# Information Ratio Question

Hi folks,

Could you please explain why a stock-based enhanced indexing strategy nomorally produce higher information ration than a derivative-based one?

Give the information ratio = Information Coefficient x (Investor Breadth)^0.5

This issue belongs to session 11-12 (Equity part)

Thanks,

where has this been explicitly stated?

I am seeing an example where the derivatives strategy has a higher IR than the stock based one.

And just for your info - IR = IC * sqrt(breadth) is an approximation and it has not been used to calculate the IR. Active Return/Active Risk has been used in Example 13.

I read in Schweser book 3, page 162:" A stock-based enhanced indexing strategy can produce higher information ratios because the investor can systematically apply her knowledge to a large number of securities, each of which would have different attributes requiring independent decisions"

I don’t understand thier explanation at all.

Yes, agree with you about exact and approximate fomula of calculating IR.

So the information ratio as its defined here by CPK is approximately equal to the other information ratio equation: Actice Return / Tracking Error, correct ? So really just another way of calculating IR?

I think since derivatives are not traded for every security so in stock based enhanced indexing strategy breadth is high (more numbers of stocks are available to play with).

In derivatives based - exposure is gained thru derivatives (less no - low IB)

In stock based - exposure is gained thru stocks (more no - high Investor Breadth (IB) )

So IR is more for the stock based enhanced indexing strategy.

nm

CPK, so is this just another way of defining / approximating / solving for the information ratio (as previously defined in the text as active return / active risk)?

there are two separate formulae provided

IR = Active Return / Active Risk

IR Approx = IC * SQRT(BREADTH)

now you need to decide which to use and when.

But they essentially give the same answer / result?

Depends on the available data, or is there some other point that dictates their use?

I would use the 2nd formulae which CPK has written, for a very large portfolio which is actually mimicking a benchmark.

And I would use the first formulae if there is no mention of indexes or mimicking the indexing anywhere in the question…

Dont know whether this is the correct approach, but these formulae appear in curriculum as I mentioned…

As you can see in Q10B reading 27 book4,

stock based start from index port and over or under weights individual stocks -> high breadth.

derivative based use derivative (futures, opt…) to expose to the benchmark and use fixed income to generate alpha -> low breadth

if we assume no diff in IC, --> IR of stock based is higher.

Thank all you guys for nice explanation. I got it.

The 2nd formula is known as Fundamental Law of active management. However, the breadth is not very well-defined.

It has been discussed as number of independent investment decisions not just the size of research universe.

I would imagine that a typical derivative based trategy use much less FI instruments to generate alpha than the number of stocks tilting required in a stock-based strategy. At least, that’s what CFA is saying.

But how the dependent/independent distinction comes into play here?

It has also been shown that the original Grinold IR formula tends to overestimate the realised IR and thus has to be adjusted downward.