Exchange rate quotes and percentage change in a currency

How do you read an exchange rate?

An exchange rate is the price of one currency in terms of another. This site writes it as A/B, which means units of currency A per one unit of currency B. So USD/EUR 1.0720 means EUR 1 costs USD 1.0720.

• The base currency (B, the denominator) is the one unit being priced.
• The price currency (A, the numerator) is the currency the price is quoted in.

A rising quote means the base currency now buys more of the price currency. The base currency has gained value and the price currency has lost it.

A/B = 1.2500USD 1.2500 per 1 GBP (here A = USD, B = GBP)

• Base currency B Memorize the one unit being priced, the denominator
• Price currency A Memorize the currency the price is quoted in, the numerator
• Direct or indirect Use it depends on who is looking
  • Direct quote Use it domestic currency is the price currency (domestic per foreign)
  • Indirect quote Use it the reciprocal (foreign per domestic)
• Two-sided price Use it dealer quotes both ways
  • Bid dealer buys the base currency, lower price
  • Offer dealer sells the base currency, higher price

Direct and indirect quotes. These depend on whose view you take. A direct quote has the investor’s domestic currency as the price currency (domestic per foreign): for an investor in Toronto, CAD/USD. An indirect quote is the reciprocal, USD/CAD. When the domestic currency appreciates, fewer units of it buy one unit of foreign currency, so the direct quote falls and the indirect quote rises. Professional markets do not use the terms. They use fixed conventions in which the base currency is written first, so the market code “EURUSD” means the USD/EUR rate.

Bid and offer. A dealer quotes two prices for the base currency. The dealer buys at the bid , the lower price, and sells at the offer , the higher price. The gap is the dealer’s spread. Quotes use four decimals for most pairs and two for yen pairs.

$$\text{bid}_{B/A} = \frac{1}{\text{offer}_{A/B}}, \quad \text{offer}_{B/A} = \frac{1}{\text{bid}_{A/B}}$$

To invert a two-sided quote, flip and swap: the new bid comes from the old offer and the new offer from the old bid. Otherwise the new bid would sit above the new offer.

How much did each currency move?

Memorize

When the A/B quote moves from $S_0$ to $S_1$, one currency appreciates (gains value) and the other depreciates (loses value). A base currency that is worth more has appreciated; the price currency, which buys less of it, has depreciated. The two percentages use different formulas.

$$\%\Delta B = \frac{S_1}{S_0} - 1$$

$$\%\Delta A = \frac{S_0}{S_1} - 1$$

Shortcuts that save time

If one currency has changed by a known percentage, the other’s change is the reciprocal.

Working backward. If the base currency appreciated 6% and the quote is now 0.8850, the old quote was 0.8850 ÷ 1.06 = 0.8349. Divide by the growth factor; do not multiply by its complement.

Exam tip Before any calculation, write the pair as A/B and circle B. Then B’s change is new over old and A’s is old over new.

Go deeper The market's naming hierarchy for pairs

Know the idea

Market convention fixes which currency is the base. The euro is the base against every other currency. Sterling is the base against all but the euro. The US dollar is the base against the rest, except that the Australian and New Zealand dollars are quoted as the base against it. This is why you see EUR/USD but USD/JPY.

Go deeper Why spreads in major pairs are tight

Know the idea

Electronic competition among many dealers pushes spreads in the most traded pairs to a tiny fraction of a percent. Less traded currencies have wider spreads, which makes them dearer to trade.