Indexing Portfolio

Full Replication:

Will underperform the index because of transaction cost (dividend, splitting), cash drag and administrative fee. Transaction cost is higher when the stocks are more illiquid.

Low tracking risk

Stratified sampling: divide into different cell and pick up representative stocks from each cell, investing equal to the cell market cap.

Less transaction cost (no need to buy illiquid ones) and no need to buy all shares

Optimization: use factor model to match factor exposures of the fund to those of the index. Objective function can be added also.

But need historical data, sensitivity may change and need frequent rebalancing

Lower tracking risk than stratified as covariance is taking into account.

Best one: Full replication for big stock and optimization for the rest.