2033 dollars lost a lot of value due to interest rate increases. Higher interest rates means that 2023 dollars would convert to more 2033 dollars, so now if you want to sell 2033 dollars for 2023 dollars you would get less back.

If the interest rates weren't increased they would just have sold their 2033 dollars and everything would be fine, a bank doesn't go under just because it takes a while to get billions of dollars, the whole issue is that they ran out of assets due to their assets having lost value.

That might be true, but it's got me thinking. Suppose you owe $100M and had $80M of cash. That would be considered both involvent and illiquid, correct? Now suppose you go out and buy $80M worth of 10 year treasuries with the cash you have. At current rates you will have $115M in 10 years, plenty of money to pay of your liabilities of $100M. Does that mean that if you're "insolvent" you can magically make yourself "solvent" by buying a bunch of bonds?

No, because you need to value the bonds at their current market value, which would presumably be 80 MM. The fact that you believe an asset will get you a certain amount of money doesn’t mean it’s worth that now.

If the debt is due in ten years, it won't be worth $100m, and you can presumably just pay it off with the cash.

They are, and this is a full-on solvency issue, not just a liquidity one. Think of it this way: suppose you have an investment that pays out $100 in 2031, plus a low rate of interest that due to interest rates increasing substantially in 2022 is now below what you can get from savings accounts or ultra-safe investments like Treasury bonds. That investment may have been worth $100 in 2021, but it's worth substantially less in 2023 because someone with $100 in 2023 could put it into those higher-interest investments and end up with a lot more money by 2031. However, banking regulations allow banks to not immediately recognize that drop in the value of their reserves by claiming they'd hold the investments to maturity.

In that context no it’s the same thing. It’s profitability and balanced books (liabilities matching assets) that are different. A business can be profitable and insolvent if cash flow temporarily dries (e.g. you can’t hold employee salaries because customers take too long to pay invoices). A viable business needs both profitability (long term) and cash flow/solvability (short term).

Unmatched assets and liabilities (like FTX) is not insolvency, it’s fraud, and mechanically causes insolvency when the cash is gone after the run.