# Tracking Error

The 2005 exams Qu1 asks whether the following statement is correct or incorrect: If we reduce tracking error of the manager with the highest active risk, this is likely to reduce the plan-wide active risk of the overall portfolio. Answer- Incorrect Reason: The individual manager’s risk can be offset by other by other individuals managers’ portfolio risk. Forcing an individual manager to mininize tracking error or mimic the benchmark could in fact raise plan-wide active risk. I am clear on the first part of the answer but the second part begining with forcing has me confused. I would have thought that any attempt to minimize tracking risk would be a good thing. Can someone please explain the rationale behind the second part.

I think we have to read both statements together. what I feel is that we should try to reduce the plan-wide active risk (by considering at the plan level when multiple portfolio mgrs are assigned) than to force an individual manager to mininize tracking error or mimic the benchmark could in fact raise plan-wide active. If the plan is entirely managed by one PF manager, then we can force him to reduce the tracking error.

although the assumption is the correlations between the equity manager’s active returns are uncorrelated and therefore: portfolio active risk = SQRT {SUMMATION [(w^2)(active risk^2)] } so i’d argue that reducing the active risk of one portfolio would in fact reduce plan-wide active risk (all other things remain constant if correlations are zero)

Let’s consider that your active portfolio consists of two managers: one is long-only, the other one is short only. Allocation to them is done in such a way that directional exposures get offset pretty well. Then if exposure of one manager is reduced, overall risk can increase.

maratikus Wrote: ------------------------------------------------------- > Let’s consider that your active portfolio consists > of two managers: one is long-only, the other one > is short only. Allocation to them is done in such > a way that directional exposures get offset pretty > well. Then if exposure of one manager is reduced, > overall risk can increase. but the question does not say the “exposure” (i.e. % total portfolio) is reduced, it states that one of those porfolio managers reduces their active risk.

Char-Lee Wrote: > but the question does not say the “exposure” (i.e. > % total portfolio) is reduced, it states that one > of those porfolio managers reduces their active > risk. it’s a matter of semantics. I took that to extreme considering managers were full blown active managers. What I talked about can be generalized to index + long-only for one manager and index + short only for another manager. Then active risk exposure consists of combination of long-only positions of manager one and short-only positions of manager 2 (and we can assume those active exposures can offset each relatively well). As manager one is forced to reduce the size of his long-only positions (while keeping the exposure to the index), he can’t offset as much of short-only positions of manager 2 and, thus, active risk can go up.

My two cents. The assumption is that tracking risk is always positive (i.e. alpha will always be positive for a fund). We know that is not the case. If you account for the same, simply by reducing the tracking error of the one portfolio may/may not reduce the tracking error for the combined position.