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). 50 Commodity A B C D Average Return 15% 15% -7% 0% Annual Production Year 1 Year 10 10 5 20 50 10 20 35 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? 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). 50 Commodity A B C D Average Return 15% 15% -7% 0% Annual Production Year 1 Year 10 10 5 20 50 10 20 35 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