An important issue with the SVB bank failure was the run on the bank with billions flowing out before the government took control. All depositors are likely to pull money if there is the expectation of a failure, but the probability increases if the deposits are above the $250,000 threshold which is protected with deposit insurance. You may still have restrictions on when the money will be available, but the threat of loss is less.
The real worry is that those depositors above $250,000 will pull their money. Large depositors will create a run on the bank through their actions because there is a greater risk that they will not get their money back. Hence, there is an incentive for these depositors to leave early.
Large deposits are hot money, so banks that have a higher percentage of their deposits base in uninsured accounts are more likely to see a run on the bank. Their "hotness" exists even if there was no risk of a bank failure because that money should be more sensitive to rate changes. If Treasuries yield more than deposit rates, the money will flow toward Treasuries. The decline in SVB deposits started before the bank risk increased.
The table below shows deposits less than $250,000 as a percentage of total deposits. Those institutions with low numbers are more likely to face bank run risk. We should expect that those banks have a higher equity premium.
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