Converting Local-Currency Returns into a Foreign Investor’s Returns
Summary
The document clarifies how to express an investment gain in a different currency. The key step is to convert the absolute profit or loss using the relevant exchange rate, rather than multiply a percentage return directly by the currency conversion factor. Its example starts with a yen-denominated position, calculates the gain in yen from the local return, and then translates that amount into dollars. The percentage return on the underlying asset remains the same when both the investment’s starting value and gain are converted at the same rate.
Currency movements matter when evaluating an international investor’s realized return across the investment period. If the investment is opened and closed in different currencies, or if the investor’s base currency changes in value relative to the asset currency, FX changes contribute to the overall result unless hedged. The answer focuses on translating a gain using a conversion factor and does not detail the timing convention for exchange rates, reinvested cash flows, or how to calculate a full-period base-currency return from start and end values.
Key ideas
- Convert the local-currency profit or loss into the target currency using an appropriate exchange rate.
- A local percentage return is not itself converted by multiplying it by the exchange rate.
- The return on an asset is unchanged by currency denomination when both its initial value and gain are translated consistently.
- Currency movements affect an international investor’s realized return when exposure spans a change in exchange rates.
- An unhedged investor may need to account separately for FX effects over the investment period.
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# How to adjust local currency returns to US$/EUR return? # How to adjust local currency returns to US$/EUR return? Iam doing research on return characteristics. As of today the scope of the research has changed from a local investor point of view to an international investor point of view. This basically means that returns have to based on returns in US$ instead of their local currency. The most obvious way would be to download all the returns again and then annualize them. But this is a fairly tedious job and time consuming. A professor told me that I could also download the historic currency rates (so for example from JPY to USD) and then multiply the returns with this number. I followed her advice in doing so and downloaded the average yearly historic rates. At first sight it looked plausible as , for example, the yearly return in AU$ was around 17 % and the conversion rate was 0.95 for that year. But looking at JPY returns, for a given year, of 16% and JPY/USD rate of 0.0126 will diminish all returns. So what am I doing wrong? ## Answer by Matt Wolf (score 2, accepted) https://quant.stackexchange.com/a/8059 You are not doing anything wrong. You just need to multiply the absolute return by the currency conversion factor. Example: You trade 200,000,000 yen notional and generate a return of 16% on that notional, then simply multiply 32,000,000 jpy gain by your conversion factor 0.0126 to yield a return of 403,200 USD. The return of 16% was generated on the asset itself, it does not matter in which currency it was originally expressed in. When you buy and sell a car and yield a return then it does not matter whether both deals were undertaken in USD or Euro, at least not for the sake of calculating the relative return. Currency considerations only come into play when you transacted the first leg of the trade in a different currency from the one of the second leg. Then part of the return will need to be attributed to fluctuations in the respective currency pair, absent any currency hedge.
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