Consider the four major commodities traded on a commodity futures exchange today (year 10). The following table lists the average annualized price movements from year 1 to year 10, as well as the production volumes, expressed in the local currency unit, today (year 10) and ten years ago (year 1).

The futures exchange has now decided to create a commodity index based on the four commodities, with weights equal to their current relative importance in economic production. These indexes are back-calculated till year 1 using today's weights.
a. Would such an index give unbiased indications over the past 10 years?
b. What suggestions do you have regarding weights that can be used to back-calculate the indexes?

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Annual Production Average Return 20% 20% -1 0% 0% Year 1 10 う 50 5 Year 10 50 20 10 20 Commodity