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# Interest rate parity theory

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## Definition of interest rate parity according to Keynes

Interest rate parity (IRP) is the theory that changes in the exchange rate between two currencies adjust for short-term interest rate differentials and changes in the forward exchange rate. With IRP, we are not talking about exchange rate parity in the strict sense (EUR/USD quoted at 1) but a level of floating parity which evolves according to the various criteria mentioned above.

This theory was developed by the famous economist John M. Keynes. Subsequently, this work was supplemented to produce covered and uncovered interest rate parity. ## Covered and uncovered IRP

For there to be a parity in the interest rate, the interest rate differential between two currencies must be equal to the change in the forward exchange rate. If there is equivalence, then the IRP is covered. If not, the IRP is uncovered.To help you understand, let's take an example.

You want to invest €10,000 in currencies with a one-year horizon. You are undecided between investing in Euros or Dollars.Let us assume that EUR/USD is quoted at 1.10 and that the short-term interest rate on USD is 1% and 0.5% for EUR.

If you are talking in terms of pure remuneration, it is preferable to buy USD since it pays you more than a Euro investment (1% against 0.5% yield - see Forex swap).However, you must take into account that the EUR/USD exchange rate will change over the life of your investment.You anticipate an exchange rate of 1.05 in one year (following your investment).

With this data, you can now calculate the actual return on an investment in Euros or Dollars.

For Dollars

You have to convert €10,000 into Dollars.When you open your position, EUR/USD is quoted at 1.10, or \$11,000 (10,000*1.10)
- The interest rate of the Dollar is 1% which means that your earnings are 11,000 * 1.01 = \$11,110
- You now have to convert these dollars back into Euros to be able to compare that outcome with the other investment. In the long term, you anticipate an exchange rate of 1.05, i.e. 11,110 / 1.05 = €10,581.
- The rate of return on your dollar investment is not 1% (USD interest rate) but 5.81% ((10,581 / 10000) - 1)*100

For Euros

The calculation is simpler.Remember that the EUR interest rate is 0.5%) so:10,000 * 1.005 = €10,050.

The dollar investment is therefore much more attractive in this case.Since the return on the two investments is different, there is no interest rate parity.
Then the IRP is said to be uncovered.

Covered IRP

Now let's assume that you estimate that in a year's time at the end of your investment, EUR/USD is quoted at 1.1054 (and no longer 1.05 as in the previous example). For the Euro investment, the calculation does not change but for the Dollar investment the final calculation changes. The investment in USD still pays you \$11,110 but if you convert this amount into Euros in one year at the rate of 1.1056, then that gives you 11,110 / 1,1054 = €10,050.
The real rate of return on your dollar investment is then identical to the rate of return on your euro investment (10,050 or €50 for the 2).There is interest rate parity. Then the IRP is said to be covered.

## Relationship between exchange rates and interest rates

In theory, interest rate parity is assumed to be covered across all currency pairs. If it is uncovered, investors will prefer to invest in the currency offering the highest return over time until the IRP is covered.Adjusting the equation between exchange rate and interest rate movements can be done in two ways.

Let's take our example from earlier with a spot exchange rate of 1.10 and 1.05 forward (forecast) for EUR/USD, with an interest rate of 1% for the Dollar and 0.5% for the Euro. We have seen in this case that the dollar investment is much more profitable than the euro investment (5.81% against 0.5%).

When investors see this, they buy Dollars massively and sell Euros. The EUR/USD pair will therefore appreciate. We saw above that to reach a covered IRP between the EUR/USD, the pair had to be quoted at 1.1054. In this case, the adjustment is made by the exchange rate.

Let's continue with our example. As the Euro is much less lucrative than the Dollar, the European Central Bank (ECB) might decide to raise its interest rate to avoid the Euro depreciating too much against the Dollar. By raising its rates, it is gradually reducing the yield differential with the Dollar, which will reduce the sales of Euro against the Dollar.The ECB might increase its rates until the interest rate parity is covered.In this case, the adjustment is made through interest rates. 