tracking error Q

CFA Level III
#21

Fin said :

“If you reduce those active returns, your active risk would actually increase.”

Question says active risk is decreased for the highest active risk manager . You’re saying active return is reduced for the manager . q does not say active return is reduced for the manager ( as in “active return is now more negative than before” ) .

If active return was more negative than before , active risk for the manager would increase , but that is not what it says . It says active risk is deliberately reduced . That means if active return was negative it is now less negative , or is active return was positive it is now less positive . In any case the mean of squared active return is less than before.

Let’s not confuse by talking about active return when it only talks about active risk.

#22

I think you are correct, and that is what I was tying to say - but I stopped short with just referring to the manager’s true active risk.

So the statement that should be kept in mind for this question is:

By reducing the manager’s “true” active risk, the Total active risk of the portfolio of managers does NOT necessarily reduce.

#23

Jana - I was actually replying to CPK’s thread. I should have been more specific.

If you execute a benchmark + 2% strategy with perfect precision your active return will be 2% but the variability of those returns are 0. If you reduce those active returns, your active risk would actually increase.

#24

I guess this just got more complex for me. “if we reduce” is the big problem. Are we forcing it to reduce or is it happening by itself. For all those who say that reducing active risk will lead to reduction in active return is not making sense. Active risk is the variablity of active return. What if the manager consistently earns the same alpha. As in there is a good active return but if the alpha is either positive or negative and constant, the active risk can be 0 as well though this is unlikely to happen. So If we reduce one manager’s active risk with no change in other manager’s active risks, isn’t the overall variability likely to be lower than before.

#25

What if the benchmark were the broad market index ( i.e. investor benchmark=active manager benchmark ) ? Would your answer be the same?

If it was different , either you should qualify the answer or say the question is not correct because it could be different because the benchmark for style is not specified.