Exchange Rates and Returns: Why an Asset Can Rise While You Lose

Choose a reference currency for the question

A reference currency is the unit in which you want to evaluate the result, such as the currency used to fund an account or pay expenses. Keep it consistent across entry and exit. A profit displayed in a trading currency cannot be compared directly with an initial budget denominated in another unit.

Investor.gov’s international-investing explanation describes exchange-rate changes as a factor that can increase or reduce returns. We apply the arithmetic principle to an illustrative digital-asset valuation here, without equating digital assets with securities or importing one product’s regulatory treatment into another.

Follow the entry and exit amounts

Assume one asset unit costs 100 quote-currency units at entry. Each quote unit is then worth two reference-currency units, so the raw reference cost is 200. At exit the asset rises to 110 quote units, while one quote unit is worth only 1.8 reference units, a 10% currency decline from two.

The exit value is 110 × 1.8 = 198 reference units before fees. Relative to the original 200, that is a loss of two, or 1%. The asset’s quoted price rose, but the currency in which that increase was measured weakened against the chosen reference. Both observations can be correct.

Multiply the factors instead of adding percentages

The asset-price factor is 1.10 and the quote-currency factor is 0.90. Their product is 0.99. Subtracting one gives −0.01, or −1%. Adding +10% and −10% would produce zero because it ignores the interaction between changes applied sequentially to the value.

For a constant quantity and common period, the gross reference-currency return is (1 + asset return) × (1 + currency-value change) − 1. Express the two inputs as decimals and define currency change in reference units per quote unit. This simple model excludes fees, deposits, withdrawals and changes in holdings.

Expanded algebra contains asset return plus currency change plus their product. In our example, that final product is −0.01. You do not need to memorize the expansion if direct amounts are clearer: convert entry and exit values consistently, then divide the difference by the entry value.

Test the formula with other hypothetical combinations

An asset rising 10% with unchanged conversion produces a 10% gross reference return. An unchanged asset with a 10% decline in quote-currency value produces −10%. If both rise 10%, the combined factor is 1.10 × 1.10 = 1.21, or +21%, rather than +20%.

An asset falling 10% while its quote currency strengthens 10% gives 0.90 × 1.10 = 0.99, again −1%. This mathematical symmetry does not establish equivalent market conditions, predictable correlations or a reliable way to offset losses. These are independent assumed scenarios for checking the calculation.

Break-even changes are not symmetric percentages

If the asset rises 10%, the currency factor that exactly offsets it before costs is 1 ÷ 1.10, approximately 0.909091. That corresponds to a decline of approximately 9.0909%, not 10%. A full 10% currency decline more than offsets the gain under our fixed-quantity assumptions.

Conversely, after a 10% currency decline, the asset needs a factor of 1 ÷ 0.90, approximately 1.111111, to restore the gross reference value. That is an 11.1111% increase. These figures are mathematical thresholds, not price targets or forecasts. Costs require rebuilding the result from actual spending and proceeds.

Add fees through the amounts actually paid and received

Return to the 200 entry value and 198 exit value. Add a hypothetical entry cost of two reference units, making initial outflow 202. Deduct a hypothetical exit cost of three, leaving proceeds of 195. Net return is (195 − 202) ÷ 202, approximately −3.4653%.

Do not add this percentage to the earlier −1% result, because the new calculation already replaces the gross comparison with fee-inclusive amounts. Likewise, do not deduct a commission again if the conversion quote already states net proceeds. Label every amount as gross or inclusive and preserve the fee currency.

If fees use a third asset or reduce the holding quantity, retain the original movements and use an explicit valuation method. A separate network transfer belongs in its own cost row. The transfer fee calculator helps isolate that stage instead of hiding network costs inside an unexplained currency-effect figure.

Check conversion direction and the kind of price

Our factor is reference units per quote unit. Its change from two to 1.8 is −10%. The reciprocal moves from 0.5 to approximately 0.555556 quote units per reference unit, an increase of about 11.1111%. Inverting a rate does not preserve the percentage magnitude with a changed sign.

Write complete units in column headers and put both dates in the same direction before calculating. Also distinguish a midpoint used for valuation from a conversion quote actually available to you. A reference valuation can be useful, but it is not necessarily cash you could receive after the relevant spread, fees and conditions.

If the quote asset is USDT, identify the token-to-cash step separately from any fiat conversion. The BTC/USDT and BTC/CAD comparison explains why a token balance and bank-dollar balance should not silently become the same unit. Changing an app’s display currency also does not execute either conversion.

Additional deposits and multiple purchases need more records

The initial example uses one unchanged holding. A new deposit during the period can increase account value without representing investment performance. Record external inflows and outflows with dates and original currencies. A simple change between two account balances does not isolate return when money was added or removed.

For staged purchases, each can have a different asset price and conversion factor. Calculate each reference-currency cost at its own time before combining them. For a partial sale, state the scope and cost-allocation method rather than comparing its proceeds with the entire original portfolio as though everything had been sold.

Reconcile the same question before judging a displayed profit

Record the reference currency, quantity, entry costs, conversion rates, times, exit proceeds or valuation and separate external cash flows. Identify whether you are measuring an unrealized valuation or a completed exit. The watchlist provides price context but cannot replace this cash-flow record.

An app may show only asset-price change, quote-currency profit or a valuation excluding exit charges. Read its definition and period first. If a discrepancy remains after aligning units, scope and costs, investigate the underlying records. A useful comparison begins with the same question and ends with amounts that can each be traced.

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