# tracking error Q

“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.” T/F?

are there any managers weights in portfolio also given?

T if others kept unchange

false

active risk is not correlated among active managers

“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.”

Overall active risk would remain same. F

Quick calc to prove:

active risk is a standard deviation so:

Mgr 1 Risk = 2%

Mgr 2 Risk = 1.5%

50/50 weight

so

[.5^2*.02^2+.5^2*.015^2]^1/2 = 1.25%

You can take out Manager 1 and risk actually increases becuase active risk is uncorrellated.

True I guess

false

T .

If active returns are un-correlated then total tracking risk is nothing but the root mean squared weighted tracking risk of all managers. If any component of the RMS weighted values is reduced , the value itself reduces. If there are correlations present then this is not straightforward.

you reduce active risk for one manager - you are also going to reduce the active return overall.

and as a result the active risk movement direction would not be known clearly.

I think it is FALSE.

Your updated equation would be [.5^2*.00^2+.5^2*.015^2]^1/2 = [.5^2*.015^2]^1/2 = .75% so the active management did decrease.

We’re not talking of IR here . We’re not saying IR goes up or IR goes down .

We’re only talking about tracking risk .

Pl read tulkuu’s q carefully:

“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.”

So how does reducing active return even matter ?

how is active risk calculated?

It is std. deviation of active returns, isn’t it?

if active return goes down … active risk WILL ALSO be affected.

But the direction is not clearly known.

Fin , truong and serious are correct .

The ans. is True.

The q does not talk about active return , but the only way one can reduce tracking risk is by cutting active return . In any case that will reduce the overall portfolio tracking risk.

I can’t think of any scenario where the “highest tracking risk manager” even matters .

All that is important is that the weights ( allocations ) are unchanged and the active returns are un-correlated.

False. “The individual manager’s risk can be offset by other individual managers’ portfolio risk. Forcing an individual manager to minimize tracking error or mimic the benchmark could in fact raise plan-wide active risk.” === tracking error is relative to manager’s normal benchmark, I think.

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.

Both arguments make sense, but it seems that “very likely” makes the call.

So the question was about “true” active risk and not total active risk?

Is Tracking error = “True” acive risk = std dev of portfolio returns-normal benchmark?

Yes, I think the “active risk” in the question is total active risk(for the manager and for the plan-wide), and the “tracking error” is the true active risk for the manager.

Correct me if I’m wrong.