Define AUD crosses
An AUD cross is any currency pair that involves the Australian dollar (AUD) but does not use the Australian dollar as the “base” or “quote” currency against the US dollar. In practice, traders compute cross rates by combining two known rates from a shared reference currency (often the US dollar), then using the result to express one currency against another through AUD.
Key idea: a “cross” rate is a derived rate. It depends on the rates used to derive it, the side of the market you start from (bid vs ask), and the arithmetic conventions (how quotes are written).
How a worked example works (with explicit assumptions)
Below is a worked, fully numeric example of how an AUD cross can be derived. This is concept-only math; it assumes you already have the two input rates and ignores live market movement.
Assumptions (state up front)
- Quotes are in the common forex convention: for a pair like X/Y, the number means “how many Y you get for 1 unit of X.”
- We use ideal mid-market style numbers only for illustration (no bid/ask spread). If real bid/ask are used, results change.
- We use a single, consistent reference for both legs (USD).
- No trading costs, commissions, or slippage are included.
- The cross is computed exactly by arithmetic; we do not enforce any real-world “no-arbitrage” constraints.
Example setup
Assume these two reference rates are given:
- EUR/USD = 1.1000 (meaning 1 EUR = 1.1000 USD)
- AUD/USD = 0.6800 (meaning 1 AUD = 0.6800 USD)
Goal: derive an AUD cross that expresses AUD relative to EUR, i.e., AUD/EUR. Following the quote convention, AUD/EUR should mean “how many EUR per 1 AUD.”
Derivation
From the definitions:
- 1 EUR = 1.1000 USD, so 1 USD = 1 / 1.1000 EUR.
- 1 AUD = 0.6800 USD.
Combine them:
- 1 AUD = 0.6800 USD
- Convert USD to EUR: 0.6800 USD × (1/1.1000) EUR/USD = 0.6800 / 1.1000 EUR
Compute:
- AUD/EUR = 0.618181… EUR per 1 AUD (approximately 0.6182)
What this number means
If AUD/EUR is ~0.6182 under these assumptions, then under those inputs you would expect 1 AUD to correspond to about 0.6182 EUR. That statement is only as reliable as the assumptions and input rates you used.
Limitations and failure modes
A “worked example” is useful, but several material limitations can cause actual outcomes to differ.
- Bid/ask effects: Real market quotes have bid and ask. If you derive a cross rate using mid-style numbers but execute using bid/ask, the effective cross you realize can be less favorable.
- Different quoting conventions: Some platforms or feeds may quote currency pairs using different formatting conventions (for example, inverted pairs). If you invert one leg incorrectly, the cross rate can be off by a reciprocal.
- Cross-rate inconsistency: In real markets, the derived cross from one provider’s EUR/USD and AUD/USD may not match the directly quoted AUD/EUR from the same or another provider at the same moment, due to liquidity, spreads, or provider methodology.
- Costs and execution: Commissions, financing, and slippage are not included in the arithmetic example. These can change the realized conversion compared with the “ideal” computation.
- Moving rates: The example assumes static inputs. In live trading, any delay between observing input rates and execution changes results.
Verification and next question
You can independently verify the math by repeating the same arithmetic with your own chosen input rates and checking the units.
A practical check is dimensional: if your intermediate step says “USD per EUR” and you want “EUR per AUD,” then the calculation should end with “EUR per AUD.” If the units do not cancel to that, you likely inverted one quote.
If you want, share a specific cross you mean (for example, AUD against a named currency other than USD) and the two input reference rates you want to start from; then the same worked method can be applied step-by-step while keeping every assumption explicit.