A client has given you $100 million to invest abroad in an equity GDP-indexed fund. There are only two foreign countries, A and B, and their GDPs are currently equal to $100 billion each. Their respective stock market capitalizations are $150 and $100 billion. The performance of the fund is compared monthly with the GDP-weighted index. Assume that exchange rates remain fixed and that there are no new listings on the stock markets, so that national market capitalizations go up and down in line with movements in the national stock indexes. Here are the stock market indexes and the published GDPs for the next six months:

a. Calculate the values at the end of each month of the two international indexes: GDP-weighted index and market capitalization-weighted index. In both cases, use the international weights (GDP and market cap) that are valid at the start of the month.
b. Assume that you build a portfolio using two national index funds. What operation should you do each month to track the GDP-weighted index?

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GDP-A 100 100 100 102 102 102 GDP-B 100 100 100 101 101 101 Index A 100 95 100 100 105 110 Index B 100 110 100 120 125 Month