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Converting Bid and Ask Quotes for an Inverse Forex Pair

Article Quant Q&A · Author: Blaze
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Summary

The document explains how to infer the bid and ask for the reciprocal of a foreign exchange quote. Given a bid and ask for AUD/USD, the implied USD/AUD bid is the reciprocal of the original ask, while the implied USD/AUD ask is the reciprocal of the original bid. Reversing the sides matters because buying one currency at a quoted price corresponds to selling the other, and the spread remains a cost of crossing the market.

The question applies this relationship to converting AUD-denominated profits or losses back to USD. The accepted answer confirms the reciprocal bid-ask logic, while advising against calling the inverse quote a theoretical pair because that terminology can confuse the discussion. The document presents the conversion principle but does not cover broker-specific execution, fees, or whether a directly quoted inverse pair is available. In practice, the reciprocal is an implied cross-rate derived from the original quote; actual conversion proceeds can depend on the executable prices and account rules offered by the venue.

Key ideas

  • The inverse pair’s bid is the reciprocal of the original pair’s ask.
  • The inverse pair’s ask is the reciprocal of the original pair’s bid.
  • Which side applies depends on whether the conversion buys or sells the currency.
  • The reciprocal quote is implied from the original market and may differ from an executable venue quote.

Tags

ForexExecutionMarket microstructure
Full text
# Implied inverse forex pair bid/ask spread


# Implied inverse forex pair bid/ask spread












I just wanted to make sure this was correct:

If AUD/USD has bid ask of 0.71999/ 0.72032, that implies there is another (theoretical) pair USD/AUD which has a bid ask of (1/aud_usd_ask) / (1/aud_usd_bid) .

The reason for the theoretical pair is that if my quote currency profits are in AUD, I only have the AUD/USD bid/ask to convert back into USD and I want to make sure I have the correct bid/ask spread for the inverse pair that I'm going to use.

Ie, if I have a profit of 1000 AUD, then to convert back into USD by purchasing USD / selling AUD, I would use 1000 AUD / (1/AUD_USD_BID)

and if I have a loss of 1000 AUD, then I'd need to buy the AUD back and sell my USD in my account. For that I would use 1000 AUD / (1/AUD_USD_ASK)

Correct?? Thanks!!

## Answer by arodrisa (score 2, accepted)

https://quant.stackexchange.com/a/21381

You are correct, but in finance, you should avoid talking about the theoretical pair you are talking about as you will make it even more confusing.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.