Why does a 10% fall in a currency’s nominal value not necessarily make its country’s goods 10% cheaper? The real exchange rate combines the nominal currency quotation with domestic and foreign price movements. Inflation differences can reduce, erase or even reverse a nominal depreciation’s effect on relative prices.
We work a 10% nominal depreciation alongside 8% Home inflation and 2% Foreign inflation, yielding only about 3.89% real depreciation under a defined quotation. We then change Home inflation, distinguish bilateral from trade-weighted real rates and explain why index movement does not by itself predict export success.
eduKateSG · The Gold Standard of Economics
Choose your reading route
Calculate the real rate · Chapters 1–3: currency, prices and exact changes.
Interpret the comparison · Chapters 4–6: inflation, trade weights and competitiveness.
Check and connect · Chapters 7–8: FAQs, references and related guides.
Chapter index
Calculation · Chapters 1–3
Interpretation · Chapters 4–6
Evidence and connections · Chapters 7–8
A nominal exchange rate states the price of one currency in terms of another. A real exchange rate compares the prices of goods or baskets across economies after allowing for the exchange rate. These quantities describe related but different aspects of international economic life.
Take the viewpoint of a resident of fictional Home, who must pay a certain number of Home currency units for one unit of Foreign currency. Define E as Home currency units per unit of Foreign currency. Under this explicit quote convention, a rise in E means the Home currency depreciates nominally: it takes more Home money to buy one unit of Foreign money.
Whether Home-produced goods become cheaper relative to Foreign-produced goods also depends on the price levels in the two countries. If domestic prices rise quickly, they can offset a nominal depreciation. If foreign prices rise, that can work in the opposite direction. The relative-price outcome cannot be read from the foreign-exchange quote alone.
The IMF’s introductory guidance defines a real exchange rate using the bilateral nominal exchange rate and a ratio of domestic and foreign price levels. The BIS similarly constructs real effective exchange-rate indicators that combine nominal exchange developments with inflation differences relative to trading partners.
This is not a forecast about exports, investment flows or currency markets. A price-relative indicator can inform a competitiveness discussion, but trade volumes also depend on contracts, product quality, supply chains, capacity and demand. The calculation is a starting measurement, not a complete causal explanation.
With E defined as Home currency per Foreign currency unit, let P* represent the Foreign price level and P the Home price level under compatible basket and index conventions. Define the illustrative bilateral real exchange rate q=E×P*/P. For a literal comparable representative good, this compares the Home-currency cost of the foreign good with the price of the domestic good.
Under this convention, a rise in q makes the foreign basket more expensive relative to the Home basket. It can be described as a real depreciation of Home. A fall in q means the opposite movement: Home has appreciated in real relative-price terms. Some data providers instead publish a real appreciation index whose direction is inverted, so the equation must accompany the interpretation.
Suppose Year 1 has E=1.20, P*=100 and P=100. The arbitrary index-level calculation yields q₁=1.20×100/100=1.20. Here the price measures are fictional indices set to 100 in the initial period, so the level 1.20 should not be read as a universal absolute law-of-one-price ratio.
For Year 2, suppose the nominal rate becomes E=1.32, Foreign prices reach 102 and Home prices 108. Then q₂=1.32×102/108=1.24667. Relative to the first-year q, the change is 1.24667/1.20−1≈+3.89%.
The Home currency depreciated nominally by 10% under this quote convention, yet the toy real exchange rate rose only about 3.89%. The 8% Home inflation and 2% Foreign inflation offset much of the change in the relative-price comparison.
Keep time windows consistent. Mixing an end-of-day exchange quote with nonmatching yearly price indices without discussing the aggregation period can generate a number that has no coherent measurement interpretation.
| Toy measure | Year 1 | Year 2 |
|---|---|---|
| E (Home/Foreign) | 1.20 | 1.32 |
| Foreign price index P* | 100 | 102 |
| Home price index P | 100 | 108 |
| Bilateral q=EP*/P | 1.200 | ≈1.24667 |
| Movement | — | +3.89% real depreciation |
CHAPTER 3 OF 8
3. Show the growth factors rather than subtracting three percentages blindly
The ratio of real exchange rates between two periods is (E₂/E₁)×(P*₂/P*₁)/(P₂/P₁). Written as gross growth factors, it is (1+nominal change)×(1+foreign inflation)/(1+home inflation) under the stated E convention.
