Overdosing on Dr Li’s Magic Formula

One persistent theme in my experience of business over the last quarter-century is how wrong-headed it is to rely on what suits business to determine the direction of the economy as a whole. A second is that intellectual narrow-mindedness can make otherwise apparently clever people do some very dumb things.

It is not that most business people aren’t clever or that they don’t understand economics; rather, it does not matter how clever they are or what they do or don’t understand, because once business is allowed its head, the natural tendency of markets toward monopoly, bubbles and assorted other economic irrationality and social disaster is inherent in business itself.

The basic principles of investment ensure that, even for a democratically minded investor, a financial return – a profit - must be extracted sooner or later, while the equally basic rules of risk management mean that the shorter the term over which that profit is made, the greater the chance of not losing it to serendipity, market vagaries or the other guy being smarter/meaner/luckier than you. Add to that the extent to which most companies – and certainly all economically significant ones – rely on investment and re-investment from bodies such as investment banks, pension funds and insurance companies, whose sole interest lies in maximising the returns on their investments, and no sooner do you leave business to its own devices than they all start rushing towards the cliff.

For allowing business to have its head is rather like shouting Fire! in a theatre: everyone rushes in the same direction, because that is where survival – which is to say, the profit - lies. And when people all start running in the same direction, two things happen. Firstly, things start to get distorted. And secondly, people start to notice that they can rely on people running that way, even though there is no obvious reason way they are. Hence bubbles: things start to rise, then people start to buy not because they can see intrinsic value in what they are buying but because they have confidence that other people will soon be willing to pay even more for what they have just bought, and they will make a tidy profit selling it to them.

Add to that the extent to which market economics became an all-conquering ideology from the 1980s onwards, and it soon became inconceivable that the interests of business and the plans of its leaders could be wrong for society as a whole. In reality, it turns out, they were completely opposed. Follies such as the Private Finance Initiative or rail privatisation should have been enough to convince any disinterested onlooker, but as far as deregulating markets was concerned, nothing was too much. So regulators had spent half a decade mouthing oxymorons such as ‘light-touch regulation’ and declining to be firm with whole industries because ‘business wouldn’t like it’.

This could only happen because the free market fantasy went right to the top. Thatcher, Reagan, Clinton, Blair, Bush and Brown all expressed a quasi-religious passion, and did not the upright Senator Phillip Gramm say, ‘Some people look at sub-prime lending and see evil. I look at sub-prime lending and I see the American Dream in action’. Indeed - where but in a dream could anyone couple human happiness with unbridled market capitalism with an untroubled mind? Or how about, ‘When I am on Wall St and I realise that that’s the very nerve centre of American capitalism and I realise what capitalism has done for the working people of American, to me that’s a holy place’. I trust someone has engraved such fine words on Senator Gramm’s retinas for future reference.

Where did all this lead to? Inevitably, right into the heart of (cliché alert!) the perfect market storm.

The absurdity of this situation is illustrated by the enthusiasm with which markets adopted David X. Li’s now-notorious equation for calculating just how risky buying and selling really were. This (somewhat medical-sounding) ‘Gaussian copula function’ in fact allowed them to work out the probability that a borrower would default on their payments. Once you have a simple answer to this question, it becomes much more profitable to lend to them (or at least, lend to a whole class of borrowers of the same kind), because you know exactly how much you can risk. You certainly don’t have to understand or pay regard to the underlying economic situation. With that, the market is reduced to a casino – from the individual punter’s point of view, most people lose their shirt, but from the house’s perspective, it’s almost impossible not to clean up.

Or at least so it seemed once Li had performed the seeming miracle of replacing all that intractably complex analysis of interacting variables and erratically fluctuating intangibles with a single neat number. This number was extremely easy to understand – a little too easy, it turned out – and allowed bankers and their minions to create a complete parallel universe populated with exotic beasts such as ‘collateralised debt obligations’ and ‘credit default swaps’. And rather like the real universe, it grew by a fantastic process of inflation that defied mere time and space, with the derivatives market quintupling in size from $100 trillion in 2002 to $500 trillion – that’s $500,000,000,000,000 - in 2007. George Soros might admit that he didn’t understand these fancy new kind of derivative and Warren Buffett might call them ‘financial weapons of mass destruction’, but the really smart guys weren’t fazed: what the hell – there was money – lots and lots of money – to be made.

