# 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)

• 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!

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.