Active Risk Squared

CFA Level II
#1

Hi,

Active Return = Rp-Rbm = Factor Return + Security Selection return.

Active risk = σ(Rp-Rbm) = Tracking error

  • The active risk of a portfolio can be separated into two components: Active Factor Risk + Active Specific Risk

Then Schweser says that Active Risk Squared = Active Factor Risk + Active Specific Risk?

First we say that Active Risk consists of Active Factor Risk and Active Specific Risk. Then it goes on to saying that Active Risk Squared = Active Factor Risk + Active Specific Risk

I do not understand why it all of a sudden says it is “Squared”?

#2

Variances are additive, standard deviations not.

#3

The confusing and annoying part here is that active specific risk and active factor risk are actually variances whereas we use standard deviation for active risk. If you look at the formula for active specific risk you can easily see this and there is also a remark in the cfai books regarding this.

Thus, “consists” seems to mean “is somehow reflecting / including” but not that you can add them simply up (without squaring first).