CFAI mock PM Stratified sampling / enhanced indexing

Question 2 of the FI item asks which portfolio used a stratified sampling approach to match the primary index risk factors. There is one portfolio whose investment style is enhanced indexing and one other portfolio whoe style is pure bond indexing.

The correct answer is that stratified sampling is used to match the primary risk factors and achieve a higher return than under full replication.

I don’t get why this answer should be self-evident. Is stratified sampling never use in pure bond indexing?

Does that means that full replication=pure indexing and stratified sampling=enhanced indexing (for both equities and fixed income)?


i dont agree that stratified sampling=enhanced indexing. stratified sampling is a method of passive indexing that reduces costs where enhanced indexing is more of a semi active approach that attemps to add alpha

It attempts to offset the indexing costs with small risk factor mismatches, not add alpha.

enhanced attempts to add value with small mismatches on certain risk factors to offsetmanagement costs where stratified simply aims to match the benchmark on primary risk factors.

Pretty much.

I’d just add a “low cost method” to SS.

But then why on the mock exam question the CFAI says stratified sampling is most likely to be used with enhanced indexing than with pure bond indexing?

The question talks about stratified sampling as an approach to match the primary risk factors, they are not talking about small mismatches. But they say the answer is enhanced indexing and not pure indexing.

You can’t really have small mismatches with the primary risk factors as far as I understand. Either it’s enhanced indexing, with mismatches on secondary risk factors, or it’s active management, with mismatches on the primary risk factors as well.

Pure Bond Indexing you are literally matching the index all the time transaction to transaction. But stratified sampling is just a sample to match the important things. By definition it wouldn’t work.

But to what I think you are trying to get at is. Can stratified sampling be used for indexing and not enhanced indexing. The answer is yes. BNY Mellon S&P 500 fund is a index fund that uses stratified sampling. But it’s not trying to enhance anything. It uses this strategy because it doesn’t have enough assets currently fully replicate the S&P 500 Index holds.

^ +1

Stratified sampling does not intend to mismatch risk factors, but it does because it’s a suboptimal method.

While enhanced indexing can mismatch secondary factors to cover for indexing costs, as opposed to full replication (or pure).

It’s not nesscarily alpha, you can lower the weights on lesser liquid securities (or increase for a liquidity premium play), or rebalance for improving tax efficency

So in my understanding stratified sampling is a passive strategy (which aims to replicate the index with a trade-off between efficiency and cost relative to pure indexing/full replication).

And enhanced indexing is a semi-active strategy (which aims to add value relative to the benchmark with tracking error constraints).

Is it correct?

If the above is correct then WHY in the Mock question it is implied that stratified sampling (which is essentially a passive strategy) is related to enhanced indexing (which is essentially a semi-active strategy) instead of being related to pure indexing (which is essentially a passive strategy)

We just told you. Passiveness is not the point, replication is.

Pure indexing does this job, stratified does not, nor enhanced indexing.

Enhanced indexing is more costly and complex to implement (almost exactly like pure replication), but covers managment and inefficency costs by deviating slightly from the index.

Stratified sampling is a piss poor method of replicating an index, which is neither costly nor effective.

It’s a spectrum of replication, you need to be passive to replicate an index, but you don’t need to be passive to match it (in fact, you can’t).