But, like unicorns, CDO’s and CDS’s – not to mention still more mysterious animals of the genus ‘CDO-squared’ - turned out to be beautiful, magical and mostly fictional. There was something there, but once the lights came up, they turned out to be little more than dead donkeys. What is more, the vast sums these true believers made were conjured up not, as it seemed both to City and Wall Street financiers and to their political accomplices, by the magic of the market, but by those very same bankers allowing a combination of ignorance and greed to create a market treadmill it was all but impossible to get off. With that, they broke all connection between business and the economy, to the point where the two became fundamentally opposed.

Hence both the illusory nature and the market triumph of David Li’s formula and the hypnotically simple ‘correlation’ it generated. For this clever tool offered to replace with a single, precise, eminently intelligible number any kind of analysis of the connection between a product’s price and the complex and imprecise underlying economic realities that gave it material value. The mere fact that the result was simply a single number should have started the alarm bells ringing – it is completely unbelievable that anything of economic significance could be meaningfully defined in such simple terms. But then the markets aren’t trying to manage the economy - they are looking for safe, swift and above all spectacular profits.

Which is what they got, for a while at least. But what was David Li’s magic number really based on? Two things: short-term thinking and the market feeding on itself. Not that David Li's model was unusual in that respect. The Bank of England director for financial stability, Andrew Haldane, has commented that 'With hindsight, the stress-tests required by the authorities over the past few years were too heavily influenced by behaviour during the golden decade' (i.e., 1998-2007). Not very smart, given how exceptional everyone knew this period really was.

Yet Li's model took this process to its extreme, by taking into account only right now.Underlying Li’s equation is the assumption that, far from trying to understand the value of an investment – which is to say, its true economic value – it is only necessary to know how much the market is currently pricing it at. Once you know that, you can estimate the risk you are taking when you buy or sell it. But such an approach can only work while the market is buying or selling in unison and is either completely static or continuously changing in the same direction. The former is almost unheard of in recent decades, while the latter can only endure while the market is in bubble-mode, and people are buying and selling at silly prices primarily because other people can be relied on to sell and buy at sillier prices still.

Eventually, however, the strains this creates are too much even for these florid times. Eventually, investors start to realise that a) they no longer have any idea what anything is really worth, b) whatever it is, it is a lot less than what the market is saying right now, so c) the prices of their assets makes no sense at all. With that, Li’s reassuringly singular equation starts point firmly downwards, and everyone starts shouting Fire! And heads for the exits. The market burns down with most people still inside, and the central mechanism for manage truly huge swathes of the entire global economy goes up in smoke.

This is yet another instance of the notorious ‘mark to market’ strategy, of course – of valuing something solely by current price rather than taking into account any notion of material (social, economic, etc.) value that might sustain its price. As the current crisis has amply demonstrated, this has the disastrous effect of exaggerating a company’s value enormously when a bull market is in progress and asset prices are all going up. This in turn allows that company to borrow far more than they would have been allowed in less bullish conditions, even though the economic value of the company has not changed. Conversely, as soon as the market turns, the company’s assets are worth less and less, its credit collapses and all those loans are called in. What has changed in the economy? Nothing. What has changed in the market? Everything. So what then happens to the economy, at whose heart these unfettered markets sit? Disaster.

And all this is epitomised in Li’s formula. It’s timescale is not so much short-term as instantaneous, so any rapid market shift can bring on a catastrophe. By reducing everything to a single index it demonstrates that its sole purpose is to price risk and feed short-term speculation, rather than calculate realistically complex economic values, and so support true investment. Its simplicity concealed far more than it revealed, to the point where 30% of the US mortgage market could be made up of sub-prime mortgages and no one noticed. By being nice and simple, it seduced mathematically illiterate managers into believing they could do magic. Which, like the sorcerer’s apprentice, they could – they sprinkled Dr Li’s fairy dust over the financial sector, and it disappeared. Finally, it values risk based solely on what the market says it is worth, which (like all speculation) is both economically trivial and completely circular. So as soon as it starts to be widely used it is almost designed to generate a bubble, and the very nature of bubbles is that they take make everyone believe that they can defy economic gravity – just like they could with the dot.com boom, the supposedly ever-expanding ‘knowledge economy’ and a host of other booms and busts. The fate of bubbles was Economics 101 then and it is Economics 101 now.

