# Covered Interest Rate Parity

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## What Is Covered Interest Rate Parity?

Covered interest rate parity refers to a theoretical condition in which the relationship between interest rates and the spot and forward currency values of two countries are in equilibrium. The covered interest rate parity situation means there is no opportunity for arbitrage using forward contracts, which often exists between countries with different interest rates.

## The Formula for Covered Interest Rate Parity Is

(1+id)=FS∗(1+if)where:id=The interest rate in the domestic currency or the base currencyif=The interest rate in the foreign currency or the quoted currencyS=The current spot exchange rateF=The forward foreign exchange rate\begin{aligned} &\left(1+i_d\right) = \frac{F}{S}*\left(1+i_f\right)\\ &\textbf{where:}\\ &i_d = \text{The interest rate in the domestic currency or the base currency}\\ &i_f = \text{The interest rate in the foreign currency or the quoted currency}\\ &S = \text{The current spot exchange rate}\\ &F = \text{The forward foreign exchange rate} \end{aligned}​(1+id​)=S

F​∗(1+if​)where:id​=The interest rate in the domestic currency or the base currencyif​=The interest rate in the foreign currency or the quoted currencyS=The current spot exchange rateF=The forward foreign exchange rate​﻿

The formula above can be rearranged to determine the forward foreign exchange rate:

F=S∗(1+id)(1+if)F=S*\frac{\left(1+i_d\right)}{\left(1+i_f\right)}F=S∗(1+if​)

(1+id​)​﻿

Under normal circumstances, a currency that offers lower interest rates tends to trade at a forward foreign exchange rate premium in relation to another currency offering higher interest rates.

### Key Takeaways

• The covered interest rate parity condition says that the relationship between interest rates and spot and forward currency values of two countries are in equilibrium.
• It assumes no opportunity for arbitrage using forward contracts.
• Covered and uncovered interest rate parity are the same when forward and expected spot rates are the same.

## What Does Covered Interest Rate Parity Tell You?

Covered interest rate parity is a no-arbitrage condition that could be used in the foreign exchange markets to determine the forward foreign exchange rate. The condition also states that investors could hedge foreign exchange risk or unforeseen fluctuations in exchange rates (with forward contracts).

Consequently, the foreign exchange risk is said to be covered. Interest rate parity may occur for a time, but that does not mean it will remain. Interest rates and currency rates change over time.

## Example of How to Use Covered Interest Rate Parity

As an example, assume Country X’s currency is trading at par with Country Z’s currency, but the annual interest rate in Country X is 6% and the interest rate in country Z is 3%. All other things being equal, it would make sense to borrow in the currency of Z, convert it in the spot market to currency X, and invest the proceeds in Country X.

However, to repay the loan in currency Z, one must enter into a forward contract to exchange the currency back from X to Z. Covered interest rate parity exists when the forward rate of converting X to Z eradicates all the profit from the transaction.

Since the currencies are trading at par, one unit of Country X’s currency is equivalent to one unit of Country Z’s currency. Assume that the domestic currency is Country Z’s currency. Therefore, the forward price is equivalent to 0.97, or 1 * [(1 + 3%) / (1 + 6%)].

Looking at the currency market in Dec. 2020, we can apply the forward foreign exchange rate formula to figure out what the GBP/USD rate should be. The spot rate for the pair was 1.35.1﻿﻿ The interest rateusing the prime lending ratefor the U.K. was 1.1% and 3.25% for the U.S. The domestic currency is the British pound, making the forward rate 1.32, or 1.35 * [(1 + 0.011) / (1 + 0.0325].

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

Covered interest parity involves using forward contracts to cover the exchange rate. Meanwhile, uncovered interest rate parity involves forecasting rates and not covering exposure to foreign exchange riskthat is, there are no forward rate contracts, and it uses only the expected spot rate. There is no difference between covered and uncovered interest rate parity when the forward and expected spot rates are the same.

## Limitations of Using Covered Interest Rate Parity

Interest rate parity says there is no opportunity for interest rate arbitrage for investors of two different countries. But this requires perfect substitutability and the free flow of capital. Sometimes there are arbitrage opportunities. This comes when the borrowing and lending rates are different, allowing investors to capture riskless yield.

For example, the covered interest rate parity fell apart during the financial crisis. However, the effort involved to capture this yield usually makes it non-advantageous to pursue.

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