The CEO's duties are what she actually does , the responsibilies she doesn't delegate. Some things can't be delegated. Fund-raising is necessary, but the CEOs contribution is in building a superb business with the money raised. Setting strategy and vision. The senior management team can help develop strategy.
Investors can approve a business plan.
But the CEO ultimately sets the direction. The CEO decides, sets budgets, forms partnerships, and hires a team to steer the company accordingly. The CEO's second duty is building culture. Work gets done through people, and people are profoundly affected by culture. A lousy place to work can drive away high performers.