Reducing tracking error and active risk

[sfad]

Questions asks is this statement correct or incorrect: “if we reduce the tracking error of the manager with the highest active risk, this is very likely to reduce the plan-wide active risk of the overall portfolio”.
Answer says: forcing an individual manager to minimise tracking error or mimic the benchmark could in fact raise plan-wide risk. Can someone please explain how plan wide risk increases if we reduce tracking error for an individual manager?

 

[S2000magician]

It depends on the correlation of that manager’s tracking error with that of the remaining portfolio. If his ups counteract the rest of the portfolio’s downs and vice versa, eliminating his ups and downs increases the tracking error.

 

[gad4]

Assuming nothing else is given , isn’t it stretching it to assume the rest of the profile happens to correlate being off the opposite direction where its given the others have lower tracking risk?

 

[MrSmart]

gad4 wrote:Assuming nothing else is given , isn’t it stretching it to assume the rest of the profile happens to correlate being off the opposite direction where its given the others have lower tracking risk?

It says ‘could’.
Depending on the correlation, and the size of such, lower tracking risk in one could mean higher in all the others (where their weights are larger as well), leading to increased plan-wide active risk.

 

[S2000magician]

gad4 wrote:Assuming nothing else is given , isn’t it stretching it to assume the rest of the profile happens to correlate being off the opposite direction where its given the others have lower tracking risk?

The problem with the question is the word “likely”. Because of that, you have to make a value judgment about the possibilities of different correlations of tracking errors.
I, for one, don’t know which way is stretching it, so I don’t know what’s “likely”. I know what’s possible, and it’s possible that reducing an individual tracking error could decrease the overall tracking error, and it’s possible that reducing an individual tracking error could increase the overall tracking error.