Worked example: real exchange rate

Real exchange rate = nominal exchange rate × (domestic price index ÷ foreign price index). Year 1: the domestic currency is worth 2.0 foreign units; both price indices = 100 → real rate = 2.0. Year 2: nominal rate unchanged at 2.0; domestic prices rise to 110, foreign prices to 102 → real rate = 2.0 × 110 ÷ 102 = 2.16. The real exchange rate has appreciated by about 8% even though the nominal rate is unchanged: exports have become less price-competitive because of higher domestic inflation.

Worked example: trade-weighted index

A country trades 50% with the USA, 30% with the eurozone and 20% with Japan. Over a year its currency rises 10% against the dollar, falls 5% against the euro and is unchanged against the yen. Change in trade-weighted index = 0.5 × (+10) + 0.3 × (−5) + 0.2 × 0 = 5 − 1.5 = +3.5%: an overall appreciation of 3.5% (index 100 → 103.5).