Nominal vs real exchange rates

What is a real exchange rate?

The nominal exchange rate is the price you see quoted: how many units of one currency buy a unit of another. It says nothing about what that money buys. The real exchange rate corrects for that by adjusting for price levels in both countries. It tells you how much foreign goods cost compared with home goods.

Quote the rate with the domestic currency as the price currency (d/f, domestic per foreign). Then the foreign price level goes on top and the domestic one underneath.

$$R_{d/f} = S_{d/f} \times \frac{P_f}{P_d}$$

What makes the real exchange rate rise or fall?

Memorize

A higher real rate (d/f) means foreign goods cost more in real terms. The home resident’s relative purchasing power abroad is then lower. Read the direction off the formula: foreign items sit in the numerator, the domestic price level in the denominator.

Real rate, domestic per foreigna higher value means foreign goods cost the home resident more

• Pushes it up (purchasing power abroad falls) Memorize
  • Foreign currency appreciates S(d/f) rises
  • Foreign prices rise P(f) rises
  • Domestic prices fall P(d) falls
• Pushes it down (purchasing power abroad rises) Memorize
  • Foreign currency depreciates S(d/f) falls
  • Foreign prices fall P(f) falls
  • Domestic prices rise P(d) rises

Change	Real rate (d/f)	Home purchasing power abroad
Foreign currency appreciates (S up)	up	down
Foreign prices rise	up	down
Domestic prices (and incomes) rise	down	up

The percentage change

Memorize

$$\%\Delta R = \frac{(1 + \%\Delta S)(1 + \%\Delta P_f)}{1 + \%\Delta P_d} - 1$$

For small changes the exam also accepts the approximation below.

$$\%\Delta R \approx \%\Delta S + \%\Delta P_f - \%\Delta P_d$$

Exam tip The sign of the real rate change tells the story, but the purchasing power change is its reciprocal: 1 ÷ (1 + change) − 1.

Why does the real rate matter?

Use it

The idea behind purchasing power parity (PPP) is that, with identical goods and no frictions, nominal rates would adjust until the same basket costs the same everywhere. In practice that fails: goods differ across countries, many services are not traded, shipping and import taxes add costs, and capital flows matter at least as much as trade flows for nominal rates. So nominal rates deviate from PPP for long periods, and real rates are a poor short-term predictor of nominal rates.

Real rates still track competitiveness. Even if the nominal rate is fixed, higher inflation at home makes a country’s exports dearer to foreigners. And a resident whose income and spending are in the same currency has no foreign exchange (FX) risk on that spending.

Go deeper Real effective exchange rates

Know the idea

Analysts often use a real effective exchange rate: the real rate against a weighted basket of a country’s trading partners. It gives one number for overall competitiveness rather than a pair-by-pair view.

Go deeper When PPP works better

Know the idea

PPP is a better guide over very long horizons, and for traded goods more than for services. Even then it holds only loosely.