Definition and how the pairs are quoted
A “worked example” means you pick starting exchange rates, state assumptions, and then calculate the numerical result step by step. For forex comparisons, you must also be precise about what each currency pair quote means.
- EUR USD refers to EUR/USD, the number of USD needed to buy 1 EUR. Example: a quote of 1.0800 means 1 EUR costs 1.0800 USD.
- USD JPY refers to USD/JPY, the number of JPY needed to buy 1 USD. Example: a quote of 155.00 means 1 USD costs 155.00 JPY.
These pairs are not mirror images in terms of “direction.” If EUR strengthens vs USD, EUR/USD can rise, but USD/JPY can move for different underlying reasons because it is a different comparison (USD vs JPY).
How a worked example works (separating mechanics from market conditions)
To compare pairs, you generally do one of two calculations:
- Conversion mechanics: convert an amount in one currency into the other using the quoted rate.
- Change over time: measure how much the quote changed (for example, from Rate A to Rate B), then translate that change into a value change for a given starting amount.
Assumptions you must state for any numeric example:
- You choose starting rates and ending rates (not real-time).
- You choose an amount to convert (e.g., 1,000 EUR).
- You assume no costs (no spreads, fees, or slippage) unless you explicitly include them.
Real markets can differ because costs and execution quality vary, but mechanics are the same.
Evidence or example: EUR/USD and USD/JPY in two transparent scenarios
Below are two independent worked scenarios. They are not forecasts; they only demonstrate how to do the arithmetic.
Scenario A: EUR/USD conversion and a quote change
Assumptions
- Starting EUR/USD = 1.0800 USD per 1 EUR.
- Ending EUR/USD = 1.0850 USD per 1 EUR.
- Starting amount = 1,000 EUR.
- Ignore costs.
Step 1: Convert to USD at the starting rate
- USD_start = 1,000 EUR × 1.0800 = 1,080.00 USD.
Step 2: Convert to USD at the ending rate
- USD_end = 1,000 EUR × 1.0850 = 1,085.00 USD.
Step 3: Compute the change
- USD_change = 1,085.00 − 1,080.00 = +5.00 USD.
Interpretation Because EUR/USD rose from 1.0800 to 1.0850, the USD value of 1,000 EUR increased.
Scenario B: USD/JPY conversion and a quote change
Assumptions
- Starting USD/JPY = 155.00 JPY per 1 USD.
- Ending USD/JPY = 154.50 JPY per 1 USD.
- Starting amount = 1,000 USD.
- Ignore costs.
Step 1: Convert to JPY at the starting rate
- JPY_start = 1,000 USD × 155.00 = 155,000 JPY.
Step 2: Convert to JPY at the ending rate
- JPY_end = 1,000 USD × 154.50 = 154,500 JPY.
Step 3: Compute the change
- JPY_change = 154,500 − 155,000 = −500 JPY.
Interpretation Because USD/JPY fell from 155.00 to 154.50, the JPY value of 1,000 USD decreased.
Limitations and risks: what can fail in real verification
- Different “base” and “quote” currencies: EUR/USD answers “USD per EUR,” while USD/JPY answers “JPY per USD.” You cannot directly compare their numeric moves without converting through a common currency.
- Costs and execution: spreads, fees, and slippage can change the realized result versus the clean calculations above.
- Measurement choice: sometimes you measure P&L in the account currency; sometimes you measure percent change on the quote; those lead to different numbers.
- Market uncertainty: outcomes vary with market conditions and cannot be inferred from a single worked example.
- Failure mode—unit confusion: a common error is multiplying or dividing by the wrong rate direction. A worked example reduces this risk because you keep the “per 1 unit” meaning explicit.
Verification and next question to ask yourself
To independently verify any EUR USD vs USD JPY worked example, check four items:
- The quoted format: “USD per EUR” for EUR/USD and “JPY per USD” for USD/JPY.
- The chosen starting amount.
- Whether you multiplied or divided correctly.
- The assumption set (especially whether costs were included).