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Deriving CAD/CHF Bid and Ask Rates from USD Currency Quotes

Article Quant Q&A · Author: Minh Long Vu
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Summary

The document asks how to derive the bid for CAD/CHF from USD/CAD and USD/CHF quotes. It compares a textbook formula, which divides the USD/CHF ask by the USD/CAD bid, with an alternative based on multiplying the USD/CHF bid by the reciprocal of the USD/CAD ask. The question frames the issue through the bank’s implied currency transactions and asks why the quoted sides differ.

No answer or worked example is included, so the document does not establish which formula is correct or explain how to choose bid and ask sides. Its value is as a prompt about quote inversion and executable cross rates: each leg’s bid or ask depends on whether the dealer is buying or selling the currency in that leg. A reader would need an authoritative explanation or market quote example to resolve the comparison; the referenced textbook image is not available in the text.

Key ideas

  • Cross rates can be constructed from two currency pairs that share a common currency.
  • The bid and ask sides used in a cross-rate calculation depend on the direction of each transaction.
  • Inverting a currency quote reverses its bid and ask sides.
  • The document poses competing formulas but does not supply a resolution.

Tags

ForexMarket microstructure
Full text
# Is this cross-rate bid/ask relationship formula correct for CAD/CHF derived from USD/CAD and USD/CHF?


# Is this cross-rate bid/ask relationship formula correct for CAD/CHF derived from USD/CAD and USD/CHF?












At my university I’m studying how to compute cross currency rates (bid and ask) using quotes against USD. In the textbook, I found the following formulas: ​

```
BID (CAD/CHF) = ASK (USD/CHF) / BID (USD/CAD)
```

I want to confirm whether this formula is correct for determining the CAD/CHF bid rate, because it goes against my reasoning. Since the bank is buying CAD and selling CHF, shouldn't it be buying USD with CHF, and buying CAD with USD, essentially giving me:

```
BID (CAD/CHF) = BID (CAD/USD) * BID (USD/CHF) = BID (USD/CHF) / ASK (USD/CAD)
```

The professor refuses to give me a detailed explanation when I asked and simply told me to "refer to the textbook".

Image from textbook (language is Vietnamese):

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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