Comparing two portfolios: Port 1 - quantitative model used to match the risk factors of the S&P 500, using just 300 stocks. Information coefficient (IC) = 0.075. Port 2 - full replication of the S&P 500, using 500 stocks. IC = 0.053 Question - Recommend which portfolio should be chosen based on the fundamental law of active management
- Higher IR
IRa=1.299 IRb=1.185 Portfolio A because the increase in breath for B does not compensate the difference in Information coefficient
agree
My bad. Misread the question. Yes Portfolio A is the correct answer.
OK- my problem is this. If someone is replicating an index without making an active decision, shouldn’t the breadth be 0? The answer is still A, of course, its just that I feel portfolio B has an IR of 0 because of this
Has to buy 500 stocks, therefore number of decisions (hence Breadth) = 500.
Correct - but is that an ACTIVE decision? He’s just replicating the index - which is pretty much a no-brainer to do
This is the fundamental law of active management being applied to a passive investment (indexing). I agree it is kind of dumb.
Good point by both serf and mwvt9. I guess I am well on my way in parking my brain and just provide the required answer. I’m told, that’s half the battle on the exam.
Weird question. They are basically implying that number of stocks = number of independent investment decisions, which is full of problematic assumptions. Do they really mean to say that the performance of GM and Chrysler are going to be statistically independent? It also seems to be looking at an index (maybe it’s an enhanced index, but if so, they should say it). The fundamental law of active management says that IR = IC * sqrt( Breadth of decisions )
because he has a chance of choosing how to replicate the index, there is an active component. I do agree that for the second example, it might not be appropriate to ask that question