# Interest Rate Differential and Fisher's Interest Rate Parity

The Fisher formula for interest rate parity, as explained here shows that for a given currency pair, the currency with the higher interest rate will depreciate relative to the the currency with the lower interest rate, over a given period of time, for it not then riskless arbitrage is possible. In other words, higher interest, weaker currency.

However, there is another point of view, as given here, that if a country hikes interest rates, then its currency will appreciate, as there will be increased demand for that currency in order to enjoy higher returns, carry-trade style. In other words,higher interest, stronger currency.

The question here is - which is correct? Or are there other assumptions which have not been accounted for here?

I hesitate to mark this question as a duplicate (of this one), but my answer will in part be a replication of part of my answer there.

Let's write the Uncovered Interest Rate Parity expression

$$(1+i_{A,t}) = \frac {S^e_{A|B, t+1}}{S_{A|B, t}} (1+i_{B,t})$$ where $S_{A|B}=$ units of currency A per unit of currency B. This is the claim. The numerator is the expected future exchange rate

Assume that $i_{A,t} > i_{B,t}$. Standard economic logic (and a few assumptions on ability to invest over borders), says that then investors would want to invest in country A. To do that they will increase demand for currency A. This should lead to appreciation of currency A. Does the UIRP say something like that?

If $$i_{A,t} > i_{B,t} \implies 1+i_{A,t} > 1+i_{B,t}$$ and so the UIRP asserts that we must have

$$\frac {S^e_{A|B, t+1}}{S_{A|B, t}} > 1 \implies S^e_{A|B, t+1} > S_{A|B, t}$$

Given how $S$ was defined the last inequality means that we expect that the currency will depreciate. Indeed, in the future. Because, what is affected in the first place by the reaction of the investors is $S_{A|B, t}$, not $S^e_{A|B, t+1}$. The reaction of the investors will decrease $S_{A|B, t}$ (which reflects the appreciation of currency A), creating expectations of future depreciation, i.e. leading to $S^e_{A|B, t+1} > S_{A|B, t}$, as the UIRP asserts. Why should we expect depreciation of currency A in the future, compared to the present? Because the inflow of funds in country A will eventually pressure $i_{A,t}$ downwards, investors will stop loving currency A so much, demand for it will eventually fall, hence eventual depreciation.

The UIRP therefore compacts two effects from a discrepancy in interest rates: a first effect of currency appreciation and a second (expected) effect of currency depreciation in the future.

Apart from that explanation, I note that the link discussing the tendnecy to appreciate says also explicitly

"However, this simple equation is complicated by a host of other factors that impact currency value and exchange rates. One of the primary complicating factors is the interrelationship that exists between higher interest rates and inflation. If a country can manage to achieve a successful balance of increased interest rates without an accompanying increase in inflation, then the value and exchange rate for its currency is more likely to rise."

In other words, the very link that talks about currency appreciation qualifies this to be subject to the fact that higher nominal interest rate does not result in higher expected domestic inflation (this alludes to the Fisher Hypotesis that the difference between the nominal interest rate and the real one is the expected inflation). This qualification essentially says that in order for the initial currency appreciation to persist, we must have differences in the real economy (i.e. that a higher nominal interest rate reflects a higher real interest rate rather than higher expected inflation).

The International Fisher Effect (which is not to be confused with the "standard" Fisher Effect that relates differences between nominal and real interest rates to expected inflation) looks at pairs of two countries. So it's not a general statement that higher interest rates always lead to a weaker currency.

Your second point describes the more generally observed phenomenon in international economics that higher interest rates might attract investors, thus the demand for the respective currency goes up which leads to an increase in exchange rates.

How - or if - the two effects interact depends on which country pairs you are looking at.