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highest costs to construct? definitely full replication.  you have to buy every security in the index, including the illiquid ones.
highest cost to maintain? optimization.  the model recommends adjustments and rebalances whenever your risk factors change, so you may have rebalancing that just isnt worth the cost (think of how in a later ready, we learn that transaction cost increases widen corridors because the hurdle rate for rebalcning increases).  stratified sampling is in the middle.  cheapest is enhancined indexing.  because its a self rebalancing index.  dont need to touch it.  only need to rebalance/reinvest when index constitutents change or dividends are paid.

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