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Do banks have to hold enough equity to cover a 100% withdrawal rate?
Yes - all banks not in financial distress will have a surplus of assets over liabilities as well as loan loss allowances, effectively deductions from the asset side of the balance sheet to account for hypothetical future credit losses. A typical ratio of equity to assets is 5-10% depending on how risky the loan book is.
If you take a typical mid-sized bank like OSB (which focuses on specialist property lending), you can see from their annual report (p. 181) that they have £25 bn assets (net of £100 mm allowance for credit losses) versus £23 bn of liabilities, leaving £2 bn of book equity (8% of assets). Approx 30x Tether's capital ratio.
However, versus Tether their asset book is more illiquid - so if the £5 bn of their liabilities that are repayable on demand were to ask for their money at the same time, they would quickly exhaust their £2.7 bn of cash on hand and have to start running down the loan book (or securitising it and pledging it to the BoE as repo collateral).
You can decide which you prefer!
https://www.osb.co.uk/investors/results-reports-presentations
EDIT: to summarise all the above, the point is that in an orderly liquidation of OSB you would expect all the depositors to get their money eventually (like the Lehman creditors did). I would be pretty sure that some depositors would get impaired if Tether were liquidated.
Do banks have to hold enough equity to cover a 100% withdrawal rate?