Tracking Error in Equity - Full Replication

CFA Level III Equities
#1

Hi guys,

I had a doubt with respect to Tracking Error in Equities in full replication.

On the one hand they claim that as the number of securities go up, the tracking Error keeps going down.

Therefore ideally the tracking Error should be low for full replication. However, more securities means more trading costs and this leads to expected return falling and thus higher tracking error.

What is the correct way to look at it?

Would a portfolio carrying out full replication have a lower tracking error or a higher one due to the costs cutting into the returns???

#2

I understand your concern, but look at it this way: Full replication does not have any tracking error.

#3

Yes. That’s correct.

For the moment I am looking at it this way.

  1. Full replication means minimum TE.
  2. However it could be more in case no of stocks is more than the no of stocks in the index.
  3. Also if the index has many stocks like 800 or 900 it is likely that even full replication may give you a higher TE.
  4. Also look at the fees in conjunction with the data.

Does this sound good?

#4

Yes, yes… I get your point, but if I correctly recall we should stick with full replication. I cannot remember if TE was calculated using std. dev. of returns gross or net of fees, commissions etc…

I could also add point 5. if there would be frequent rebalancing, it would again trigger new costs, thus increasing TE → just to point I understanding you well.

Actually there is no strict optimal nr of securities held in index that should indicate if full replication or strat. sampling should be used, but would say around 1,000 liquid securities would be a solid rule of thumb number.

Maybe someone else can give you better answer…