# Calculating currency indexes weights?

I was looking at this formulas:

USD_INDEX= 50.14348112 × EURUSD^-0.576 × USDJPY^0.136 × GBPUSD^-0.119 × USDCAD^0.091 × USDSEK^0.042 × USDCHF^0.036


and

EUR_INDEX =  34.38805726 x (EURUSD^(0.3155) x EURGBP^(0.3056) x EURJPY^(0.1891) x EURCHF^(0.1113) x EURSEK^(0.0785))


I was wondering why those currencies where chosen and how could I calculate, for example, the USD_INDEX if I use other currency pairs? For example:

USD_INDEX = CONST * EURUSD^A * GBPUSD^B * USDJPY^C * USDCAD^D * AUDUSD^E * NZDUSD^F * USDCHF^G


How could I determine/estimate CONST, A, B, C, D, E, F and G?

Also, I was kinda surprised that for USD_INDEX the EURUSD constant was -0.576 and the EUR_INDEX the EURUSD constant was 0.3155. I would have expected that the second one was 1 minus the first one, so the sum of both of them adds 1.

• If you look at the absolute values of the exponents, they add up to 1. The sign is determined by the direction in which the currency affects the index (for example higher EUR -> weaker Dollar Index -> exponent has been made negative). – noob2 Jan 2 at 9:35
• They add up to 1 because they represent the fraction of the imports+exports with the named countries that are priced in each specific one of those countries' currencies. – noob2 Jan 2 at 9:43
• Hi @noob2. Yes, I noticed that. But how can I determine the exponents of custom index? What should be taken into account? And how should indexes like JPY_INDEX handled? Because, as far as I understood, it would be something like JPY_INDEX = 1/(NZDJPY * CHFJPY * EURJPY * GBPJPY * USDJPY * CADJPY * AUDJPY) and all their respective exponents, right? – Pedro Pablo Severin Honorato Jan 2 at 19:57