A trader sees USD/EUR at 1.0850 spot and 1.0875 ninety-day forward. The euro trades at a forward premium. That single fact tells you eurozone interest rates sit below US rates, the arbitrage chain you need to master.
Currency pairs are written A/B where A is the price currency and B is the base currency. The quote tells you how many units of A buy one unit of B. USD/EUR = 1.0850 means one euro costs 1.0850 dollars. Euro is the base. Dollar is the price.
KEY: Identify base and price first. The denominator in the notation is the base. One unit of base equals the quoted number of price units.
A cross-rate is the exchange rate between two currencies that you calculate from their quotes against a third, common currency. Dealers quote most currencies against the dollar, so the dollar is usually the link. If you observe USD/EUR and USD/GBP, you derive EUR/GBP by chaining the quotes so the common currency cancels.
Common mistakes
- Reversing base and price. USD/EUR = 1.0850 means 1 EUR costs 1.0850 USD, not 1 USD = 1.0850 EUR. The slash points to base. Always read the denominator as base.
- Using mid-rates in a bid-ask cross. The bid pairs the bid of the numerator quote with the ask of the denominator quote. In Example 3 the EUR/GBP bid is 1.1511. Trap: 1.1521 from mid-rates, or 1.1531, the ask.
- Multiplying instead of inverting in cross-rates. With USD/EUR and USD/GBP, you cannot multiply directly to get EUR/GBP. Both USDs sit in the numerator and refuse to cancel. Invert one first.
Bottom line
- Quote convention is price/base. USD/EUR = 1.0850 means 1 euro (base) costs 1.0850 USD (price)
- Cross-rate: chain quotes so the common currency cancels, inverting a quote first when needed. (A/B) × (B/C) = A/C
- Covered interest rate parity sets the forward by arbitrage, not forecast: F/S = (1 + r_price × t) / (1 + r_base × t). Higher-rate currency trades at a forward discount
- Forward points = (F − S) × scaling factor (10,000 for most pairs, 100 for JPY pairs); outright forward = spot + points / scaling factor, bid to bid and ask to ask
Exam shortcut
For base vs. price: "the slash points to base, the denominator is the base." For interest rate parity direction: "high rate, low currency forward". The higher-interest-rate currency trades at a forward discount, because the forward must cancel its interest advantage or arbitrage would be free. For a bid-ask cross, write both quotes so the common currency cancels, then pick the pairing that gives the lower bid.
The full lesson (about 2,901 words, 19 min read) adds 5 worked examples, all 7 common mistakes, a self-check, free in the app.
Learning objectives
- exchange rate calculations
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