## Interest Rate Parity

If we assume that significant covered interest arbitrage opportunities do not exist, then there must be some relationship between spot exchange rates, forward exchange rates, and relative interest rates. To see what this relationship is, note that, in general, Strategy 1, from the preceding discussion, investing in a riskless U.S. investment, gives us 1 + RUS for every dollar we invest. Strategy 2, investing in a foreign risk-free investment, gives us S0 X (1 + Rfc)/F1 for every dollar we invest. Because these have to be equal to prevent arbitrage, it must be the case that:

Rearranging this a bit gets us the famous interest rate parity (IRP) condition:

There is a very useful approximation for IRP that illustrates very clearly what is going on and is not difficult to remember. If we define the percentage forward premium or discount as (F1 - S0)/S0, then IRP says that this percentage premium or discount is approximately equal to the difference in interest rates:

interest rate parity (IRP)

The condition stating that the interest rate differential between two countries is equal to the percentage difference between the forward exchange rate and the spot exchange rate.

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Very loosely, what IRP says is that any difference in interest rates between two countries for some period is just offset by the change in the relative value of the currencies, thereby eliminating any arbitrage possibilities. Notice that we could also write:

In general, if we have t periods instead of just one, the IRP approximation is written as:

EXAMPLE 225 ■ Parity Check

-:—' Suppose the exchange rate for Japanese yen, S0, is currently ¥120 = \$1. If the interest rate in the United States is RUS = 10% and the interest rate in Japan is Rj = 5%, then what must the forward rate be to prevent covered interest arbitrage? From IRP, we have:

F1 = So X [1 + (Rj - Rus )] = ¥120 X [1 + (.05 - .10)] = ¥120 X .95 = ¥114

Notice that the yen will sell at a premium relative to the dollar (why?).

unbiased forward rates (UFR)

The condition stating that the current forward rate is an unbiased predictor of the future spot exchange rate.

How are the international markets doing? Find out ,at cbs.marketwatch.com.

How are the international markets doing? Find out ,at cbs.marketwatch.com.

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