A CEO will run investments for you so you don't have to click them anymore. The CEO does have some idle time between ticks. The time CEOs are idle/inactive depends on the level of the CEO.
On the Game Help page in the CEO paragraph it says the following: however the CEO will never be perfect, so you can still manually click on properties to make them run faster, This is true, however on certain levels you won't notice it anymore because of the speed increases you will gain through achievements.
The formula used for the CEO idle time is Investment-Time / CEO level. Lets say a Gas royalties without achievements for speed increase takes 2 seconds to complete. If your CEO is level 1 this means the property will run, then it waits 2 seconds and it will run again.
A few examples for the first 10 levels of the CEO.
In the examples the investments have no speedbonus.
I don't have the proof for it yet but I'm pretty sure that the idle time is based on the investment time after speedbonusses and not base time.
While I was writing this I wasn't sure but finding out that a level 16 Saudi Field CEO should have an idle time of 2.5 minutes I can say for sure that my CEO isn't idle that long.