## What is Covered Interest Rate Parity?

Covered interest rate parity says that investment in a foreign instrument that is completely hedged against exchange rate risk will have the same rate of return as an identical domestic instrument, therefore, this implies that the forward exchange rate can be determined depending upon the interest rate earned on the domestic and the foreign investment and the Spot exchange rate between the two currencies.

### Explanation

As per the international parity conditions, it is theorized that if the required preconditions are met, then it is not possible to make a risk-free profit from investing in a foreign market which is giving a higher rate of return, one such condition for covered interest rate parity, the foreign security should be completely hedged.

There are various kinds of parity conditions that deal with the interlinking of measures such as the Current Spot rate, Forward exchange rate, Expected future spot exchange rate, Inflation differential, and Interest rate differentials.

### Formula to Calculate Covered Interest Rate Parity

Following is the formula for Covered interest rate parity:

**F**Forward exchange rate i.e. the exchange rate of a forward contract to buy one currency for another at a later point in time,_{f/d}=**S**Spot exchange rate i.e. the exchange rate to buy one currency for another in the current period,_{f/d}=**i**Domestic interest rate and_{d}=**i**Foreign interest rate_{f}=**360**days a year is used as a convention, we may use 365 days also

This actually implies that if the investor is aware of the domestic and foreign exchange rate and the current spot rate, he can determine the forward exchange rate and if the actual forward exchange rate in the market is different from the one calculated by him, there is a chance of arbitrage profits and the CIRP will not hold.

### Assumptions

#### #1 – Perfect Information

- All market participants are aware of and alert about market inefficiencies so that as soon as any such efficiency occurs, they act to drive it away.
- For example suppose the return in one market is lower and higher in another market, in such a situation, the market participants will exchange the low return currency and invest the money received from this transaction in an instrument denominated in the higher return currency.
- At the time of maturity, the money invested in the higher return currency will be taken out along with the interest and converted back to the lower return currency leading to an arbitrage profit. As more and more investors start making such profits, the higher interest rate currency will depreciate and the lower interest rate currency will appreciate offsetting the increased returns from interest-rate disparity and the parity will be in place again

#### #2 – No Transaction Cost

The parity condition assumes that there are no transaction costs related to investment in the foreign or domestic market which could nullify the no-arbitrage situation

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#### #3 – Identical Instruments

The domestic and foreign instruments should be identical in aspects such as default risk, maturity, and liquidity, etc. Capital should flow freely between markets to avoid liquidity constraints.

#### #4 – Stable Markets

The financial markets should be not facing any kind of regulatory pressures or stress and must be working freely and efficiently.

### Example of Covered Interest Rate Parity

Let’s say we are dealing with the USD/EUR currency pair for a European investor, for whom the EUR is the domestic currency and USD is the foreign currency, and we are given the following information:

- 05 which implies that USD 1.05 is required for every EUR 1
- Domestic interest rate – 3%
- Foreign Interest Rate – 5%
- The investment period is 1 year or 360 days
- We need to calculate this

Using the covered interest parity formula, we can solve for the forward rate.

So if the forward rate is the same as that calculated above, there won’t be any profit in investing at the higher interest rate abroad. Now suppose if the forward rate in the market is misquoted and is 1.09, there is a possibility of arbitrage profit.

Under covered interest arbitrage, we hedge our position and therefore we take the following steps:

- We are assuming that the forward rate should be 1.0704 while the actual forward rate is 1.09
- Borrow USD 1.05 at a higher interest rate
- Sell the borrowed USD at the spot rate for EUR 1
- Now the exposure is that we have to return the USD 1.05 and 5% interest on the same, therefore we hedge this exposure by entering into a forward contract in which we will exchange EUR for USD at the forward exchange rate of USD 1.09 per EUR
- We are left with EUR 1, and e invest the same at 3% interest rate
- At the end of 1 year, we have EUR 1.03 with us
- We are supposed to pay back USD 1.05 x 1.05 = USD 1.1025
- Converting the EUR 1.03, we get 1.03 x 1.09 = USD 1.1227 by fulfilling the forward contract we had entered into at the beginning
- So we make a riskless profit of 1.1227 – 1.1025 = USD 0.0202

### Covered Interest Rate Parity vs Uncovered Interest Rate Parity

- Under the CIRP, the risk is completely hedged, even in the arbitrage example explained above, we have hedged our position by entering into the forward contract in step 4, in case of uncovered interest rate parity, as the name suggests, we don’t enter into the hedge
- Uncovered interest rate parity deals with
*expected*spot rate during the tenure of the investment and implies that the exchange rate movement will offset the interest rate difference - In the covered interest rate parity both domestic and foreign interest rate returns are known in domestic currency terms because the forward rate is hedged. While in case of the uncovered interest rate parity, the foreign interest rate return in domestic currency terms is unknown and un-hedged and is approximated to

- Uncovered interest rate parity assumes that the forward rates are unbiased predictors of expected spot rates, however, such is not the case for covered interest rate parity.

### Conclusion

- Finally, we are now aware that the CIRP has certain unrealistic assumptions that might not hold true and therefore the forward rates may be misquoted in the market and there could be an arbitrage opportunity.
- There is a counterintuitive assumption underlying the appreciation and depreciation of the two currencies involved to offset the effect of the difference in the interest rates, which may not always occur.

### Recommended Articles

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