Management Fee & Active Risk

CFA Level III
#1

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

#2

What’s the definition of tracking error?

#3

Sd of active return.

#4

And the definition of active return?

#5

Active return is portfolio return - benchmark return

#6

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

#7

Return for the investor

#8

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

#9

Return of investor/sd(return of investor)

#10

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.)

#11

Portfolio return-benchmark return- management fee

#12

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?

#13

Same.

#14

VoilĂ !

1 Like
#15

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

#16

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.

1 Like
#17

Thanks

#18

My pleasure.