Direct answer
An exchange rate depreciation happens when one currency loses value compared with another currency between two dates (or times). A worked example shows this clearly: if 1 unit of currency A buys fewer units of currency B after a change, then currency A has depreciated versus currency B.
Mechanism or definition
An exchange rate is usually quoted as the amount of one currency needed to buy one unit of the other currency. Because quote conventions differ, the first step in any calculation is stating the convention explicitly.
In this article, a simple convention is used:
- The exchange rate is quoted as B per A (how many units of currency B you get for 1 unit of currency A).
- Depreciation of A vs B means the value of A falls, which under this convention means the rate decreases over time.
A worked example therefore only needs:
- an initial exchange rate (rate at time 1),
- a final exchange rate (rate at time 2), and
- the starting amount in currency A (or currency B) to translate the impact into money terms.
Evidence or example
Example setup (all assumptions stated)
Assume:
- Currency A is “USD” and currency B is “EUR” (labels only; the arithmetic applies to any pair).
- The quote convention is EUR per USD.
- Time 1 rate: 1 USD = 0.900 EUR.
- Time 2 rate: 1 USD = 0.810 EUR.
- You start with 100 USD at time 1.
- Ignore transaction costs, fees, taxes, and any conversion frictions.
Step 1: Compute the depreciation percentage
Under the chosen quote convention (EUR per USD):
- Initial rate = 0.900
- Final rate = 0.810
- Change = 0.810 − 0.900 = −0.090
- Percentage change = (−0.090 / 0.900) × 100 = −10%
Interpretation: USD depreciated versus EUR by 10% under this quote convention.
Step 2: Compute the amount impact
At time 1:
- 100 USD × 0.900 EUR/USD = 90.0 EUR
At time 2:
- 100 USD × 0.810 EUR/USD = 81.0 EUR
Difference in EUR value:
- 81.0 EUR − 90.0 EUR = −9.0 EUR, which matches the 10% change.
Limitations and risks (failure modes)
- Quote convention mismatch: If someone uses A per B instead of B per A, the sign of the “depreciation” interpretation can flip. Always rewrite the convention before calculating.
- Timestamp mismatch: Rates taken at different times (or from different sources) can produce different results even if the currencies are the same.
- Trading costs and spreads: The worked example ignores costs. In practice, the effective rate you receive can differ from the mid-market rate due to bid/ask spreads and provider fees.
- Currency redenomination vs relative value: “Depreciation” is relative. A currency can depreciate against one currency while appreciating against another at the same time.
- Non-identical product terms: If you convert via specific instruments or jurisdictions, the effective conversion may follow different rules than the simplified spot-rate arithmetic.
Verification or next question
To independently verify an exchange rate depreciation calculation:
- Write down the exact pair and the exact quote convention (e.g., EUR per USD or USD per EUR).
- Record the initial and final rates from the same source family and comparable timestamps.
- Compute either the percentage change in the quote rate or the translated amount using the starting currency amount.
A next useful question is: “If the same market move is quoted as USD per EUR instead, what happens to the percentage calculation and interpretation?”