1. There is not much in the way of market pressure in the "Great Moderation" banking system (weak regulation, deposit guarantees) to drive out risky banks - they are a net gain for investors (ignoring the agency effect of bankers screwing their shareholders through bonuses), since bank failures represent a form of subsidy to the financial system. Some shareholders get some of the stock wiped out, but it is all limited liability; others profit magnificently.
2. The libertarian banking system that we saw in C19th (little regulation, no systematic deposit guarantees) does seem to have the right market pressure, but it seems to be yet more unstable since we saw it face regular bank runs followed by grand-scale financial collapse - the 19th century was more economically unstable than the 20th century for this reason, with the UK (then dominant in finance) having 5 major financial crises; one of which (the 1873 panic) led to a depression lasting 2 years longer than the Great Depression. So your frequency's "low enough levels" seems to be around every 20 to 25 years.
3. So deposit guarantees of institutions in exchange for effective regulation that avoids the dangerous effects of excessive leverage, so outlawing your risky bank, seems to be the way forward. Unfortunately it is in the interests of these financial institutions to subvert regulation, so designing such regulation is hard ("who could have forseen that the banks accounts could have mispriced risky assets and moved gigantic liabilities off balance sheet yet again?")
This isn't really a Black Swan issue, it's an agency issue where neither depositors nor regulators understand what banks are doing. But Black Swans do tend to crowd around important, hard to figure out areas of endeavour.
1. There is not much in the way of market pressure in the "Great Moderation" banking system (weak regulation, deposit guarantees) to drive out risky banks - they are a net gain for investors (ignoring the agency effect of bankers screwing their shareholders through bonuses), since bank failures represent a form of subsidy to the financial system. Some shareholders get some of the stock wiped out, but it is all limited liability; others profit magnificently.
2. The libertarian banking system that we saw in C19th (little regulation, no systematic deposit guarantees) does seem to have the right market pressure, but it seems to be yet more unstable since we saw it face regular bank runs followed by grand-scale financial collapse - the 19th century was more economically unstable than the 20th century for this reason, with the UK (then dominant in finance) having 5 major financial crises; one of which (the 1873 panic) led to a depression lasting 2 years longer than the Great Depression. So your frequency's "low enough levels" seems to be around every 20 to 25 years.
3. So deposit guarantees of institutions in exchange for effective regulation that avoids the dangerous effects of excessive leverage, so outlawing your risky bank, seems to be the way forward. Unfortunately it is in the interests of these financial institutions to subvert regulation, so designing such regulation is hard ("who could have forseen that the banks accounts could have mispriced risky assets and moved gigantic liabilities off balance sheet yet again?")
This isn't really a Black Swan issue, it's an agency issue where neither depositors nor regulators understand what banks are doing. But Black Swans do tend to crowd around important, hard to figure out areas of endeavour.