For our example the factors are 1.10, 1.02 and 1.08. Multiply and divide: q₂/q₁=1.10×1.02/1.08≈1.03889. The real depreciation is therefore about 3.89%. This identity exactly connects the selected period-to-period changes; no first-order approximation was needed.
A quick approximation is nominal depreciation plus foreign inflation minus Home inflation, or 10%+2%−8%=4 percentage points. It is close in this example but not identical to the exact 3.89% change. Multiplying gross factors is the proper exact arithmetic.
A tempting mistake is to say that a 10% nominal depreciation makes every Home export 10% cheaper to foreigners. Domestic producer prices can change, import-intensive exporters can face higher input costs, firms may alter their mark-ups and foreign customers may price goods in a different currency. The nominal quote alone cannot predict the ultimate transaction price.
Another mistake is to invert E accidentally. One Foreign currency unit became more expensive from 1.20 to 1.32 Home units, a 10% increase. The reciprocal quote in Foreign units per Home currency falls from 1/1.20≈0.8333 to 1/1.32≈0.7576, a decline of around 9.09%, not 10%. Quote conventions matter for percentage changes too.
Explain each number before computing a real rate: the exchange-rate direction, which economy is Home, what each price index measures, the base and the calendar interval. An unexplained formula can give a numerical result with the wrong economic sign.
Retain a 10% nominal depreciation and 2% Foreign inflation. Now let Home inflation be 15% instead of 8%. The real-rate growth factor becomes 1.10×1.02/1.15≈0.97565, giving a change of approximately −2.43%.
The Home currency still depreciates nominally: E has risen from 1.20 to 1.32. Yet under this definition the Home real exchange rate falls, indicating a real appreciation. Faster Home inflation outweighed the nominal exchange-rate change when comparing the selected prices.
This is a useful counterexample to the claim that the direction of a nominal exchange rate determines the direction of international relative prices. What matters to q is the combined price and currency movement. A sufficiently strong relative domestic inflation increase can reverse the real comparison.
Suppose instead Home prices rise only 2%, matching Foreign inflation. With the same 10% nominal depreciation, q rises exactly 10% in this toy index calculation because the price ratio is unchanged. This special case explains why exchange-rate movements sometimes map closely into real-price changes, but it does not justify assuming matched inflation without evidence.
The response also depends on the chosen price measure. Consumer prices, producer prices, unit labour costs and export prices need not move together. Choosing one can be appropriate for one question and less appropriate for another. A price-based real exchange rate is always a constructed indicator, not the unique cost of every traded product.
Describe the sign explicitly: with q=E P*/P, a positive change is a Home real depreciation; a negative change is a Home real appreciation. A BIS-style appreciation index uses the opposite direction. Mixing those signs in a report can reverse the entire headline.
| Nominal E change | Foreign inflation | Home inflation | Real q movement |
|---|---|---|---|
| +10% | +2% | +8% | ≈+3.89% |
| +10% | +2% | +15% | ≈−2.43% |
| +10% | +2% | +2% | +10.00% |
Most economies trade with many partners and compete with their exporters in third-country markets. A bilateral real exchange rate against one currency therefore answers a narrower question than a trade-weighted real effective exchange rate. The country may depreciate against one partner and appreciate against another.
The BIS effective exchange rate series uses geometric trade-weighted averages of bilateral exchange rates, with relative consumer-price changes incorporated into the real measures. Its weighting framework reflects manufacturing trade and third-market competition, and the weights are updated as the trade structure changes.
A simple invented two-partner example makes the logic visible. Suppose a Home currency’s real exchange comparison moves up 10% against partner A but down 10% against partner B, under one consistently defined direction. If their schematic weights are 60% and 40%, a geometric weighted factor is 1.10^0.60×0.90^0.40≈1.015, a rise of about 1.5%.
That number is not the arithmetic average 0.60×10%+0.40×(−10%)=2%, and neither formula should be passed off as a reproduction of the BIS’s full methodology without applying the provider’s weights, quote convention and chaining rules. Our two-partner exercise only demonstrates why weights and index construction matter.
An appreciation of a BIS REER index is defined as an increase in the BIS series. This is the reverse sign from an increase in our q convention, which was described as a real depreciation. Always state which series or formula is being used.
