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Building a Currency-Basket Index for Gold

Article Quant Q&A · Author: babelproofreader
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Summary

The document explains how to express gold’s price against a basket of currencies to reduce dependence on any single currency’s movements. Its example basket combines fixed amounts of US dollars, euros, and Japanese yen, then converts the basket value into one currency and calculates how many baskets equal an ounce of gold.

The basket’s composition determines the resulting index, so the method does not produce one uniquely correct measure of gold’s value. Weights could instead reflect currencies’ roles in international trade or their countries’ shares of global output. The example offers a construction concept, not evidence that this particular basket is stable, representative, or suitable for a trading strategy.

Key ideas

  • A currency basket can provide a reference unit for measuring a commodity’s price across currencies.
  • The example values fixed amounts of dollars, euros, and yen before comparing the total with gold’s price.
  • Changing the basket weights creates a different index.
  • Weights can be chosen to reflect economic criteria such as trade importance or GDP.

Tags

CommoditiesForexMulti-asset
Full text
# How to create a currency independent commodity index


# How to create a currency independent commodity index












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.

## Answer by Alex C (score 1)

https://quant.stackexchange.com/a/39214

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).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.