full replication / stratified sampling

is there a certain number of stocks or bonds that we have a consensus on to where full replication becomes too expensive and you move on to stratified sampling?

I don’t think so. It really depends on the context.

From what I’ve seen, the best you can do for the traditional indexes, such as the S&P500, the Russell 1000, etc, is stratified sampling/optimization.

My understanding was that if it is below 1,000 and liquid, then full indexing would make sense. Otherwise, Stratified Sampling or Optimization become necessary. Optimization leads to lowest tracking error.

I think 1000 is quote in the text. But that number can be smaller if a large number are thinly-traded.

just to make sure, there’s no threshold for amount to be invested? as in, in order to do a full replication, you need $X

It largely depends on the facts given in the case.

One figure I remember: 5 Mio is not enough to do full replication for a bond portfolio because of their large lot size