An exchange rate is a price with two currencies in it, so writing one down requires saying which currency is being priced and which is doing the pricing. Two conventions do that, both in daily use, and they put the currencies in opposite order.
How is a currency pair written?
The market convention writes a pair as BASE/QUOTE, and the number is how many units of the quote currency buy one unit of the base. On a dealing screen, USD/INR = 84.5000 means 84.5000 rupees per dollar. EUR/USD = 1.0840 means 1.0840 dollars per euro. USD/JPY = 151.20 means 151.20 yen per dollar. The base is the currency you get exactly one of.
The CFA convention writes the same relationship as price currency / base currency, so the currency in the numerator position is the one doing the paying. Under that convention the same rupee-dollar price is written INR/USD = 84.5000, because it takes 84.5000 units of the price currency to buy one unit of the base currency. Identical number, identical meaning, currencies in the opposite written order.
Neither convention is wrong and neither is going away. The way to survive both is to refuse to read the slash at all. Say the number with its units attached, every time: "84.5000 rupees per dollar." Once the sentence has units in it, the notation becomes decoration.
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Common mistakes when reading exchange rate moves
Two consequences follow immediately, and both are examinable.
- The direction trap. For
USD/INRquoted as rupees per dollar, a rise from 84.5000 to 88.0000 means the dollar has become more expensive, so the dollar has appreciated and the rupee has depreciated, even though the rupee is the currency named second and the number went up. The base currency strengthens when the number rises. Always. - The asymmetry trap. The two percentage moves are not equal and opposite. Going from 84.5000 to 88.0000, the dollar appreciated by 88.0000 / 84.5000 − 1 = 4.142012% against the rupee. The rupee depreciated by 84.5000 / 88.0000 − 1 = −3.977273% against the dollar. The relationship is exact: if one currency appreciates by x, the other depreciates by x / (1 + x), and 0.041420 / 1.041420 = 0.039773, which is the rupee's move to nine decimal places.
The asymmetry is small at 4% and unignorable at 40%. A currency that halves in value against the dollar has fallen 50%, and the dollar has risen 100% against it. Reporters routinely quote the smaller of the two numbers when the story is a crisis and the larger when the story is a recovery, and the two numbers describe the same event.
How do you quote the reciprocal rate?
The reciprocal quote is the same drill from the other side. At 84.5000 rupees per dollar, one rupee costs 1 / 84.5000 = 0.01183432 dollars, or 1.183432 US cents. At 88.0000 it costs 1.136364 cents. Compute the reciprocal rather than eyeballing it. Sign errors hide inside a reciprocal, because both numbers look plausible.