Management Fee & Active Risk

Could anyone explain why management fees does not affect active risk(tracking error)? I am unable to understand?

What’s the definition of tracking error?

Sd of active return.

And the definition of active return?

Active return is portfolio return - benchmark return

And what’s the active return net of management fees? (In a formula, such as you have, above.)

Return for the investor

But what’s the formula (like the formula for active risk that you gave, above)?

Return of investor/sd(return of investor)

OK, things are getting weird now.

You said that the formula for active return is portfolio return - benchmark return

That’s the formula for active return before management fees.

So, what’s the formula for active return after management fees. (It will look very similar to that one.)

Portfolio return-benchmark return- management fee

There we go.

And management fees are considered a constant percentage of (beginning) asset value.

So, tracking error before management fees is:

tracking\ error_{gross\ of\ fees} = \sigma\left(portfolio\ return_i - benchmark\ return_i\right)

and tracking error after management fees is:

tracking\ error_{net\ of\ fees} = \sigma\left(portfolio\ return_i - benchmark\ return_i - c\right)

where c is the (constant) management fee.

So the question is: if you compute the standard deviation of a set of numbers, then compute the standard deviation of a new set of numbers which are the old numbers minus a constant, how do those standard deviations compare to each other?


VoilĂ !

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Just a follow up question does performance fee also have same effect on TE?

If it’s a constant percentage, yes.

If not (e.g., you pay a performance fee only above a given hurdle rate), then no: it will change the tracking error.

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My pleasure.