Direct answer: a worked example of CHF crosses
A worked example of CHF crosses shows how a CHF-based exchange rate can be computed from two related quoted rates, using explicit arithmetic and assumptions. Here, “worked example” means you start with clearly stated input rates, define what they represent, convert them step by step, and then compute the implied CHF cross rate.
A CHF cross is a currency pair where CHF is one of the currencies and the other currency is not USD. In practice, you may see it quoted directly (as a cross quote) or you may derive it from two separate market quotes. The worked example below demonstrates the derivation idea without relying on any live prices.
Mechanics: definition, pair direction, and inputs
To work an example, you need to be precise about quote direction and how to combine rates.
1) Quote direction Exchange-rate quotes are commonly expressed in one of two ways:
- A/B: the amount of currency B per 1 unit of currency A.
- If instead your data source provides the inverse rate (B/A), you must invert it before combining.
2) What you combine for a CHF cross Suppose you want a CHF cross between CHF and another currency (for example, EUR/CHF or USD is not involved in the final cross). A common derivation uses two “legs” that each connect CHF to a reference currency.
For an example, we will derive EUR/CHF using two assumed market quotes:
- EUR/USD: the number of USD per 1 EUR.
- USD/CHF: the number of CHF per 1 USD.
3) The key arithmetic If:
- EUR/USD = X USD per EUR
- USD/CHF = Y CHF per USD then multiplying gives:
- EUR/CHF = (EUR → USD → CHF) = X × Y CHF per EUR
If your assumed inputs were the inverse of these directions, you would invert accordingly. That is why stating directions is a required assumption.
Worked example (fully stated assumptions)
Goal
Compute a hypothetical EUR/CHF implied rate from assumed EUR/USD and USD/CHF quotes.
Assumptions (no live data)
- We use the quote convention:
- EUR/USD is USD per 1 EUR.
- USD/CHF is CHF per 1 USD.
- We assume exact arithmetic with no rounding, and we ignore costs and execution differences.
- We assume the market quotes are consistent with each other (no arbitrage constraints are violated in this hypothetical setup).
Chosen input values
- EUR/USD = 1.10 (USD per 1 EUR)
- USD/CHF = 0.92 (CHF per 1 USD)
Step-by-step calculation
- Convert 1 EUR to USD using EUR/USD:
- 1 EUR = 1.10 USD
- Convert the resulting USD to CHF using USD/CHF:
- 1.10 USD × 0.92 CHF/USD = 1.012 CHF
- Therefore the implied cross rate is:
- EUR/CHF = 1.012 CHF per 1 EUR
Cross-check using the inverse form
If you rearrange the logic, you can derive USD/CHF from EUR/CHF and EUR/USD, but only if your directions match. This is a practical verification method: re-run the arithmetic with inverses when needed, and confirm you return to the original inputs.
Limitations and risks: why results may differ in real conditions
Even if the arithmetic is correct, real-world cross rates can diverge from the implied value.
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Spreads and pricing conventions Market quotes often differ for buying vs selling. Using a single “mid-like” number in a worked example ignores bid/ask spreads, which can materially change the effective conversion.
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Execution quality The ability to trade at the quoted rate depends on liquidity and order size. Slippage can cause the actual realized conversion to differ from the implied calculation.
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Rounding and unit definitions Different platforms may display rates with varying decimals and may apply pip-based conventions. Small rounding choices can accumulate when chaining conversions.
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Failure mode: wrong direction The most common failure mode in cross calculations is using an inverted rate. If EUR/USD is treated as “EUR per USD” rather than “USD per EUR,” the derived CHF cross will be wrong.
Verification and next question
To independently verify a CHF cross worked example, do three checks:
- Confirm the quote directions match the arithmetic (A/B vs B/A).