to prove themselves by showing their returns.
The main topic is how to prove (explain) their return.
One of them might be Buffet's written statement, as in http://www.berkshirehathaway.com/letters/2015ltr.pdf
What is other way to prove his/her equity curve?
One might be saying "Over the last 10 years, my curve is ALWAYS between 10% and 20%, over the index change." - This is 15% in average. / However this is a lot better than saying "ALWAYS between 5% and 25%" / Of course everything is annual compounded return.