Don't judge a hedge fund by its pamphlet

Portfolio managers have an interest in sounding as impressive as possible when advertising their services. They often charge high fixed rates, and so, need to justify their fees. The numbers that matter for the customer are real returns, but managers are free to instead report their average annual return.

One measure of real returns is the compound annual return, found (in the example of a 10 year investment) by solving for the effective annual return $r_e$ for which $\displaystyle (1+r_e)^{10} = S_{10}/S_0$ .

If a fund manager wants to sound more capable than they really are, would they advertise their average annual return, or their compound annual return?