rate of depreciation. It is because, in an uncovered interest rate parity condition, investors do not benefit from any forward cover.

### More Resources

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