International Finance Theory and Policy
by Steven M. Suranovic

Finance 80-6

# Interest Rate Parity with Fixed Exchange Rates

One of the main differences between a fixed exchange rate system and a floating system is that under fixed exchange rates the central bank will have to “do something” periodically. In contrast, in a floating system, the central bank can just sit back and watch since it has no responsibility for the value of the exchange rate. In a pure float at least, the exchange rate is determined entirely by private transactions.

However, in a fixed exchange rate system the central bank will need to intervene in the foreign exchange market, perhaps daily, if it wishes to maintain the credibility of the exchange rate.

We’ll use the AA-DD model to explain why. Although the AA-DD model was created under the assumption of a floating exchange rate, we can reinterpret the model in light of a fixed exchange rate assumption. This means we must look closely at the interest rate parity condition, which represents the equilibrium condition in the foreign exchange market.

Recall, that the AA-DD model assumes the exchange rate is determined as a result of investor incentives to maximize their rate of return on investments. The model ignores the potential effect of importers and exporters on the exchange rate value. That is, the model does not presume that purchasing power parity holds. As such, the model describes a world economy that is very open to international capital flows and international borrowing and lending. This is a reasonable representation of the world in the early 21st century, but would not be the best characterization of the world in the mid 1900s when capital restrictions were more common. Nonetheless, the requisite behavior of central banks under fixed exchange rates would not differ substantially under either assumption.

When investors seek the greatest rate of return on their investments internationally, we saw in section 20-1 that the exchange rate will adjust until interest rate parity holds. Consider interest rate parity (IRP) for a particular investment comparison between the US and the UK. IRP means that RoR\$ = RoR£. We can write this equality out in its complete form to get,

where the left hand side is the US interest rate and the right hand side is the more complicated rate of return formula for a UK deposit with interest rate i£. (See chapters 10 and 20 for the derivation of the interest rate parity condition). The last term on the right represents the expected appreciation (if positive) or depreciation (if negative) of the pound value with respect to the US dollar.

In a floating exchange rate system, the value of this term is based on investor expectations about the future exchange rate as embodied in the term Ee\$/£, which determines the degree to which investors believe the exchange rate will change over their investment period.

If these same investors were operating in a fixed exchange rate system, however, and if they believed that the fixed exchange rate would indeed remain fixed, then the investor’s expected exchange rate should be set equal to the current fixed spot exchange rate. In other words, under credible fixed exchange rates, Ee\$/£ = E\$/£. Investors should not expect the exchange rate to change from its current fixed value. (Note, in section 90-5 we will consider a case in which investors expected exchange rate does not equal the fixed spot rate.)

With Ee\$/£ = E\$/£the right hand side of the above expression becomes zero, and the interest rate parity condition under fixed exchange rates becomes,

i\$=i£

Thus, for interest rate parity to hold in a fixed exchange rate system, the interest rates between two countries must be equal.

International Finance Theory and Policy - Chapter 80-6: Last Updated on 4/7/05