Anyone know why currency indices are calculated with exponentials and multiplication? E.g. Code: USDX = 50.14348112 × EURUSD^ -0.576 × USDJPY^0.136 × GBPUSD^-0.119 × USDCAD^0.091 × USDSEK^0.042 × USDCHF^0.036 What does this do differently from just coming up with your own weights and using addition and multiplying each currency by the weight you determine? Also how does one make any use of this when you might have very differently priced products in each place? i.e., if you give two products a weight of 0.1 (10%) but one is priced 500 to 1 USD and another 0.0005 then a 10% move in each will have a completely different impact on the index. How do you account for this?
Where did you obtain this specific approach from? Looks highly unusual to me and at first glance does not make sense. The exponent weights seem to be derived from trade data. That is also why I never look at the "published" dollar index but built my own currency baskets.
https://www.theice.com/publicdocs/data/ICE_FX_Indexes_Methodology.pdf https://www.theice.com/publicdocs/futures_us/ICE_Dollar_Index_FAQ.pdf