1. [3 points] ** initially only stocks 1 through 5 are in the index ** Day 0 is the first day of the index (referred to as index inception date). Assume the index is market-capitalization weighted and compute the index divisor such that the index level is 100 on Day 0.

2. [3 points] Use the above information to compute the return to the index on Day 1 assuming it is market-capitalization weighted. Report the new index level and the index return.

3. [3 points] At the end of Day 1, the index committee removes stock #3 and replaces it with stock #6. Using the above information, compute the new index divisor after the replacement.

4. [3 points] Compute the Day 2 return to the index. Report the new index level and the index return.

5. [3 points] Now assume Stock 1 splits 2-for-1 at the end of Day 2 and at the new price is 2.75 and shares outstanding are 160 million. What is the new index divisor at the end of Day 2?

6. [15 points] Repeat a. to e. for a price-weighted version of the index.

7. [5 points] Compute the Day 1 return to a version of this index that is equally weighted. At the end of Day 1, assuming no rebalancing since Day 0, what will be the new weights? If the index were to be rebalanced to restore equal weights at the end of Day 1, indicate the necessary adjustments in terms of the percentage of the portfolio that must be traded to restore equal weights.

Day 0 Day 1 Day 2 Stock Price Price Price 1 5 5.25 5.5 2 150 145 144 Shares Outstanding 80,000,000 1,500,000 500,000 10,000,000 5,000,000 2,500,000 Shares Outstanding 80,000,000 1,500,000 500,000 10,000,000 5,000,000 2,500,000 Shares Outstanding 80,000,000 1,500,000 500,000 10,000,000 5,000,000 2,500,000 3 200 190 185 4 75 76 77 5 60 61 63 6 99 100 105