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Foreign Exchange | FX101
What is a Cross Rate & How To Derive One
The US dollar (USD) is the currency against which all other currencies are priced. Any exchange rate (AUDCAD for instance) that does not involve the USD is considered a "cross rate". Currency cross rates are not usually quoted outside of a few significant market pairs: EURGBP, EURJPY, EURCHF and AUDNZD.
If you are trying to derive the rate at which you would change your base currency and it does not involve USD you may need to find the cross rate.
In order to do this you have to find two currency pairs: one that contains your home currency and the other must contain the foreign currency that you want to exchange it with. Next, determine what type of quote each of your two selected currency pairs is and apply the corresponding rule for deriving a cross rate.
- Direct Quote: 1 foreign currency unit = x home currency units
- Indirect Quote: 1 home currency unit = x foreign currency units
How to Derive a Cross Rate from a Direct Quote & Direct Quote:
Rule: Divide the terms currency by the base currency on the opposite side.
Example:
Derive the rate for JPYAUD
| Bid | Ask | ||
|---|---|---|---|
| USDJPY | 119.25 | 119.65 | USD is base, JPY is term |
| USDAUD | 1.0485 | 1.0535 | USD is base, AUD is term |
| The JPYAUD Bid rate | = divide the term currency bid by the base currency ask | ||
| = 1.0485 / 119.65 = 0.008763 | |||
| *this is the rate at which the market buys JPY and sells AUD | |||
| The JPYAUD Ask rate | = divide the term currency ask by the base currency bid | ||
| = 1.0535 / 119.25 = 0.008834 | |||
| *this is the rate at which the market sells JPY and buys AUD | |||
Rule: multiply on the same side
Example:
Derive the rate for EURAUD
| Bid | Ask | ||
|---|---|---|---|
| EURUSD | 1.3798 | 1.3858 | |
| USDAUD | 1.0432 | 1.0502 | |
| The EURAUD Bid rate | = Multiply the term currency bid by the base currency ask | ||
| = 1.3798 x 1.0432 = 1.4394 | |||
| this is the rate at which the market buys EUR and sellsAUD | |||
| The EURAUD Ask rate | = Multiply the term currency ask by the base currency bid | ||
| = 1.3858 x 1.0502 = 1.4553 | |||
| this is the rate at which the market sells EUR and buysAUD | |||
Rule: divide the base currency by the terms currency on opposite sides of the spread.
Example:
Derive the rate for GBPEUR
| Bid | Ask | ||
|---|---|---|---|
| GBPUSD | 1.9850 | 1.9950 | GBP is base, USD is terms |
| EURUSD | 1.3460 | 1.3520 | EUR is base, USD is terms |
| The GBPEUR Bid rate | = divide the base currency bid by the terms currency ask | ||
| = 1.9850 / 1.3520 = 1.4682 | |||
| this is the rate at which the market buys GBP and sells EUR at 1.4682 EUR per GBP. |
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| The GBPEUR Ask rate | = divide the base currency ask by the terms currency bid | ||
| = 1.9950 / 1.3460 = 1.4821 | |||
| this is the rate at which the market sells GBP and buys EUR at 1.4821 EUR per GBP |
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