Combining Local Equity Returns with Foreign Exchange Returns

Summary

The note explains how a foreign investor can calculate an equity return in their home currency by combining the asset’s local-currency price change with the currency’s exchange-rate change. For an investor measuring returns in US dollars, first express each day’s share price in dollars using the matching yen-to-dollar conversion, then calculate the change between the converted values. This produces the multiplicative relationship between local and foreign-exchange returns.

The question’s formula is correct when the exchange-rate return is defined consistently with the desired conversion direction. The answer also highlights that the chosen FX fixing matters: currency markets trade around the clock, so different observation times can yield different translated returns and may not match a data vendor’s convention. Aligning the currency quote direction and timing with the vendor’s methodology is therefore necessary for comparison.

Key ideas

• A home-currency return is calculated from asset prices converted into that currency on both dates.
• The combined return equals the product of one plus the local return and one plus the FX return, less one.
• Define the FX return using the quote direction that matches the desired currency conversion.
• The FX fixing time can affect the result because currency markets trade across time zones.

Tags

# Getting Returns from Local Currency to USD


# Getting Returns from Local Currency to USD












I want to get the daily returns in USD given returns in local currency (say Japanese Yen).

Say for example, on February 3rd according to Factset, the returns of Inpex Corp (Japan) are:





The approach I used was this:

- JPY-USD on Feb-02 is: 113.311 (FX(0))

- JPY-USD on Feb-03 is: 112.789 (FX(-1))

R_USD = (R_Local+1)x(FX_rate+1)-1

FX_rate = (FX(-1)/FX(0))-1= 0.004628111 (It's FX(0)/FX(-1) if you have the exchange rate in the desired currency).

R_USD = 0.143709068 (different to what we are supposed to get in R_Desired).

Do I need to consider something else? What do I need to get that return to be as the one Factset gave back.

Thanks for your time!

## Answer by Richi Wa (score 1)

https://quant.stackexchange.com/a/33739

It is rather easy: The local return is the rate of change of the price in local currency: $$ r_{loc}= P_t/P_{t-1} - 1 $$ where $P_t$ is the local price (in JPY). If you are a USD ivnestor, then you calculate the price in USD: $$ r_{USD}= \left(P_t * (1 \text{ JPY in USD on day } t) \right)/\left(P_{t-1} * (1 \text{ JPY in USD on day } t-1) \right) - 1. $$ and for a return $$ r = X_t/X_{t-1}-1 $$ it is equivalent to write $$ 1+r = X_t/X_{t-1}. $$ Thus above you can write: $$ r_{USD}=(1+r_{local})*(1+r_{FX})-1. $$ Thus your formula is correct. Just consider that the above calculation depends on the fixing of the FX-rate. As FX is traded around the clock it very much depends on this.

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