A lot of people seem to hold some version of both of the following beliefs:

  1. Banks have artificially low capital levels because of implied government subsidies, and
  2. Shadow banking is undercapitalized and should be subject to bank-like regulation.

This combination of views strikes me as a bit of a paradox, or at least as requiring explanation. If too-big-to-fail banks can operate unsafely because everyone knows that they'll be bailed out in times of trouble, then presumably getting rid of their protections as banks would force them to become safer. Which would imply that non-bank, market-based financing mechanisms -- shadow banks -- are safer than the subsidized banks. But in fact the people who worry about too-big-to-fail bank subsidies tend to think that the shadow banks are even riskier and should move in the other direction, to be more like banks. Each side of the system seems to be under-capitalized relative to the other.

There are ways to resolve this tension, most straightforwardly by just saying, "but the shadow banks have the same sorts of too-big-to-fail protections as the big banks," which is fine I suppose. Or you can leave the tension unresolved and try to figure out, well, would banks be safer if they were more like shadow banks, or would shadow banks be safer if they were more like banks?

But it might also be useful to abstract away from all of that and just say:

  1. Finance is fundamentally the business of putting things in pots and then selling debt against those pots.
  2. In the actual world there are different sorts of pots subject to different rules about how much and what sorts of debt you can sell against them.
  3. But, if none of those rules existed, you could nonetheless find a market-clearing level of how much (safe) (ish) debt a given pot of assets could support.
  4. It might be worth doing that.

If only to inform the rules that you make in step 2. Like if it turns out that the "natural" level of leverage for bank-y type assets is, say, 80 percent (i.e. 20 percent capital), then the fact that, I don't know, JPMorgan is actually about 92 percent levered would seem bad, and you might want to change the regulations to make JPMorgan less levered. If the natural level is 97 percent, you'd have other conclusions.

The project of finding a natural leverage level is complicated by two things. One, different pots of assets can support different levels of leverage, so you can't get a generic answer. That's not really a serious problem; in theory, you could make your model detailed enough to, as it were, risk-weight different assets (and combinations of assets) to figure out the market-clearing leverage ratio for any particular pot of assets.

The bigger problem is that there are not a lot of trades "in nature." So, for instance, collateralized debt obligations were very much a mechanism for putting assets (here, mortgage loans) into a pot and having the market tell you how much debt you could issue against them and at what rates. So they sort of fit the bill. But in fact they seem to have been motivated more by banks dodging capital regulation and arbitraging rating agencies than by purely economic players trading with each other for their respective economic advantage.

Post-crisis creatures like business development companies, collateralized loan obligations, mortgage real estate investment trusts, hedge fund purchases of correlation books, etc., are all plausible candidates for market data, though for each of them you could make the case that prices are distorted by some sort of regulatory arbitrage, or more boringly by implied too-big-to-fail protection, or even more boringly by artificial Fed-fueled bubbles or whatever.

Anyway, though, a really good project would be to try to build a model of natural capital requirements based on market prices observed in shadow bank-y transactions, but that seems like it would be hard.

Failing that, here is a paper by some Stanford business school people -- William Gornall, who seems to be a Ph.D. student, and Ilya A. Strebulaev, an associate professor -- that I found pretty interesting. There's a lot here but what I liked is that it calculates an expected level of bank leverage based on a reasonably small set of assumptions, which are primarily economic -- what would unregulated unsubsidized actors do to maximize their economic returns? -- rather than regulatory or subsidy-related. In other words, it mostly looks to find a natural rate of bank leverage, which is sort of the thing I wanted.

It's 88 percent. That is, a bank should have debt equal to about 88 percent of its assets. Or 12 percent equity capital. Higher than JPMorgan's, lower than the Admati-Hellwig 20 percent or the Brown-Vitter 15.

How do they get there? There are three important things. The first is that their theoretical model consists of banks lending money to firms. That is ... not really what banks do! At all! In fact, loans to companies make up about 11.5 percent of banks' balance sheets, and in the middle market most loans come from BDCs and CLOs rather than from banks. Banks seem to be mostly in the mortgage business.

