Currencies are so frigging’ tricky lol…I think I got it now…but still curious about a few things. Can any of the BRILLIANT guys/gals comment on these points.
This is more a mathematical curosity If a EUR/USD changes by x% why does the USD/EUR also not change by x%. Mathamatically since the number are just reciprocals, should’nt the change % be identical?? I know we need to convert the currencies and then measure the change % again, but why (mathematically speaking) are the percents different??
This has to do with the CFA rules Is the Total Return=domestic return in % + the currency return in % OR is it (1 + r dom)(1+r curr). The text uses both approaches randomly (as far as I can tell)
I will try to answer both:
The demoninator is different (duh ). The larger the denominator the smaller the change. Think about it like this. 1/2 = 50%. 2/1 = 200%. The difference in change is double. You have more invested with a larger base. 3 apples losing two you lost 66%, but 1 apple you get 3 it’s 200% gain. When u minus 1 to get the percentage the discreptence is so much more since 1/1 has a small base.
The most appropriate answer is (1+fx)(1+fc). The first one you posted is approximation since it’s missing (fx)(fc). I just usually multiple all the returns out and divide it by the base price of the asset, that way I don’t have to think.
I’'d use the multiplication approach: Rdc = (1+Rfx) * (1+Rfc) since that’s the formula in the book…