Bank capital is funding which often can't be lent out

Time and again, various academic publications explain to us that bank capital is actually cash funding, and therefore raising capital to meet higher requirements does not constrain lending, in fact it helps banks lend more.

The underlying accusation, barely disguised behind a cynical tone, is that bankers do not understand capital is funding. I am afraid the issue is more that many non-bankers do not seem to realise that raising capital requirements and raising capital are not the same thing, but opposing factors which often cancel each other out. I will demonstrate that with a simple example below.

Let's start with a bank which has 100 in loans, and a capital requirement of 10%. So its liabilities are 10 in capital and 90 in client balances. Now the authorities raise capital requirements to 15%. Suppose the bank goes out and raises that extra 5 in capital. Now its liabilities are 90 client balances, and 15 in capital. And its assets are 100 in loans and 5 in cash. Can it now go and lend the extra 5? No, it can't. Because the 100 in existing loans requires exactly the 15 capital it has. If it lends the 5, that means another 15% or 0.75 in capital is required. So the bank faces a choice of either leaving the cash in the central bank or shortdated government bonds at negative interest, or (economically the better option) reduce client balances. (Note that if the bank is leverage constrained, even holding cash or govvies is impossible, and since most serious banks apply the higher of regulatory capital or their own capital calculation, government bonds are often not an option either way)
Neither course of action leads to the new lending that is supposed to be possible.

The conclusion is that capital raised because of increasing capital requirements is funding which can't be used for more lending.

As always, when confronted with facts, people with an opinion get irritated. The heated statements about banks needing more capital have nothing to do with this: that is either true or not, but in neither case does the outcome lead to more lending. By the same token, explaining that investors have it all wrong when they look for 10% ROE's is nice as an opinion, but a company raising money pays that market price, whether politician and journalists like it or not.

I can't help but find it frustrating that taxpayers fund professors to think about complex matters and help us get the right answers, yet they often fail to properly think even about simple matters like this one and then come up with incomplete, misleading or simply wrong answers.