Direct answer
A worked example of floating exchange rates is a numerical scenario where you start with an initial exchange rate, specify assumptions (no fees, or fixed fees), then show how a later exchange rate changes the value of a position in another currency.
Mechanism or definition
An exchange rate is the price of one currency in terms of another. In a floating exchange-rate system, that price is not fixed to a single level; it moves when demand and supply for currencies change. Those changes can come from many factors, such as relative interest rates, inflation expectations, trade flows, risk sentiment, and currency market dynamics.
To do a worked example, you need to separate stable mechanics from variable conditions:
- Stable mechanics: the arithmetic relationship between rates and currency amounts.
- Variable conditions: the exchange rate you assume for “before” and “after,” plus any transaction costs and timing effects.
A clear way to define the direction is to choose a quote convention. In this example, we will use: EUR/USD = 1.1000 means 1 EUR buys 1.10 USD.
Worked evidence or example (with explicit assumptions)
Assume:
- Quote convention: EUR/USD.
- “Before” time (T0) exchange rate: 1 EUR = 1.1000 USD.
- “After” time (T1) exchange rate: 1 EUR = 1.0800 USD.
- Currency amounts: You start with 1000 EUR.
- Fees/spreads: None (we treat this as an idealized assumption).
Step 1: Convert EUR to USD at T0
- USD amount at T0 = 1000 EUR × 1.1000 USD/EUR = 1100 USD.
Step 2: Convert back using the new floating rate at T1
- If the same EUR amount were valued at T1 in USD terms: USD value at T1 = 1000 EUR × 1.0800 USD/EUR = 1080 USD.
Step 3: Compute the change
- Change in USD value = 1080 USD − 1100 USD = −20 USD.
Interpretation (without promising outcomes):
- Because EUR/USD went from 1.1000 to 1.0800, the USD value of 1 EUR fell. That is consistent with EUR depreciating against USD under this quote convention.
Same mechanics, different assumption: include a fixed cost
Now add one additional assumption to show a common failure mode (net results differ from “pure rate” math):
- Assume a flat transaction cost of 5 USD when converting at T1 (idealized and simplified).
Then the net USD after Step 2 becomes:
- Net USD = 1080 USD − 5 USD = 1075 USD.
Relative to the original 1100 USD, the net change is −25 USD, not −20 USD.
Limitations and risks (material failure modes)
- Quote convention risk: If you accidentally use the inverse quote (USD/EUR instead of EUR/USD), your interpretation flips. Always state the convention.
- Timing risk: Using “T0” and “T1” as if you could enter and exit instantly ignores the reality of delayed execution and different observed rates.
- Transaction costs and spreads: Real conversions often include bid/ask differences, commissions, and fees. Worked examples that ignore these can overstate the closeness between “rate movement” and actual net results.
- Model risk from assumptions: The example treats T1 as a known future rate. In reality, you only know rates after they occur, and historical movements do not guarantee similar future behavior.
Verification or next question
To independently verify a floating exchange-rate example, you can:
- Recompute the arithmetic using the same quote convention and the same assumed T0 and T1 rates.
- Check whether your direction is consistent: if EUR/USD falls, the USD value of 1 EUR falls.
- If you want realism, replace the “assumed T1” with a specific observed exchange-rate value from a published time series, then redo the calculations with the exact dates you choose.
A useful next question is: how would the numbers change under the inverse convention (USD/EUR) and with a bid/ask spread assumption?