The world's big financial institutions have long seemed answerable to no one but themselves. The Third Basel Accord is intended to save banks from themselves, but the trouble is in the mathematics.
Banking goes back to the future
If you're bracing yourself for another year of grim financial news, take heart. The world's banking industry has just moved into a bright, new era of safety and stability.
Well, that at least is the idea behind the long-heralded launch last week of the Third Basel Accord. Named after the Swiss-based Basel Committee on Banking Supervision, set up in 1974 by various international central banks, "Basel III" is designed to stop financial institutions taking unacceptable risks and trashing the world's economy when they go bad. But the mathematics behind its financial engineering could be its undoing.
Basel III aims to do this by demanding that banks have the means to clean up their own mess, rather than dumping it on taxpayers.
Needless to say, this laudable aim has sparked huge controversy.
Critics of Basel III say the demand that banks triple the size of their financial "air bags" has delayed the end of the global recession while they build up their capital reserves.
Meanwhile, banks have warned that being forced to hoard capital rather than punt it in the markets will force up charges to clients.
Sure enough, many countries - including the US and the whole of the EU - have already fallen at the first hurdle, failing to meet the January 1 deadline for the introduction of Basel III.
Still, the pain must surely be borne if security and stability are to return to the banking sector. But will Basel III achieve this?
To those unfamiliar with the technicalities of financial regulation, the new rules certainly look impressive, with all their arcane terminology and mathematics.
But to anyone remotely familiar with the origins of the global financial crisis, this complexity alone is grounds for concern.
The very name Basel III reflects the fact that the new regulations are simply the latest attempt to plug gaps in the previous two incarnations. Yet all these patches, upgrades and makeovers would not have been necessary had banks not proved so adept at getting around the last lot.
And their motivation for doing the same with Basel III remains intact, because the way to make big money is to take big risks.
The architects of the new regulations do not deny this fact of financial life; they want to ensure that the risks are balanced by the means to cope with the consequences.
Ironically, that simple aim is the cause of all the complexity, as a morass of arcane mathematics is seen as the best way to identify and control those risks.
But dig deeper into the regulations and another irony hoves into view. By trying to tackle the sources of risk that caused the global financial crisis, Basel III drives banks to seek other, even less well understood, forms of risk in their quest for profits.
And when they do this, the "rocket scientists" working at banks have a habit of using mathematical ideas, which, for all their apparent sophistication, are hopelessly simplistic.
You don't need any mathematical expertise to see what's wrong with these ideas - though a PhD is handy for bamboozling others into taking them seriously.
Take the case of the so-called Gaussian copula. Don't be intimidated by the name; it's just the combination of the name of a German mathematician famed for his work on chance events, plus the Latin word for something that connects two things together (not to be confused with a cupola, which is a dome-like roof).
In the financial world, the Gaussian copula was seen as the way to appease regulators over a key problem: estimating the risk of entire sets of assets going bad at the same time.
Once upon a time, everything had been nice and simple. An asset, such as a bond, paid interest at a rate tied to the risk of it never paying out: the higher the risk, the higher the interest offered.
Historical records could give a handle on the likely risk of that happening, from close to zero for government "gilts" to something much higher for corporate bonds.
But in their ceaseless search for new revenue streams, banks created new types of assets by pooling assets such as mortgages.
Working out the appropriate interest rate - and keeping regulators happy - demanded estimates of the risk involved.
The problem was that all the ingredients had their own risk figures. Worse still, these risk figures were obviously not independent: during a recession, mortgages start going sour across the board.
The Gaussian copula seemed to offer a way of dealing with all this. Fed with the risk figures for each asset, plus a measure of how connected ("correlated") they are, it spat out the risk of an entire pool of the assets going bad.
All very impressive - as long as the figures fed in are reliable. And this is where non-mathematicians will smell a rat. Surely the level of "correlation" varies over time, adding uncertainty to the final result?
Indeed it does, and some financial experts warned of this long before the global financial crisis hit.
Then there's the problem of sourcing reliable risk figures for each individual asset. Lacking historical records, financial institutions guesstimated them - and got them hopelessly wrong.
In the aftermath of the crisis, studies of top-rated "triple-A" assets revealed that their true risk of default was often hundreds of times higher than the estimated figure.
Of course, the disastrous reliance on the Gaussian cupola is now well recognised among bankers and regulators alike - earning it the moniker of "the formula that killed Wall Street". But what hasn't changed is the determination of banks to find new sources of revenue - not least to make up for profits lost to all that regulation.
So ignore the talk of Basel III ushering in a new era of financial propriety. Chances are it will go the way of its predecessors, undermined by bonus-hungry PhDs wielding weapons of mass bamboozlement.
Robert Matthews is visiting reader in science at Aston University, Birmingham, England