Optimal amount of active risk for a constrained portfolio

CFA Level II Portfolio Management
#1

For a constrained portfolio, the formula for the optimal amount of active risk is:

oa = TC x IR* / SR x st dev benchmark , where IR* = IR of an otherwise unconstrained portfolio

Do we agree this is the exact same formula than that of the unconstrained portfolio, i.e. oa = IR / SR x st dev benchmark? (where IR is the IR for the constrained portolio … > IR = IC = BR^0.5 x TC )

I’m asking cause in Schweser Qbank (question 603887 for example), they keep calculating the optimal amount of active risk using (i) the first formula with TC, and (ii) IR instead of IR*. I guess that’s wrong since they take TC twice into account, am I correct?

#2

Its the exact same formula. The TC for an unconstrained portfolio is 1. That should help clear this up.

If you always use/only memorize this formula oa = TC x IR* / SR x st dev benchmark and just know that the TC for an unconstrained portfolio is 1 you should be fine.

#3

So Schweser is wrong… Thanks

#4

I thought the above confirms the two formulae are identical, why do you conclude otherwise?

If TC=1 you can ignore it and IR* simply means optimal IR. It is just a matter of notation, isn’t it? The subject matter is the same.

#5

exactly…

IR* just means the IR for the “optimal” active fund which is assumed to be unconstrained under the Basic Fundamental Law. That’s the only difference.

There is only need to memorize the Full Fundamental Law formulae - the formulas that include TC. The formulas for basic fundamental law are the same except that TC is assumed to be 1.