Edit: I realize now that I forgot to specify that I meant a single $101 loan in my original comment.
No. This is the fundamental misconception alluded to earlier. A bank with $100 of assets and $100 of liabilities can made a $50 loan and wind up with $150 of assets and $150 of liabilities. Deposits are a bank's liability. Every fractional-reserve bank is insolvent in the short run. (This is inherent to leverage.)
More realistic: a 10% reserve requirement. Bank has $100 of assets, of which $10 are reserves, and $98 of liabilities. ($2 equity.) Customer wants to borrow $20. Can the bank make the loan? The answer is yes. It winds up with $120 of assets including $10 of reserves, a deficiency. So it borrows $2 in the interbank markets and winds up with $12 of reserves against $120 of assets. Note that the liability side doesn't even come into play: that's a capital-requirement question, where defining what counts as an asset to what degree is a tomes-thick discussion [1].
That's why we have reserve and capital requirements. Leveraged banking doesn't work without supervision. Because can’t and shouldn’t aren’t naturally enforced.
1: https://www.federalreserve.gov/monetarypolicy/reservereq.htm
- The reserve ratio. This is the amount of reservable (read deposited) cash that is required to be held by the bank in cash equivalents compared to the amount of deposits on their books. This is typically (for instance in the US) a regulatory capital requirement of a central bank to its member commercial banks. But note its only a second order limit on what the bank can loan out as the loans (or investments, or CDS' or bitcoin) on the books are not part of the equation. What this _really_ does is increase the cost of capital of deposits, making them more expensive for the banks to use for other activity. Prior to the pandemic many types of reservable deposits already had 0% ratios and the headline amount was 3%. This is the _least_ important limit on bank balance sheets for loans.
- Another is the regulatory asset:liability capital controls. Banks can be subject to many different regulators, and they all have a variety of balance sheet rules (and those rules encompass many other things like risk processes and other operations) but always banks must keep more assets on the books than liabilities. But! Thats not a stop to lending, because loans are assets, instead thats to ensure depositors are made whole. The stop to lending is the actual balance of assets is also regulated. Those balance of assets are scored both against market risk and credit risk. Too many loans on the books without enough cash will blow those limits up and get them in trouble with their regulators.
- The loan to deposit ratio. This is explicitly what it sounds like, the amount of money loaned compared to the amount of money deposited. In the US this is not actually part of any regulatory regime limiting the amount a bank can loan*. Instead it is a market based limit that the owners (investors/shareholders) of the bank keep track of to understand how liquid the bank is and how safe the bank is as an investment. This is important because depositors have senior claims in the case a bank goes belly up. Currently, investors look for a .8 loan to deposit ratio. During the pandemic the industry was sitting at around .6, which is one of the reasons the Fed removed the reserve requirement. They wanted banks to put more deposits to use in lending so they made it cheaper to do. Banks with high loan to debt ratios very frequently go out of business so have extremely expensive fund raising costs, therefore its something they take pretty seriously.
If you are curious what the lending amounts look like in practice, the last number is probably the easiest to understand and get access to. As I said, the industry sits well below 1:1 on loans to deposits. You can find some that approach 6 to 1 or even sometimes higher but those are typically distressed banks. The central bank reserve requirement is much more lenient than that and always has been.
* Loan to deposit ratios are a part of some regulations about bank size, but only as benchmarks.
See my above example for why capital ratios, which consider asset quality and liabilities, are superior to reserve requirements.
"Transfer" loses its colloquial meaning at this level of banking granularity.
Interbank transfers involve two components: a message and settlement. If our aforementioned bank's customer "transfers" their $20 to another bank, the message would go across SWIFT or CHIPS or whatever, and then the sender's bank would credit the recipient bank's account at the sender's bank. (The intrabank case is trivial.)
If the customer asks for their $20 in cash or to be transferred via Fedwire, on the other hand, the latter being both a messaging and settlement system, run risk emerges. The bank needs to borrow against or sell assets to generate liquidity. (The Fed extends daylight overdraft protection [1], but that's a specific case of its lender-of-last-resort duty.)
But the bank becomes insolvent only when it is forced to fire sell assets or recognize their dubious value. Not when it extends the loan. Nor even when the customer demands their cash. At both those times, the balance sheet balances. It's just exorbitantly levered.
None of this says a bank should do this. Just that it can. In a system where deposits are loaned out, this cannot happen. In our system, where loans create deposits, it can. The former is the toy model we teach in school.
[1] https://www.investopedia.com/terms/d/daylight-overdraft.asp
In the long term... any bank that is careful not to have too many insolvent loans is guaranteed an inflow of money from the capital and interest repayments - some of which will be on their books, and some will be coming from money deposited at other banks, effectively transferring the asset cash back.
It's actually quite an elegant system at this level. Horribly fragile with respect to losses on loans though.