No, SVB was solvent as long as their assets didn’t have to marked to market, once there was a bank run they became insolvent. If the SVB assets are liquidated they will not cover the deposits.
Same with their mortgage-backed securities.
Ish. On a mark-to-market basis they had insufficient reserves. That's closer to insolvency than illiquidity. The mismanaged duration is closer to illiquidity. But not of the sort a lender of last resort could save them from.
Hold-to-maturity assets are not required to mark to market, for example.
And it's not based on what they paid for it from what I gather, it's based on what the total payout will be when it matures.
Imagine a bank takes demand deposits and pays a variable rate of the base rate minus 1%. The bank then makes fixed rate, 30 year mortgage loans that it intends to service itself at the base rate plus 2% (portfolio loans).
Interest rates then go up.
Bang: that bank just became insolvent. Is this actually the model of the world you want?
I'm not sure what the problem is, this model to me actually seems reasonable. The alternative is to claim that "We are solvent as long as our clients keep deposits in our bank and are happy with an interest rate lower than our competitors for 30 years".
In fact the scenario you're describing is basically what happened to SVB except the interest rates increased more.
I guess the main issue is that generally banks do take a risk by borrowing short and lending long, and hope that things work out in the end.
This is irrelevant in a scenario where every client wants to withdraw their money, because the only way SVB can fulfill that is by selling their HTM assets at the current market price, which will be at a heft discount compared to where they bought them.