An indirect currency quotation expresses an exchange rate as units of foreign currency per unit of the chosen home currency. It answers a budget question: how much foreign currency can one home-currency unit buy? A larger indirect quote means the home currency buys more foreign currency, provided the currencies and quotation basis stay fixed.
“Home” must be declared. It may be an investor's reporting currency or the domestic currency chosen for an analysis; it is not determined by the currency pair's market spelling. HMRC's quotation definitions explicitly take a home-currency viewpoint.
Convert the budget, then check the units
Take USD as home and EUR as foreign. Suppose the synthetic indirect rate is
Ignoring spreads and fees, a USD 120 budget buys
The dollars cancel. Conversely, to fund a EUR 100 payment, divide by the indirect quote: USD. Multiplying that euro payment by the same numerical quote would use the wrong direction. Keep the exact fraction until the final rounding.
A synthetic exchange without spread or fees. An indirect quote converts a home-currency budget by multiplication; divide a foreign payment by that quote to find the required home amount.
The reciprocal is the direct currency quotation for the same USD-home perspective:
Under the base-first currency-pair convention described by CME, EUR/USD = 1.20 means USD 1.20 per EUR 1. Here EUR is the base currency. The slash in a market pair label does not give the dimensional units of its number. Writing the inverse as USD/EUR changes the base currency; calling a quote “indirect” instead identifies the home-currency viewpoint. With EUR chosen as home, the original 1.20 USD per EUR is itself indirect.
A rising quote means more purchasing power abroad
If the synthetic indirect quote rises from to 0.90 EUR per USD, the same USD 120 now buys EUR 108, an extra EUR 8. The home dollar has appreciated against the euro. Its reciprocal direct quote falls. A statement that “the exchange rate rose” therefore needs units before it can tell you which currency strengthened.
Reverse dealer sides as well as the number
An executable bid–ask spread needs two reciprocals. Suppose a synthetic dealer quotes 1.19 bid / 1.21 ask USD per EUR. The dealer buys euros at the bid and sells euros at the ask. Reversing the quote gives:
| Quotation | Dealer bid | Dealer ask |
|---|---|---|
| Direct, USD per EUR | 1.19 | 1.21 |
| Indirect, EUR per USD |
The old ask becomes the new bid after inversion. A dealer selling EUR 100 for USD 121 is simultaneously buying USD 121 for EUR 100. That is why the reversed bid is EUR per USD. Taking reciprocals without swapping sides would put the bid above the ask. CME's conversion documentation uses this offer-to-bid and bid-to-offer reversal.
For more worked dealer conversions and cross rates, read FX: quotations and conversions. Its public preview introduces the lesson, and a signed-in free account opens the full material.
Sources
- HMRC, Corporate Finance Manual CFM12020: direct and indirect quotations from a declared home-currency perspective.
- CME Group, Understanding FX Quote Conventions: base-first currency-pair notation and the units of its price.
- CME Group, E-quivalents Help: reciprocal conversion swaps dealer bid and offer sides.
- Reserve Bank of Australia, Exchange Rates Overview: the two directions in which any exchange rate can be expressed.
- John C. Hull, Options, Futures, and Other Derivatives, ninth Global Edition, Pearson, 2018, Section 5.10, p. 139: domestic-currency pricing and market quotation direction can differ.