# 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:

• In USD: 0.1740694 (R_Desired)
• In JPY: 0.13843775 (R_Local)

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!

## 1 Answer

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.

• This is key: the stock price and the exchange rate must be observed simultaneously. "Closing" prices may not be simultaneous, the japan stock exchanges close (I think) at 2:30am new york time, the FX market at 17:00 New York time. Apr 19, 2017 at 12:26
• @noob2 and Richard thank you guys both. I thought that was not a "big deal", but I seem to be very wrong. So what you mean is that the closing time that's reported might vary with each timezone? Because that's the price I'm using, closing price. Should I try to search for a price that coincides with Japan market close better and see if I can get the return I want? Apr 19, 2017 at 21:52
• If you work globally then you will not find a point in time when all markets just closed (stocks and FX). If you want to match the return delivered by factset then you have to aske them which FX fixing they use. Apr 20, 2017 at 6:19