But it would be quite wrong to blame David Li and his equation. Many experts warned against taking it seriously. So did David Li - though that didn’t stop him making his fortune out of it. In fact it makes more sense to ask not how the Li formula destroyed the financial markets, but how the financial markets, with their superficiality, their collective egoism, their indifference to long-term consequences and their power to strong-arm anyone caught up in them to play economically and socially insane games, created an audience for Li’s formula.

But what about all those clever business people who declined to heed the many warnings? The regulators who endorsed its use, even though one Standard + Poor analyst remarked ‘Let’s hope we are all wealthy and retired by the time this house of cards falters’? The politicians who gave business the ‘light-touch regulation’ it wanted? All those clever free-market acolytes from the Wall St Journal, the FT and the Economist? Yes, I think we can blame them. Not that I blame them for being wrong; but I do blame them for being so utterly uncritical, so deaf and blind, so patronising to those who questioned their shallow fantasies and so cowardly when the end was in sight. Unlike explorers searching for Eldorado, they had every reason to know exactly where we were heading.

They just preferred not to notice until it was too late – for all of us.

So why don't corporations use markets themselves?

Like most unrepentant lefties, I get tired of hearing people talk about markets as though they we some kind of panacea rather than the combination of adolescent abstraction and crooked game they obviously are to anyone who bothers to work out how they really operate.

But just to cut through the usual theological speculation (which would, I am quite sure, have shocked Adam Smith, who seems to have been generous, humane and sophisticated moral philosopher who distrusted business deeply), would someone please point me at, say, three major corporations that organise their own internal operations as a market?

Can't think of even one? Me neither.

But worst of all, they won't solve our current environmental or energy problems. Why not? Because of this.

Elementary, my dear Watson

It's strange where lessons in management can be gleaned from.

Having recently read all the Sherlock Holmes stories (not for the last time, I suspect), I can assure the reader that Holmes never utters the words, ‘Elementary, my dear Watson’. ‘Elementary’ sometimes, and ‘My dear Watson’ often, but never together. Conan Doyle's son used it in an attempt to prolong Holmes’ career, though not to any enduring effect.

Of course, that should not stop anyone ‘quoting’ Holmes/Conan Doyle to that effect. It is a very good phrase. In John Lennon’s case, it has even been embellished - twice:

Harrybelafonte, my dear Whopper

and

Ellafitzgerald my dear Whopper (both from A Spaniard in the Works, Jonathan Cape, 1965)

As Umberto Eco has observed, William of Ockham (c. 1285-1349) was clearly an ancestor of Sherlock Holmes (fl. 1887-1927). When the famous detective asserted that:

How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth. (Arthur Conan Doyle, The Sign of Four)

… he was only reiterating his philosophical forebear’s famous dictum that one should always prefer the hypothesis which calls for the least number of assumptions. Or, in Ockham’s own words:

Entia non sunt multiplicanda praeter necessitatem

- which is to say, entities should not be multiplied unnecessarily. It’s an attractively simple, all-purpose principle, a sort of intellectual Swiss Army knife, and it’s interesting that such otherwise dissimilar figures as Holmes and Ockham should agree on this issue. Not only did they live six centuries apart but, as nominalist philosopher/amateur coiffeur and consulting detective/cocaine addict respectively, their experience could scarcely have been more different.

At first sight it seems that this most striking convergence must surely betoken a profound truth. Surely such a preposterous yet consonant mésalliance can only rest on a deeper meaning? But does their agreement indicate a verity spanning half a millennium and more, or merely a prejudice so commonplace that only the most foolhardy - or the most brilliant - would think to challenge it? Mere endurance is not evidence, one way or the other. After all, slavery was considered the natural order for millennia.

