# Uncovered Interest Rate Parity: Definition, Formula, and Key Insights

## What Is Uncovered Interest Rate Parity (UIP)?

Uncovered interest rate parity (UIP) is a theory that suggests how differences in interest rates between countries relate to expected changes in currency exchange rates. It explains that if one country has higher interest rates, its currency should depreciate to prevent arbitrage opportunities. While UIP helps in economic models, its assumptions can limit real-world applicability. UIP is different from covered interest rate parity, where forward contracts are used to lock in exchange rates and eliminate risk.

### Key Takeaways

*   Uncovered interest rate parity predicts that interest rate differences between countries equal expected changes in their exchange rates.  
    
*   When UIP holds, there can be no risk-free profit from currency arbitrage due to exchange rate adjustments.  
    
*   UIP theory assumes that countries with higher interest rates will see their currencies depreciate.  
    
*   Covered interest rate parity involves forward contracts to hedge against currency risk, unlike UIP, which does not.  
    
*   There is limited empirical evidence supporting UIP in real-world conditions due to market inefficiencies and economic factors.

## How Uncovered Interest Rate Parity (UIP) Works

Uncovered interest rate parity is related to the "law of one price." This economic theory states that the price of an identical security, commodity, or product traded anywhere in the world should have the same price regardless of location when currency exchange rates are taken into consideration. In a free market without trade restrictions, price differences should only result from exchange rate variations.

If UIP holds, you can't earn extra returns by investing in a high-yield currency and shorting a low-yield one. Uncovered interest rate parity assumes that the country with the higher interest rate or risk-free money market yield will experience depreciation in its domestic currency relative to the foreign currency.

> **Important**
>
> UIP assumes a foreign exchange balance, where a U.S. Treasury bill's expected return matches a foreign asset's return after accounting for currency rate changes.

The law of one price exists because [arbitrage](https://www.investopedia.com/terms/forex/f/forex-arbritrage.asp) eventually erases asset price differences between locations. The law of one price theory is the underpinning of the concept of [purchasing power parity](https://www.investopedia.com/terms/p/purchasingpower.asp) (PPP).

Purchasing power parity states that the value of two currencies is equal when a basket of identical goods is priced the same in both countries. This applies a formula to compare securities in markets trading different currencies. Since exchange rates change often, the formula helps find mispricings in global markets.  
  

## Calculating Uncovered Interest Rate Parity: Formula & Steps

The formula for uncovered interest rate parity is:  

$\begin{aligned} &F_0=S_0\frac{1+i_c}{1+i_b}\\ &\textbf{where:}\\ &F_0=\text{Forward rate}\\ &S_0=\text{Spot rate}\\ &i_c=\text{Interest rate in country }c\\ &i_b=\text{Interest rate in country }b \end{aligned}$

### How to Calculate Uncovered Interest Rate Parity

Uncovered interest rate parity is based on the theory that countries with high interest rates tend to have currencies that often depreciate. This is calculated through the formula above, which takes the spot exchange rate between the two currencies and multiplies it by the interest rate in one country, divided by the interest rate in the second country. 

In theory, the expected spot exchange rate will be equal to the gap between the two countries’ interest rates.

However, if this does not materialize, investors can make a profit by taking a loan in a low-interest-rate currency and using it to purchase a high-interest-rate currency. 

> **Fast Fact**
>
> A currency with a lower interest rate will trade at a forward premium relative to a currency with a higher interest rate. For example, the U.S. dollar typically trades at a forward premium against the Canadian dollar; conversely, the Canadian dollar trades at a forward discount versus the U.S. dollar.

## Comparing Uncovered vs. Covered Interest Rate Parity

Both uncovered and covered interest rate parity relate to risks that arise from the exchange rates between currencies.

Covered interest parity (CIP) theorizes that the relationship between the [spot](https://www.investopedia.com/terms/s/spotprice.asp) and [forward](https://www.investopedia.com/terms/f/forwardrate.asp) currency values and the interest rates of two countries should be in equilibrium. Investors making use of CIP can use forward or futures contracts to cover exchange rates to hedge their market risk.

Uncovered interest rate parity (UIP) involves forecasting rates and not covering exposure to foreign exchange risk. There are no forward rate contracts, and it uses only the expected spot rate.

> **Fast Fact**
>
> There is no theoretical difference between covered and uncovered interest rate parity when the forward and expected spot rates are the same.

## Challenges and Limitations of Uncovered Interest Rate Parity

The main limitation of uncovered interest rate parity is that it is theoretical. There is only limited evidence to support UIP under real-world conditions. However, economists, academics, and analysts still use it as a theoretical and conceptual framework to represent rational expectation models. UIP requires the assumption that capital markets are efficient.

Empirical evidence has shown that over the short- and medium-term, the level of depreciation of the higher-yielding currency is less than the implications of uncovered interest rate parity. Many times, the higher-yielding currency has strengthened instead of weakened.

## What Is Interest Rate Parity in Simple Terms?

Interest rate parity looks at two core components: the currency exchange between two countries and each currency’s interest rate. Interest rate parity is a theory that suggests that the difference between these two countries is equal to the changes in the foreign exchange rate over a given time period.

## What Are the Two Types of Interest Rate Parity?

The two main types of interest rate parity are covered and uncovered. Covered includes the use of forward or futures contracts that are intended to cover exchange rates and serve as a hedge against risk. Uncovered does not involve these forward contracts to cover foreign exchange risk, hence uncovered. 

## What Would an Uncovered Interest Arbitrage Imply?

Uncovered interest arbitrage implies that foreign exchange investors can turn a profit through taking out a loan in a currency that has a low interest rate and buying a foreign currency with a high interest rate. 

## The Bottom Line

UIP explains how exchange rates adjust based on interest rate differences between countries. But it doesn’t always hold because of factors like monetary policies and market distortions, which create opportunities for investors to profit from interest rate differences. Unlike covered interest rate parity, UIP doesn’t use forward contracts, so investors are exposed to exchange rate changes. Despite its limitations, UIP can be useful to help understand how exchange rates move.