It've very very minimal what they do. The overall performance of the executive is determined by his selection of right hand men. The executives main skill is managing the board and selecting the right people to do things for them.
The executive is not talented at creating, building or running a company. His main talent is selecting the people who do it for him. Also honestly, all this "value setting" stuff is trivial. Ultimately the people underneath him adapt to what works regardless of values.