According to Tales from the top, a CEO should concentrate on - strategy/vision, customers, finance, and inspiration/corporate culture. CEO has four key result areas in all. To this, Konosuke Matsushita may add supplier/partner relations.
According to Parkinson Law, the No. 1 is to do whatever others cannot and will not do, including switching off lights before leaving office etc.
According to Titan, John D Rockefeller shirked everything. He also advised others to shirk and to concentrate on thinking how to make more money for his Standard Oil.
According to Andrew Carnegie, a CEO like him can run a company like US Steel with about 2 hours every morning. But then, you may later have to hear "Meet You in Hell" from your second-in-command.
Please check out What Only the CEO Can Do in HBR too.
Compiling their wisdom with what I have read from the list in one of my previous posts, I would say that a CEO should concentrate on
- Goals, Strategy, Vision
- Suppliers and partners
- Corporate Culture, Leadership, Inspiration, Inspection
Frankly, what the CEOs do is boring. We all know their KPI (key performance indicators.)
How they carry out those tasks, how they execute is the key.