“Liquidity” vs “solvency” in bank runs
and some notes on Silicon Valley Bank
Originally posted to LessWrong.
epistemic status: Reference post, then some evidenced speculation about emerging current events (as of 2023-03-12 morning).
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. (Normally, government debt pays off a bit every month and then a large amount at the end, but that's just the same thing as having a portfolio of single-payout (or "zero coupon") notes with different sizes and maturity dates, and the single-payout notes are easier to think about, so I'm going to use them here.) 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