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Read the initial direction
Let a fictional domestic-per-foreign quote rise from 1 to 1.10. A fixed one foreign unit increases in domestic value by 10%. The movement is measured relative to the initial quote of 1.
Invert both endpoints
The foreign-per-domestic quote changes from 1 to 1/1.10 = 0.909091. Its percentage movement is 0.909091/1−1 = −9.090909%, rather than −10%.
| Direction | Start | End | Movement |
|---|---|---|---|
| Domestic per foreign | 1 | 1.10 | +10% |
| Foreign per domestic | 1 | 0.909091 | −9.090909% |
Check the consistency identity
The factors 1.10 and 1/1.10 multiply to one. This confirms that the quotes are reciprocals. Using a negative 10% factor of 0.90 would give product 0.99 and would not return the original unit.
Apply the direction required by the conversion
For a domestic-return calculation using a domestic-per-foreign formula, invert a foreign-per-domestic source quote before calculating movement. Retain the source quote and transformed quote so the unit change can be checked.