Tell real exchange rates apart from nominal ones and find the percentage move in a currency
The idea
The nominal exchange rate is the price of one currency in another. The real exchange rate adjusts it for relative price levels, measuring purchasing power: real rate (price/base) = nominal rate x (base country price level / price country price level). Its percentage change is roughly the nominal change plus base-country inflation minus price-country inflation. A real appreciation makes a country's goods less competitive abroad. For percentage changes, the base currency's change is the change in the quote itself. To find the price currency's change, invert the quote first: if USD/EUR rises from 1.25 to 1.30 the euro gains 4.00% but the dollar loses 3.85%. The two moves differ in size because each is measured against a different starting value.
A practice question
The real exchange rate differs from the nominal exchange rate because it:
- includes a dealer's bid-offer spreadWhy not: Bid-offer spreads are a feature of dealer quotes on nominal rates and have nothing to do with real rates.
- adjusts for relative price levels — correct
- is quoted only for forward deliveryWhy not: Forward rates are nominal rates for future settlement; real rates concern purchasing power, not settlement date.
The nominal rate is the price at which one currency trades for another. The real rate adjusts it for price levels in the two countries, measuring the relative purchasing power of goods and services.
A harder one
The JPY/USD rate, quoted as yen per US dollar, moves from 150 to 140. The percentage change in the value of the yen against the dollar is closest to:
- +6.67%Why not: This is the size of the dollar's fall, (140 - 150)/150; the yen's change must be measured with the yen as the base.
- -6.67%Why not: The quote fell, but the quote prices the dollar; fewer yen per dollar means the yen strengthened, not weakened.
- +7.14% — correct
Invert to put the yen in the base: USD per yen goes from 1/150 to 1/140, a change of 150/140 - 1 = +7.14%. A currency's rise and the other's fall differ in size because they use different bases.
The hardest tier
Over a year the USD/EUR rate (dollars per euro) rises 4%, eurozone inflation is 3% and US inflation is 1%. The percentage change in the real USD/EUR rate is closest to:
- +6.1% — correct
- +2.0%Why not: This swaps the inflation terms: the base (euro) inflation should raise the real rate and US inflation should lower it.
- +4.0%Why not: This is the nominal change only, ignoring the different inflation rates in the two economies.
Real change = (1.04 x 1.03/1.01) - 1 = 6.06%, roughly 4% + 3% - 1%. The euro has appreciated in real terms, so eurozone goods have become less price-competitive against US goods.
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