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FX/Interest Rate Parity Question

I am having trouble understanding the relationship between FX rates and interest rates. Under interest rate parity, the country with the lower interest rate experiences currency appreciation, so that the real returns between countries become equal. If real returns are not equal, covered interest arbitrage is possible. But, in contrast, one of the factors that can cause a country's currency to appreciate or depreciate is differences in interest rates, where low interest rates cause capital to be invested elsewhere leading to decreased demand for the currency, and depreciation. It seems that the two factors, interest rate parity and using interest rates as a measure of investment opportunities, and as a result capital flows don't jive? Am I missing something?

Interest rate being referred in Interest Rate Parity is Nominal Rate. However, capital flows are more related to real interest rates.

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Thanks, that's helpful.

What if inflation is zero in both countries? Say for example, country A had a real and nominal interest rate of 4%, and country B had a real and nominal rate of 5%. Under interest rate parity, country A's currency would appreciate, so that returns are the same, right? But capital flows to the country with the higher real rates would make country B's currency appreciate and A's depreciate?

Still a bit confused.

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This sounds like a short term inequality b/w these two countries. in the long term when things return to parity these interest rates would be the same.

If you haven't read reading 19 yet I would suggest it. It goes into all the long term parity and short term inequality stuff.

Basically the linear approx. for the Internation Fisher Relation says it all:
in parity:

Int(FC) - Int(DC) = Infl.(FC) - Infl.(DC)

So, if inflation is zero in both countries, then the difference in interest rates b/w both countries (in parity) would be 0.

The IRP formula works only when assuming parity.

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This is my understanding of FX and Interest rates

Lower interest rates means low cost of borrowing which means cheaper goods which means higher exports, as exports rise and foreign currency inflows increase, local currency starts appreciating due to increased demand and spending power increases which leads to rising imports.

As imports increase - inflation increases as cost of input rises which would lead to higher interest rates to cure inflation

So lower interest rates will lead to appreciating currency – which increasing purchasing power and increase imports, which eventually cause inflation and increase interest rates and depreciate the currency. This is a repetitive cycle

Inflation is an important driver for the level of interest rates.

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