# Management Fee & Active Risk

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

Whatâ€™s the definition of tracking error?

Sd of active return.

And the definition of active return?

Active return is portfolio return - benchmark return

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

Return for the investor

But whatâ€™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

Thatâ€™s the formula for active return before management fees.

So, whatâ€™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?

Same.

VoilĂ !

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

If itâ€™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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Thanks

My pleasure.