Covered Interest Rate Parity Definition

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.

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

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

$F=S*\frac{\left(1+i_d\right)}{\left(1+i_f\right)}$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.

Covered interest rate parity is calculated as:

1. One plus the interest rate in the domestic currency should equal;
2. The forward foreign exchange rate divided by the current spot foreign exchange rate,
3. Times one plus the interest rate in the foreign currency.

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.

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 current currency market as of January 2019, we can apply the forward foreign exchange rate formula to figure out what the GBP/USD rate should be. The current spot rate for the pair is 1.32. The interest rate – using the one-year LIBOR rate – for the U.K. is 1.17% and 3.029% for the U.S. The domestic currency is the British pound, making the forward rate 1.296:

$1.296=1.32 * (1 + 0.0117) / (1 + 0.03029)$1.296=1.32∗(1+0.0117)/(1+0.03029)

Covered interest parity involves using forward contracts to cover exchange rate. Meanwhile, uncovered interest rate parity 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 difference between covered and uncovered interest rate parity when the forward and expected spot rates are the same.

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.

Discover how to trade forex using interest rate parity.