Optimal Amount of Active Risk

CFA Level II Portfolio Management
#1

For some reason I cannot wrap my head around the below formula (find the optimal amount of active risk). It just doesn’t make any intuitive sense to me.

StDev*(Ra) = IR/SR(b) * StDev(b)

ll the other formulas in the curriculum so far I have had no issue coming up with a logical explanation for, but I cannot for this one. How is the optimal amount of active risk an investor should take related to the ratio of the information ratio (excess return per unit of active risk) to sharpe ratio (excess return per unit of benchmark total risk) and then multiplied by the st. dev. of the benchmark? Just doesn’t have intuitive appeal to me. Maybe I am just getting too bogged down with this and should just memorize and leave it at that?

#2

same for me

#3

At risk of looking stupid for posting an answer to my own question I will since someone else had the same question. I have to credit the folks at Kaplan for the answer.

The intuition behind the formula is that the higher the information ratio (i.e. the more active return per unit of active risk) the more active risk the investor will take (i.e. the more you will be putting in the active portfolio vs. the benchmark portfolio).

This chapter is giving me fits and just seems like it is coming from Mars…