Interest Rate Parity
Interest rate parity enforces an essential link between spot exchange currency rates, forward currency exchange rates and short-term interest. It specifies a relationship that must exist between the spot interest rates of two different currencies if no arbitrage opportunities are to exist. The relationship depends on the spot and forward exchange rates between the two currencies.

The following example illustrates what interest rate parity is and why it must exist.

Example:
Assume the following data for the euro (¬) and the U.S. dollar ($):

One-year forward exchange rate ¬/$ = 0.909

Spot exchange rate ¬/$ = 0.901

One-year interest rate, euro 7%

One-year interest rate, dollar 5%

A speculator could borrow dollars at 5%, convert them into euros and invest the euros at 7%. The speculator would be making a profit of 2%.

However, at the end of the time period, euros will need to be converted to dollars so that the initial borrowing can be repaid. The speculator runs the risk that dollars may have depreciated relative to the euro during that time period.

The speculator's position can potentially be made into a risk-free one by purchasing a forward exchange contract so that the exchange rate used to convert euros back to dollars is a known one.

Over one year, the speculator would experience the following exchange rate loss:(0.901 - 0.909) ÷ 0.901 = -0.9%

Because of the 2% interest rate differential, the speculator makes a net profit of 1.1% for each dollar borrowed. This is a certain gain, as all exchange and interest rates were fixed and known at the beginning of the trade, and no capital had to be invested in the position either!

If such rates existed in the real world, enormous swaps of capital would be made to take advantage of such a risk-free arbitrage. To prevent this from occurring, the forward discount rate would have to equal the difference in interest rates. Note that if the discount forward rate is greater than the interest rate differential, the arbitrage will be made in the other direction.

The actual mathematical relationship is slightly more complicated than what was specified above because a perfect arbitrage would require that the forward contract cover both the initial principal borrowed plus the accrued interest. For the rates discussed above, the speculator would actually need to hedge, for every dollar borrowed, 0.901 (1.07) = 0.964.

The interest rate parity relationship between two currencies can be expressed (using indirect quotes) as:

Formula 5.4

(Forward rate - Spot rate) ÷ Spot rate = (rfc - rdc) ÷ (1 + rdc)
or (F - S) ÷ S= (rfc - rdc) ÷ (1 + rdc)

Where rdc is the risk-free interest rate of the domestic currency, rfc is the risk-free interest rate of the foreign currency and the exchange rates quoted are indirect quotes expressed as the number of units of the foreign currency used to obtain one unit of the domestic currency.

The interest rate parity relationship can also be expressed as:
F × (1+ rdc) = S × (1 + rfc)

Look Out!
Note that currencies trading at a premium are associated with lower interest rates. Weak currencies must have high risk-free interest rates to compensate for expected depreciation.

Foreign Exchange Parity Relations

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