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The formula and the sign convention
Let s be the spot exchange rate quoted as units of domestic currency needed to buy one unit of foreign currency. The approximate IFE relationship is:
Expected percentage change in s ≈ idomestic − iforeign
The sign depends entirely on how the exchange rate is quoted, so state the convention before interpreting the formula. Two common quotations give opposite readings:
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| Exchange-rate quotation | What a higher domestic nominal rate implies | Interpretation |
|---|---|---|
| Domestic currency per one unit of foreign currency (for example, dollars per euro, when the domestic currency is the dollar) | Expected increase in s | Domestic currency expected to depreciate |
| Foreign currency per one unit of domestic currency | Expected decrease in the quoted rate | Domestic currency expected to depreciate (same economic result, opposite sign) |
In both cases the economic message is identical: the high-rate currency is expected to lose value. Only the arithmetic sign changes.
How the relationship is derived
The IFE is not a standalone law. It is the end result of chaining three assumptions together, as laid out in the IMF’s long-run derivation:
- Fisher relation in each country. The nominal interest rate equals the real interest rate plus expected inflation. Apply this at home and abroad.
- Equal long-run real rates. If real rates are assumed to align across countries over the long run, the nominal interest differential reflects the expected inflation differential.
- Long-run purchasing power parity (PPP). Ex ante PPP ties the expected inflation differential to the expected change in the nominal exchange rate.
Combining these steps produces the IFE-style result: the interest-rate gap approximates the expected exchange-rate change. Because each step is an assumption rather than an identity, the relationship need not hold in any particular month or year.
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A worked illustration
Suppose the domestic nominal rate is 6% and the foreign rate is 2%, and the quotation is domestic currency per unit of foreign currency. Let the current spot rate be 1.50. The IFE approximation implies an expected rise of about 4% in the quoted rate over the period the rates refer to, so the expected one-period rate is about 1.56. This is an illustration of the arithmetic, not a forecast. The same numbers would not tell you the actual rate a year later, because the realized change can differ substantially from the expected one.
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The empirical record is the part most often oversimplified. Several sources point to the same caution from different angles.
IMF working paper: mixed and inconclusive
An IMF working paper on this topic concludes that “Empirical evidence on this issue is mixed and inconclusive.” It also discusses competing readings of interest-rate differentials. A gap can reflect expected inflation and expected currency depreciation, but interest rates and exchange rates can also move in the same direction when capital flows respond to them.
IMF literature survey: interest differentials explain little
An IMF literature survey reports that extensive evidence finds interest-rate differentials explain only a small portion of subsequent exchange-rate changes. This is the strongest reason not to convert the IFE into a point forecast.
ECB speech: a high correlation, but not a forecast test
A 2017 European Central Bank speech reports a 0.85 correlation between short-term interest-rate differentials and euro–dollar exchange-rate movements over 2005–2011. Two qualifications matter. First, this is a contemporaneous correlation measured in one sample, not a general measure of how well the IFE predicts exchange rates. Second, the speech notes that a contemporaneous correlation does not directly test the uncovered interest parity prediction about today’s differential and tomorrow’s exchange-rate move. The same speech describes a weaker relationship for longer-term interest differentials, where term premiums are among the possible explanations.
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Federal Reserve research: a different horizon, a different mechanism
Federal Reserve research shows that under uncovered interest parity combined with a mean-reverting exchange-rate assumption, a rise in U.S. interest rates can coincide with an immediate dollar appreciation. That is a short-run asset-price response. It is not the same as the IFE’s implication of expected depreciation over a specified horizon. When comparing claims, check the model’s assumptions and time horizon first.
Why the relationship breaks down: risk premiums
The IFE assumes, in effect, that investors treat domestic and foreign assets as close substitutes. When they do not, the gap between interest differentials and realized exchange-rate changes can include several components, according to an IMF study on imperfect substitutability:
- Exchange-rate risk premium: compensation for uncertainty about the currency itself.
- Sovereign risk premium: compensation for the risk that the issuing government defaults or restricts payments.
- Political risk premium: compensation for policy or political events that could affect returns.
- Forecast error: the gap between what was expected and what actually happened.
A high-rate currency may therefore stay strong for long periods if investors demand a premium, or if the rate gap reflects risk rather than expected depreciation.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How the IFE relates to other parity conditions
The IFE is often confused with other parity conditions. The table below separates them by what each links and the assumption that does the most work.
| Condition | What it links | Key assumption that matters most |
|---|---|---|
| International Fisher Effect | Nominal interest differential and expected exchange-rate change | Fisher relations hold in both countries, long-run real rates align, and long-run ex ante PPP holds |
| Purchasing power parity (PPP) | Price levels or inflation differentials and exchange rates | Goods arbitrage brings price levels into line over time |
| Uncovered interest parity (UIP) | Interest differential and expected spot-rate change | Domestic and foreign assets are perfect substitutes, so no risk premium separates them |
| Covered interest parity (CIP) | Interest differential and the forward exchange rate | The forward contract hedges exchange-rate risk, so the link is an arbitrage relation rather than an expectation |
The practical distinction: CIP concerns a hedged, forward-priced relationship; UIP and the IFE concern expected, unhedged movements. UIP and IFE are close relatives, but the IFE adds the Fisher and PPP steps described above.
Common mistakes when using the IFE
- Treating it as guaranteed. A higher interest rate does not mechanically cause depreciation. The IFE is conditional, and the evidence is mixed.
- Skipping the quotation. Without the exchange-rate convention, the sign of the prediction is undefined.
- Reading a correlation as a forecast. A contemporaneous co-movement between rates and currencies does not show that today’s rate gap predicts next period’s currency move.
- Ignoring risk. Differences between theoretical parity and realized returns often reflect risk premiums, not just forecast error.
- Mixing horizons. Short-run asset-price responses and long-run expected depreciation are different claims.
Further reading
For the derivation in a broader course setting, international financial management textbooks cover the Fisher effect alongside real interest-rate parity and the other international parity conditions. Look for a treatment that states the quotation convention and the assumptions explicitly, since those are the parts most often lost in summaries.
The IMF and ECB sources cited above are the best starting points for primary material. Check their publication dates and the samples they use before applying a finding to a current market, because interest-rate regimes and capital-flow conditions change over time.
The International Fisher Effect is useful as a lens: it tells you what a rate gap would imply under specific assumptions, and it tells you where those assumptions tend to fail.
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