How to reconcile 1) the International Fisher Effect and 2) rising interest rates leading to currency appreciation?

Question

The International Fisher Effect implies that a currency with a lower nominal interest rate will appreciate against another currency with a higher nominal interest rate. However, in general, a currency with a rising interest rate will also appreciate (by attracting investors).

How can this apparent paradox be resolved? Is it that the rising interest rate causing currency appreciation is more related to the direction of the change (of the difference) in nominal interest rates, and that the IFE is more referring to the absolute difference in nominal interest rates - or is it something else, e.g. currency appreciation from rising interest rates in the short run, but the opposite movement in the longer run?

EDIT: this question isn't really about interest rate parity or anything arbitrage related. Instead, Instead the question is about forecasting, esp. in the current environment. Concretely, if e.g. USD's nominal interest rates go up (or are expected to go up), can we expect USD to appreciate or depreciate vs e.g. the EUR? In the short term it seems to be USD appreciation, but in the longer run if high USD interest rates (vs EUR rates) are maintained, then would depreciation be the result - if so, how much appreciation or depreciation compared to the starting point?

Answer 1

It's the expected exchange rate (not current) which is identical to interest rate parity. See for example this answer or this one. While the current spot increases for the higher rates country, the expected exchange rate is depreciating.

Regarding your comment, if it's above or below 1:1 depends on the quotation. For example, for EURUSD (EUR being base, hence how many USD per EUR), if US interest rates are above EUR rates, the "long-run" effect on exchange rates will be a depreciation of the USD vs EUR. However, an appreciation in EUR means that the exchange rate is expected to be above 1:1 (say 1.05), not below.

Copying parts of the answer in one of the links, we get (adapted for your 1:1 example), that in the UIP equation.

$$(1+i_{\\\$})={\frac {E_{t}(S_{{t+k}})}{S_{t}}}(1+i_{c})$$

or rearranged:

$${{S_{t}}}\frac {(1+i_{\\\$})}{(1+i_{c})} = E_{t}(S_{{t+k}})$$

If you think of EURUSD now (how many USD per EUR, say 1.0, if the US interest rate is 10% and the EUR rate is 5% you get (for a year), the value of

$${1.0}*\frac {(1+0.1)}{(1+0.05)} \approx 1.047619$$

In other words, you need more USD per EUR - the USD depreciated, EUR appreciated.

Insofar, you are right that any higher interest in one country will be offset by an expected depreciation in that country's currency so that an investor will be equally well off. The immediate effect of an (unexpected) interest rate will be an appreciation in that currency, but neither IFE nor UIP look at the effect on current spot.

Wikipedia's IFE page pretty much explains the same as well.