For an actual country, identify the trade partner basket, base period, whether the series is bilateral or effective, which deflator is used and whether the comparison is nominal or real. Without those details, a statement about ‘the currency becoming more competitive’ remains insufficiently specified.
| Schematic partner | Real-rate change | Weight |
|---|---|---|
| A | +10% | 60% |
| B | −10% | 40% |
| Geometric weighted factor | ≈1.015 | Illustration only |
A real exchange rate summarises a relative-price comparison. It does not automatically establish whether exporters can supply goods, whether foreign buyers want them, or what happens to profit margins. Global supply chains, imported intermediate inputs, contract currencies and demand elasticities all influence actual trade responses.
If a Home manufacturer imports most of its materials, nominal depreciation may raise the Home-currency cost of those inputs. Even when the product becomes relatively cheaper abroad in an index, the firm’s margin could deteriorate. Another exporter with mainly domestic inputs may face a different response.
Exchange-rate pass-through into consumer prices can be partial and delayed. Retailers and importers may absorb some cost movements in margins, hold inventories, or face contracts fixed in particular currencies. Consequently, a one-period spot exchange rate and a broad CPI do not establish the effective price change of a particular product shipment.
A real depreciation also need not signal that a currency was previously ‘overvalued’. Assessing equilibrium valuation requires assumptions about productivity, saving, investment, trade structure and macroeconomic fundamentals. The IMF notes why reliable claims of currency misalignment are difficult.
Treat the exchange rate as one piece of a broader decision framework. To understand inflation, study import prices and consumption weights. To understand exporters, examine product-specific prices, unit costs and markets. To understand welfare, include real wages and the household’s consumption basket.
A careful public report should separate three claims: the index moved, some relative-price incentives changed under the index model, and specific economic outcomes actually followed. Each requires different evidence.
What is nominal depreciation? Under a quoted Home-currency-per-Foreign-unit exchange rate E, it is an increase in E: buying one Foreign currency unit takes more Home money.
What is real depreciation under this article’s convention? It is an increase in q=E×P*/P, meaning the foreign price basket becomes dearer relative to the Home basket under the defined measures.
Why did a 10% nominal depreciation become 3.89% real depreciation? The illustrative Home CPI rose 8% while the Foreign CPI rose 2%, offsetting much of the nominal change in the relative-price calculation.
Can a nominally depreciating currency appreciate in real terms? Yes. Under the chosen formula sufficiently high Home inflation can more than offset nominal depreciation.
Does the BIS REER index use the same sign as q? No. BIS defines an increase in its published REER index as real appreciation. Preserve the provider’s quote convention.
Does REER measure the exact price of an export shipment? No. It aggregates selected relative prices and currencies and does not include every firm’s costs, contracts or product-specific margins.
Is a real depreciation always beneficial? No. The consequences depend on households, imports, exports, debt, inflation transmission, output capacity and broader economic structure.
Does an index above 100 prove overvaluation? No. An index level normally states a change relative to the chosen base period; an equilibrium valuation claim needs further economic modelling.
Why use geometric rather than arithmetic aggregation? Published effective-rate methods use geometric weighting to combine proportional bilateral changes under their chosen methodology. A simple arithmetic average is not an automatic substitute.
The portable method has three stages: define the nominal currency quotation, specify which domestic and foreign prices are compared, and calculate the ratio of gross changes. Only then interpret the direction, using the exact sign convention of the chosen indicator.
Redo the original example with Home inflation of 15% instead of 8%, retaining nominal depreciation of 10% and Foreign inflation of 2%. The real ratio becomes 1.10×1.02/1.15≈0.97565, which reverses the sign. Explain why nominal and real movements can disagree without contradiction.
Follow the Gold Standard of Economics parent hub and Gold Standard of Macroeconomics for the wider price and output framework.
Read CPI, the GDP deflator and import prices for the choice of price index, and Nominal pay and real wages for another purchasing-power calculation. Terms of trade and real income offers a different international-price interpretation.
For learning transfer and navigation, see Learning Transfers into Life and How X Works.
Sources checked on 22 October 2026: IMF: Real Exchange Rates—What Money Can Buy, BIS: Effective Exchange Rates, and INSEE: Nominal and Real Effective Exchange Rates. All numerical scenarios here are original hypothetical calculations, not actual exchange quotations or forecasts.