Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: "Liquidity" vs "solvency" in bank runs (and some notes on Silicon Valley Bank), published by rossry on March 12, 2023 on LessWrong.
Epistemic status: Reference post, then some evidenced speculation about emerging current events (as of 2023-03-12).
A "liquidity" crisis
There's one kind of "bank run" where the story, in stylized terms, starts like this:
A bank opens up and offers 4%/ann interest on customer deposits.
100 people each deposit $75 to the bank.
The bank uses $7,500 to buy government debt that will pay back $10,000 in five years (let's call this "$10,000-par of Treasury notes", and call that a 5%/ann interest rate for simplicity). We're going to assume for this entire post that government debt never defaults and everyone knows that and assumes it never defaults.
The thing you hope will happen is for every depositor to leave their money for five years, at which point you'll repay them $95 each and keep $500—which is needed to run the bank.
Instead, the next week, one customer withdraws their deposit; the bank sells $100-par of T-notes for $75, and gives them $75 back. No problem.
A second customer withdraws their deposit; oops, the best price the bank can get for $100-par of T-notes, right now after it just sold a bit, is $74. Problem.
But next week, let's say, it would be possible to sell another $100-par for $75 again.
At this point, the simplified bank is stuck. If it sells ~$101-par of T-notes to return the $75 deposit, it won't have enough to pay everyone else back, even if the withdrawals stop here! But if it doesn't give the depositor back $75 right now, then bad things will start to happen.
Equity capital: A liquidity solution
So, we fix this problem by going back in time and starting with an extra step that's now required by law:
Before taking $7,500 of deposits, the bank has to raise 10% of that—so, $750—of what we'll call "equity capital". Equity capital will get used to fill the gap between asset sales and returned deposits
Now, the final step of the original story goes differently:
$1 of equity capital, plus the $74 from the T-notes sale, go to repaying the withdrawn deposit.
Now the bank has 98$75 of deposits, and $749 of equity capital. If nothing happens until next week (when the T-note price will go back to $75), everything will be fine. (In fact, the bank now has 10.19% of deposits in equity capital, making it safer then before.)
A third customer withdrawal forces the bank to sell another $100-par of T-notes at $73, and use $2 of equity capital to repay the deposit. Now the bank has $747 of equity capital, 97$75 of deposits, and a equity-to-deposits ratio of 10.27%.
A fourth customer withdrawal forces the bank to sell another $100-par of T-notes at $72, and use $3 of equity capital to repay the deposit. Now the bank has $744 of equity capital, 96$75 of deposits, and a equity ratio of 10.33%. Even as the withdrawals force the bank to sell T-notes for greater and greater losses (relative to the $75 that the price will go back to next week), the equity ratio stays above 10%.
Until...
The fourteenth customer withdrawal forces the bank to sell another $100-par of T-notes at $62, and use $13 of equity capital to repay the deposit. Now the bank has $659 of equity capital, 86$75 of deposits, and a equity ratio of 10.22%.
The fifteenth customer withdrawal forces the bank to sell another $100-par of T-notes at $61, and use $14 of equity capital to repay the deposit. Now the bank has $645 of equity capital, 85$75 of deposits, and a equity ratio of 10.12%.
The sixteenth customer withdrawal forces the bank to sell another $100-par of T-notes at $60, and use $15 of equity capital to repay the deposit. Now the bank has $630 of equity capital, 84$75 of deposits, and a equity ratio of 10.0%.
...and here is where the oops happens. Still, we're much better th...