You only need an emergency fund if you do not have access to credit at reasonable terms. Investments you don't touch outside of emergencies coupled with open lines of credit should outperform excessive "emergency" savings. After all, lines of credit are typically free when you don't use or need them, while not getting the best rate of return on your savings isn't.

EDIT: I was reminded of a relevant saying: If you’ve never missed a flight, you’re spending too much time in airports.. Similarly, if you never have to borrow money for emergencies, your investments are too liquid.