What is the difference between these two methods for constructing an equity index? And what is the equivalent for making a bond index?
optimization incorporates covariances between assets. Strat Sampling assumes all uncorrelated.
Strat sampling takes samples of the sectors. Optimization matches the risk factors of the index as a whole As a result, optimzation generally has less tracking error
Stratified sampling assumes uncorrelated factors for constructing the index and is best suited for illiquid stocks (as it doesn’t need to be rebalanced). Optimization take covariances of relevant risk factors into account. As Jscott points out it usually has less tracking error, but needs to be rebalanced (not good for illiquid stocks) and the model must be updated as factors change.