Plenty of studies show there may be no correlation between CEO pay and their performance! Have a look through the results of: https://www.google.com/search?q=ceo+pay+correlation

Another example was the guy that built a successful baseball team from low paid players (what was the book called?) which showed low pay did not mean low performance in a discipline where outcomes could be measured (much easier than CEO, so you would expect better correlation of pay with performance for sports).

Edit: Moneyball (baseball is as foreign to me as rugby is to Americans?).