Next, they make use of the fact that banks' assets have much lower volatility than firms' assets, because banks' assets consist of loans to lots of firms and are thus more senior and more diversified than firms' assets. So, "Borrower asset volatility of 40% leads to bank asset volatility of 1.7 %, consistent with empirical evidence," meaning that banks are much safer than borrowers and can afford to lever up more. The particular 88 percent number comes from some rough but plausible assumptions about firm-asset volatility and correlation, tax rates, distress costs, etc. in the real world.

Finally, they argue that "previously unstudied supply chain effects mean that highly levered financial intermediaries are the most efficient," which is unfortunately mostly about the incidence of the interest tax deduction. I realize that is not a particularly sexy argument for those who want to clamp down on bank leverage in part by getting rid of the interest tax deduction, but there it is.

So I mean I'm not gonna go around saying that the right level of bank capital is 12 percent, and that's not what this paper argues. (They argue more sophisticated things about capital regulation and moral hazard and stuff but I am parting ways with them here.) Nor could it, really, since it computes theoretical capital levels based on a model of banks' business that is mostly not true. Still, at least it's a capital model based on the banks' business, rather than beginning with subsidies and regulations. That's an interesting start.

  1. Depends on what you mean by "shadow banks." Are money market funds and the tri-party repo market too big to fail? Oh, sure, probably, why not. Is the typical business development company? Mehhhhh.

  2. I mean, nobody knows what a shadow bank is, so whatever. I once looked at this with regard to mortgage REITs and business development companies, two flavors of shadow banks, and got sort of pro-shadow-bank results. Money market funds are strictly an exercise for the reader. (Step 1 of the exercise: Are money market funds 100 percent levered, or 100 percent unlevered?)

  3. Oh gosh here we're abstracting way way way away from what those actual assets might be. Obviously banks have different kinds of assets and a different mix will lead to a different "natural" leverage ratio.

  4. In the most boring GAAP way, just $2.26 trillion in liabilities divided by $2.46 trillion in assets, obviously there are various IFRS, Basel, etc., ways to get to other numbers.

  5. This seems too obvious to require citation. Nonetheless here is a good book on the question. Here is an obvious ratings-arbitrage trade that also happens to be delightful.

  6. Their thank-yous section starts with Anat Admati, also at Stanford, which is interesting. In some ways their whole project is adverse to hers: Her starting assumption sometimes seems to be that there is no good reason for a bank to have more debt than any other company, and that banks are highly leveraged solely because of too-big-to-fail subsidies. And this paper is like, well, no, obviously that's wrong.

  7. Well. There are two subsidies that have an effect here. One is the tax subsidy for debt: Because debt is tax-deductible and equity is not, both banks and non-bank industrial firms have an incentive to borrow more. But on their model a lower tax rate would actually increase bank leverage, while decreasing non-bank leverage (see Table 3 on page 51 of the paper).

    The other is that they need an input for costs of distress, and your intuition might be "well, banks have artificially low distress costs because they'll be bailed out." Here: "We set firm and bank distress costs ... at 0.1. For firms, this assumption is likely conservative. Some recent estimates, such as Davydenko, Strebulaev, and Zhao (2012), find that, conditional on experiencing distress, large firms incur sizable total distress costs of 20%{30% of asset value at the time of distress onset. In a theoretical work, Glover (2012) suggests that distress costs can be even higher. There is little empirical evidence on bank bankruptcy costs. James (1991) finds direct bank bankruptcy costs equal to 10% of assets."

    Their default assumption is a 10 percent cost of bank distress; changing that to 20 percent lowers bank leverage from 88.4 percent to 86.5 percent, so it's not a huuuuge deal.

  8. Also, not that you care, I find this section very confusing. The idea is that firms cannot capture all of the benefits of the tax deduction because after all the interest they pay to their creditors is taxable to those creditors -- but that if they pay it to highly levered banks, those banks get to deduct their own interest costs and so raise the tax efficiency of debt. All perfectly sensible. But then: Those banks are paying interest to someone, no? You can't just stop with the banks, can you? Maybe you can; I guess banks lend to each other a lot. Still, feels weird.

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To contact the author on this story:
Matthew S Levine at mlevine51@bloomberg.net