Uncovered Interest Rate Parity (UIP): Definition and Calculation

What Is Uncovered Interest Rate Parity (UIP)?

Uncovered interest rate parity (UIP) theory states that the difference in interest rates between two countries will equal the relative change in currency foreign exchange rates over the same period. It is one form of interest rate parity (IRP) used alongside covered interest rate parity. If the uncovered interest rate parity relationship does not hold, then there is an opportunity to make a risk-free profit using currency arbitrage or forex arbitrage.

The Formula for Uncovered Interest Rate Parity Is:


$\begin{aligned} &F_0=S_0\frac{1+i_c}{1+i_b}\\ &\textbf{where:}\\ &F_0=\text{Forward rate}\\ &S_0=\text{Spot rate}\\ &i_c=\text{Interest rate in country }c\\ &i_b=\text{Interest rate in country }b \end{aligned}$​F0​=S0​1+ib​1+ic​​where:F0​=Forward rateS0​=Spot rateic​=Interest rate in country cib​=Interest rate in country b​

How to Calculate 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 this 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 through taking a loan in a low interest rate currency and using it to purchase a high interest rate currency. 

A currency with a lower interest rate will trade at a forward premium in relation 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.

What Does Uncovered Interest Rate Parity Tell You?

Uncovered interest rate parity conditions consist of two return streams, one from the foreign money market interest rate on the investment and one from the change in the foreign currency spot rate. Said another way, uncovered interest rate parity assumes foreign exchange equilibrium, thus implying that the expected return of a domestic asset (that is, a risk-free rate like a U.S. Treasury bill or T-bill) will equal the expected return of a foreign asset after adjusting for the change in foreign currency exchange spot rates.

When uncovered interest rate parity holds, there can be no excess return earned from simultaneously going long a higher-yielding currency investment and shorting a different lower-yielding currency investment or interest rate spread. 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.

UIP is related to the so-called “law of one price,” which is an economic theory that states 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—if it is traded in a free market with no trade restrictions.

The “law of one price” exists because differences between asset prices in different locations should eventually be eliminated due to the arbitrage opportunity. The law of one price theory is the underpinning of the concept of purchasing power parity (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 relates to a formula that can be applied to compare securities across markets that trade in different currencies. As exchange rates can shift frequently, the formula can be recalculated on a regular basis to identify mispricings across various international markets.

The Difference Between Covered Interest Rate Parity and Uncovered Interest Rate Parity

Covered interest parity (CIP) involves using forward or futures contracts to cover exchange rates, which can thus be hedged in the market. Meanwhile, uncovered interest rate parity (UIP) involves forecasting rates and not covering exposure to foreign exchange risk—that is, there are no forward rate contracts, and it uses only the expected spot rate.

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

Limitations of Uncovered Interest Parity

There is only limited evidence to support UIP, but 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 time periods, 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.

The Bottom Line

Uncovered interest rate parity is based on the theory that foreign exchange rates smooth out the differentials between the interest rates of two different countries. However, this theory may not always hold. Macroeconomic factors, such as monetary policy, distortions in foreign exchange markets, and time horizons can affect the validity of this theory.

For this reason, investors may use this as an opportunity to earn money through taking a loan in a domestic currency with low interest rates and buying a foreign currency with higher rates as market imperfections and other factors affect the movement of currencies.