I'm looking for insights on a methodology to create my own bespoke index, specifically a gold index. I'd like to take the price of gold in various currencies, along with the different cross rates between these currencies, and create a kind of fundamental "price of gold" index that is invariant to the changes in the values of each currency wrt the other currencies.
Create a "currency basket" consisting of: one third of a dollar (USD 0.33), one third of a Euro (i.e. EUR 0.33) and "one third of 100 Yen" (i.e. Yen 33.33). These amounts are chosen because they are worth approximately the same at this time, and because these are the 3 main world currencies (other than 人民币).
Now calculate the price of one ounce of gold in terms of this basket. (In 2 steps: convert these currency amounts into a single currency (for ex. dollars) and then see how many times this amount is needed to buy 1 ounce of gold).
Of course if the basket is chosen differently you get a different commodity index, so there an infinite number of commodity indexes that you can choose from, depending what "basket" you choose. For example you could have a basket where the currency weights are chosen in terms of the importance of the currency in international trade, or on the share of world GDP or whatever).