Investment banking is not just advice. They also finance deals (i.e. come up with a few billion to make it happen) and execute - buy all the outstanding shares,

Investment banking is not just advice. They also finance deals (i.e. come up with a few billion to make it happen) and execute - buy all the outstanding shares, or sell new ones in your IPO. And since those kinds of deals don’t come along every day, they maintain the capability by executing as broker and dealer all the rest of the time. (I know, I’m simplifying a lot. Hope it helps get the idea across)