# Fed fund market after QE

I read that before 2008, reserves of the banking system (vault cash and reserves at the Fed) fluctuated between \$40 billion and \$80 billion. However, as a result of quantitative easing, reserves exceeded \\$2.5 trillion over the next 5 years. With such an increase in the magnitude of the reserves, one would think that every bank has excess reserves nowadays, so do banks still borrow Fed funds in the overnight market? It seems one would guess no bank is ever short of reserve with that much reserve in the banking system. Does it still happen that a bank's reserve falls short of the required reserve ratio? In addition, why would a bank be willing to hold so much reserves at the Fed? Since the reserves is increased through open market operations, can't a bank simply hold on to government securities instead of agreeing selling them to Fed in exchange for reserves? Is it just because the interest paid on reserves? What if a bank can use that asset to generate a higher return than the low interest rate on reserves? I am hoping to get some clarifications on my confusions.