Question 12 of Reading 44 (SS16)

Question 12 on p109 of CFAI Reading #44 asks to calculate value for international GDP-weighted and market cap-weighted indexes for each of the given months (given GDPs and Index values for each of the two countries). Using GDP values of two countries we compute weights to be used in GDP-weighted index calculation. To get the actual value of the GDP-weighted index they calculate weighted average return of two countries and multiply Index value for previous month x (1+weighted avg return). I thought I can get the same answer by calculating weighted average index value of two countries (using values of Index A and Index B and GDP-weights calculated above), i.e. skipping the return calculation. However, my answer is different. Can anyone explain?

.

comp_sci_kid, ?

If you skip the return calculation, you would have to assume that weights are the same each month for example: in month 3, both indexes are at 100. Weighted average of the indexes according to you would be 100. Ok, but you come from a previous period where weights are different to initial ones, so the monthly % change of each index (that moves each index back to 100, for example) will have a different impact in the previous value of the aggregate index, because weights for each index are different than initial ones hope I am not confusing you even more