For $100 of assets, and $100 of bank equity, let, say, $10 of that equity be traded — enough to establish a liquid market. Then, let $90 of that equity is held by a downstream entity or entities— a fund, special purpose vehicle, holding company or other money bucket. I’ll call it a holding company, and return to legal structures below. The holding company, in turn, issues $10 of holding company equity and $80 of debt.
The good news is that the bank can never fail, and if the holding company becomes insolvent, Cochrane suggests that it could quickly force debt holders to accept a new mix of (less) debt and some equity.
The bad news is that the debt of the bank holding company, which is the closest thing to bank money in his world, will not trade at par. It will trade at a discount, which will be small if the bank seems to be doing well and large if the bank seems to be doing poorly. For transaction purposes, that sort of money is noisy, so it will not really work. If it would work, then nobody would be bothered by a money market fund that can “break the buck.” In order to avoid breaking the buck, money market funds have to stick to non-risky assets.
I think that in order to work as money, financial liabilities have to trade at par. If a firm has risky assets and most of its liabilities trade at par, then I think it has to be subject to runs (assuming no deposit insurance). I don’t see any way around that.