Direct and Indirect FX Quotes: Perspective and Reciprocals

Make the perspective explicit

If USD is the domestic currency, a quotation of 1.10 USD per EUR is direct from that perspective: it states the domestic amount for one foreign unit. The reciprocal, approximately 0.909091 EUR per USD, is indirect from the same perspective. A EUR-based observer uses a different domestic reference, so the labels can reverse.

CME's FX quote-convention lesson explains quotation relationships. In a technical worksheet, writing the units often communicates more reliably than using direct or indirect without a stated viewpoint.

Invert a single indicative rate

Assume an illustrative EUR/USD midpoint of 1.1000 USD per EUR. Its reciprocal is 1 ÷ 1.1000, approximately 0.909091 EUR per USD. Multiplying the two unrounded rates gives one. This identity is a useful check for rate direction, but midpoint arithmetic does not represent the price of a two-sided transaction.

If an amount is in EUR and the desired result is USD, multiply by USD per EUR. If the only available rate is EUR per USD, divide by it. Writing the amount and units before the operation helps prevent an apparently plausible but reversed conversion.

Swap sides when inverting bid and ask

Suppose a hypothetical EUR/USD market shows bid 1.1000 and ask 1.1002 USD per EUR. The reciprocal USD/EUR bid is 1 ÷ 1.1002, approximately 0.90892565 EUR per USD. Its ask is 1 ÷ 1.1000, approximately 0.90909091. The lower reciprocal number remains the bid.

Inverting each side without swapping would create a bid above the ask. This is a unit-and-transaction error, not a new arbitrage opportunity. Actual execution can additionally depend on quantity, liquidity, fees and the time at which the quotes were available.

Do not negate percentage returns mechanically

If the first rate rises from 1.00 to 1.25, its return is +25%. The reciprocal falls from 1.00 to 0.80, a −20% return. The changes describe the same relative valuation from opposite directions, but each percentage uses a different starting denominator.

That distinction matters when comparing charts, backtest returns or account-currency translations. Reversing a price series requires calculating its reciprocal series and then recomputing returns. Simply multiplying every return by −1 is not generally exact.

Check contract conventions before comparing screens

A currency futures display and a spot platform may not use the same quotation direction or scale. Consult the specific contract rather than assuming a familiar pair label is sufficient. Record domestic perspective, pair order, quote units, whether the number is bid, ask or midpoint, and the timestamp. For copy-account reconciliation, these fields should be resolved before comparing price differences or attributing them to execution. This reference describes quotation arithmetic and does not establish that two instruments are operationally interchangeable.