Fundamental Law of active management

CFA Level II Portfolio Management
#1

What’s the difference between these two formulas and which one to use in what situation??

IR = IC x (BR)^1/2

IR = TC x IC x (BR)^1/2

thanks.

#2

First one is for an unconstrained portfolio and the second one is for a constrained portfolio.

#3

Gigaloo correctly answered. In the first equation you may also put (TC) if is easier to remember but also remember that for unconstrained portfolio TC is always 1 while for constrained portfolio is always less than 1.

#4

What kind of constraints are we talking about?

Is TC>1? In othe words an uncostrained portfolio has a bigger or smaller IR compared to a constrained portfolio?

#5

I did not find that TC may be > 1 if unconstrained portfolio TC is 1.

#6

We know that a high IR is a measure of good manager performance. If we regard constraints as “problems” for the manager and the fact that

Uncontrained IR= IC x (BR)^1/2

Constrained IR = TC x IC x (BR)^1/2

I can make following conclusions:

  1. Unconstrained portolios should produce higher IR

  2. Constrained portfolios will have a lower IR by a factor of TC, so TC<1

  3. If TC>1 in a given portfolio the manager is a sucka.

#7

I don’t get this. Is larger TC better or worse?

#8

Now I remembered…

TC is a correlation coefficient. As such it can’t be greater that 1…

#9

Transfer coeffecient is basically means if you as a manager have great prediction skills ie high information coefficient are you able to turn that skill into reality by realising higher returns for your portfolio. Constraints mean you are not allowed to short sell or not allowed to invest in particular funds beacuse of which you are not able to realise what you had predicted.So tc=1 no constraints and better for you.

#10

Intuitively I am inclined to believing large TC = good

But considering that IC x BR > TC x IC x BR (i.e. TC is smaller than 1 I believe the following is also true:

If TC is closer to zero, the constrained IR is also close to zero, which means, as far as the portfolio manager is concerned, the gap between constrained and unconstrained portfolios is larger. What does this mean? Give the manager more liberty and he will produce better results. Conclusion? Lower TC is a testament to better managerial skills.

#11

TC is basically how well you can implement your skills at predicting active returns and translating that into active weights given contraints.

If a PM is so constrained to the point where they can’t do anything (as krokodilizm mentioned) the TC would essentially be zero. The original equation without TC is Grinold’s model with the simple assumption that you can implement your predictions freely into bets made within the portfolio.

IC captures how well a PM can predict excess returns.

I would disagree with krokodilizim regarding a lower TC signifying better managerial skills since a lower TC would reduce IR. The ultimate goal is a higher IR as this signifies a greater value added return per unit of risk. The greater the TC the better.

BR is how many independent forecasts a PM has predicted.

#12

Constraints on the active weights.

Suppose that your optimal active weight on equities is +20%. If you’re not allowed (for whatever reason) to have an active weight greater than 10%, then your portfolio is constrained.

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