What have banks mostly done with their "excess reserves" obtained during QE

Question

I put excess reserves in quotes because I know that in many countries there are no reserve requirements, so what I really mean by "excess reserves" is reserves in excess of what banks like to maintain for the purposes of making settlements between each other (is there a special name for this kind of excess?). My hunch is that they have used them to buy bonds or shares from non banks, creating new demand deposits in the process. Or have they mostly left those reserves in their accounts at the central bank?

EDIT: I know that reserves can not be used directly by a bank to purchase something from a non-bank. But reserves enable these purchases because they may be needed in settlement of the purchase.

EDIT: Given the nature of the answers so far, perhaps it may clarify this question if I give some hypothetical answers...

1. The banks could have said to themselves "Perhaps, before 2008, we had underestimated how much reserves were really needed, the new reserves from QE were actually required after all and not 'excess' in any way. Let's just leave them in place and collect the interest on them that the fed pays"
2. Having these new excess reserves allow us to purchase more bonds and/or shares from non banks. Let's buy some.
3. Having these new excess reserves allow us to make more loans than before, so let's increase our lending.

Given that there was so much uncertainty about what the effects of QE would be when it started I have no doubt whatsoever that research will have been done into exactly how banks employed the extra reserves.

Answer 1

If banks would do something with excess reserves they would cease to be excess reserves. Excess reserves at central bank are safety buffer. When banks want to reduce their excess reserves they get cash. They can't be directly used to purchase something.

Answer 2

There are a lot of common misunderstandings around this subject. The act of QE by a central bank injects funds into the economy (specifically, the previous owners of government bonds now own cash). There are only a couple of things that can happen to this cash - it can be deposited in a bank, thus contributing to a bank's excess reserves; or , it can be invested in the Fed's reverse repo facility (or equivalent facility of other CBs). If it goes into bank excess reserves, these reserves are deposited at the Fed. Note that if an individual bank decides instead to loan the money out,or indeed buy bonds from non banks for example, it just ends up in another bank so it doesn't change the overall picture for the banking system as a whole. So the question of what banks have done with the excess reserves really doesn't mean anything. By definition all excess reserves end up back at the Fed. The question could make sense for an individual bank, and one can see some variations - some banks have preferred to buy assets, and some others have been happy to have large cash balances.