irritating arithmetic

bank regulation unfortunately makes no sense whatever

“Every accounting system is a mental prison” was the first substantial post on this ‘stack (it’s also intimately linked to a key chapter of “The Unaccountability Machine”, available for pre-order!).  So far, though, I’m conscious that I’ve mainly made this point in the context of government accounting systems, and that I might have given the impression that escaping the mental prison is an easy thing to do.

So here – because it’s topical – is an example from another field where I’m quite familiar with the territory.  It happens to be the case that bank capital requirements form an accounting system which is a particularly bizarre and dystopian mental prison.  Despite often involving quite sophisticated statistical modelling, it could be argued that they have some massive mathematical inconsistencies themselves.  Let’s list a few fairly simple facts:

Marginal costs do not, in general, add up to the total.  Straightforward for anyone who’s done economics or accounting. Rationally, decisions should be made on the basis of marginal cost (can you produce one more unit at a cost less than you could sell it for?).  But if there are overhead or fixed costs, then the sum of the marginal cost of each unit of output will add up to a smaller number than the total cost.  So there’s always a problem in both trying to respect the marginal cost rule, and the constraint that total revenues have to be at least equal to total costs. Trying to deal with this is one of the reasons that airlines and newspapers go bust so often.

Marginal risks, do not, in general, add up to the total.  Banks and financial institutions ought to operate on a principle analogous to the marginal cost rule, pricing their lending or other products to cover both the operating cost and the financial risk.  But risks don’t add up easily either.  In general, unless all the risks are perfectly correlated (in which case there’s really only one risk), the risk of the entire portfolio will be less than the sum of individual risks.  New business really ought to be considered depending on its contribution to the total risk of the institution.

Regulatory capital requirements do, in general, have the additive property.  On the other hand, the way that bank capital rules are written is usually such that you can calculate the requirements for each product, then add them up and you get the total.  There are some rules which aren’t quite like this – usually in the area of “market risk” – but they tend to add a lot of complexity to the system, and they are not usually well liked.  This means that the marginal regulatory capital requirement for a new piece of business is not equal to its marginal risk, except by pure chance.

Regulatory capital constraints are almost never binding.  This might not matter as much as you’d think, though, because in a sense, the marginal regulatory capital requirement for a single new piece of business is usually zero.  It’s zero because nearly all banks operate with a comfortable margin of safety above the bare minimum regulatory requirement. (They do this because bad things happen if you breach the requirement).

I don’t think these are fixable problems  – when you’re trying to describe a very high-variety business in consistent and fixed terms, you’re doing the equivalent of trying to flatten out a globe into a map. There are bound to be distortions, it’s just a matter of trying to minimise the extent to which they cause problems.  But problems they do cause.

A good way to run things, in the knowledge of the distortions set out above, would be for the regulators to say

“here’s the capital calculation – for god’s sake don’t take it too seriously, it’s just a bunch of rules of thumb meant to give a number roughly in proportion to the size of your business and the kind of things you do.” 

And for the bank managers to say

“yup, that amount of capital is doable for us, we’ll try to make sure we have a bit more just to be sure.  And then we’ll think about the total amount in the context of the overall business plan for the next few years, so that we’re growing our capital base roughly in line with the overall size of the bank”.

You would be surprised at the extent to which this does not happen.  Much more common is a situation in which the bankers say

“Well, making a business plan based on our own estimates of marginal risks so that we can attribute capital to each bit of business and decide whether it’s a good or bad return … that sounds hellish complicated, particularly when the regulators have given us this handy handbook. Let’s just use those as the marginal capital requirements for our internal accounting too.”

And then the regulators say:

“yes, those are the marginal capital requirements! Now we’re going to shift them around a bit, in order to penalise or incentivise things that we consider good or bad, possibly on the basis of our own projections of macro risk, but possibly for totally unrelated policy reasons!”

And then politicians and lobbyists say something like “mmm, is that one part of blood in ten thousand parts water? Smells like opportunity!”.

It is not at all difficult to get into a situation which very much looks as if the banks have delegated some of their most crucial management functions to a regulatory handbook, while the regulators are doing impromptu industrial policy. The big original sin that lands you in the mental prison is, in this case and many others, taking a set of numbers that you have to calculate for one purpose, and using them for another purpose because it’s cheaper and easier than starting again from scratch.