# Covered Interest Rate Parity

## 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. Additionally, the covered interest rate parity refers to the situation in which the no-arbitrage condition is satisfied with the use of forward contracts. As a result, there are no interest rate arbitrage opportunities between those two currencies.

## BREAKING DOWN 'Covered Interest Rate Parity'

The 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.

## Formula

Under the covered interest rate parity, the following formula must hold true, otherwise there would be an arbitrage opportunity: (1 + id) = (S / F) * (1 + if).

The formula above could be rearranged to determine the forward foreign exchange rate, in which F = S * ((1 + if) / (1 + id)).

Where:

id is the interest rate in the domestic currency, or the base currency

if is the interest rate in the foreign currency, or the quoted currency

S is the current spot foreign exchange rate

F is the forward foreign exchange rate

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.

## Example

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 good 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%).