This morning the European Central Bank published a research paper titled "Profit distribution and loss coverage rules for central banks."
The paper dryly outlines how central banks account for profits and losses, and how those profits and losses are distributed to the shareholders of those central banks—usually the state in which they are based.
The paper is useful though, for one very important point it makes. As the ECB engages on its expanded €80 billion per month asset purchase program, questions will arise over what would happen should the central bank make a loss on those purchases.
In talking about profitability of a central bank the ECB says in its paper that it is not necessary for a central bank to make money, as this is not a useful measure of the efficacy of the bank. While noting that profitability may be useful for a central bank's credibility, the paper makes the critical point that losses made by a central bank do not lead to the bank needing to be recapitalized, or the bank becoming insolvent.
The ECB makes this point in a footnote on page 10:
"Central banks are protected from insolvency due to their ability to create money and can therefore operate with negative equity."
Central banks cannot run out of money because they are the ones that create the money. And you cannot run out of something you can create yourself.
While it is unlikely that this paper will forever extinguish confusion over central bank capital, it does at least include a handy cut-out-and-keep footnote to be used whenever someone warns about the risks of a central bank making a loss.