What should we do when ‘impossible’ turns out to be only the name of that part of reality for which our prejudices have no place, to sustain which we therefore have to introduce ever more - and ever more incredible - assumptions? Should we be whipping out that Swiss Army knife again when the situation really calls for is an intellectual linear accelerator? Is the principle of parsimony merely a principle of false economy?

For example, there is the question of cosmology. Leaving aside the obvious facts that the Earth is flat, stands still, and the Sun rotates around it once a day (to which either may have subscribed), Holmes and Ockham would both have taken a dim view of Copernicus. In fact according to Watson, Holmes was unaware that the Copernican revolution had ever taken place, so their intellectual alliance is obviously all the closer. And one cannot help but feel that Ockham would have felt much the same, if not about a heliocentric universe as such then certainly about the rather radical re-jigging of the cosmos Copernicus was proposing.

In assessing the change wrought by Copernicus, it is important to recognise why his theory was so appealing. First and foremost, Copernicus’ solar system did not work any better than Ptolemy’s, and indeed was in most respects an attempt to save the Copernican fundamentals such as a closed space, the circle as the perfect form of celestial motion, the epicycle and the eccentric as basic explanatory tools, and so on. Indeed, Copernicus’ account predicted the position of the stars rather worse than Ptolemy's. Nor was it more economical: not only did it call for exactly the same suite of spheres and epicycles but now there were 48 of the latter instead of just 40.

In fact, the only major difference was that the solar system was now centred on the Sun rather than the Earth. No basic change in the fabric of the heavens, no shift of method. Only a change in the arrangement of things. Of course this was pretty reasonable, given the appalling implications of a truly unbounded space combined with the lack of stellar parallax. In other words, there were almost no additional ‘entities’ or assumptions, yet what was needed was the complete re-conceiving of the universe - something which both Ockham and Holmes would have reviled.

Thus, the entire history of astronomy between Ptolemy’s atlas of the Heavens and Copernicus setting to with a chain saw consisted precisely of the kind of minimalist thinking Ockham called for - the same structure exactly, only with more or less epicycles. The problem is that possible/impossible is not the only dimension of knowledge. It might be so, if we already knew all the dimensions of reality, and could therefore derive every possible truth from first principles. But we don’t, so we must respect Holmes’ and Ockham’s right to believe what they please, but concur with Aristotle that:

A likely impossibility is always preferable to an unconvincing possibility. (Poetics, 24, 1460).

For, as an only marginally less prominent philosophical figure has explained:

The impossible often has a kind of integrity to it which the merely improbable lacks. How often have you been presented with an apparently rational explanation of something which works in all respects than one, which is just that it is hopelessly improbable? Your instinct is to say, ‘Yes, but he or she simply wouldn’t do that. ’... The [impossible] merely supposes that there is something we don’t know about, and God knows there are enough of those. The [improbable], however, runs contrary to something fundamental and human which we do know about. We should therefore be very suspicious of it and its specious rationality... If it could not possibly be done, then obviously it had been done impossibly. The question is how? (Douglas Adams, The Long Dark Tea Time of the Soul, p. 132)

As usual, fiction is so much more truthful than mere fact (leaving aside the debatable conclusion...). ‘The facts’ are so often little more than a rag-bag, picked over now and then as circumstances dictate; great fiction, on the other hand, is deduced with geometric precision from a central truth, a overriding vision of the inexorable logic which underpins the merely correct.

And from time to time a revolution occurs that reminds us that, beneath the seeming self-evidence of the possible and the impossible there is a more or less hidden framework of concepts which determine what can even exist for us while thinking and reasoning in that mode. And there is no guarantee that the Universe is confined by the concepts which currently confine our minds. Thus, Copernicus’s universe was not merely unknown to Ptolemy; he might well have found it inconceivable. Likewise the relationship between Newton and Einstein and, I suspect, Darwin and quite a few eminent neo-Darwinians.

In short, intellectual history is the history not of intellectual accumulation but of intellectual struggle. And that struggle is not only a struggle to wrest truth from the Universe, but also a struggle to prise the beams from our eyes. Hence the transmutation not only of one scientific method into another, but also of base common sense into science - and, perhaps, science into some form of reason for which science and morality, politics and art are all one. Same for cognitive development.

Now what has all this to do with management? It really comes down to the all but universal management mantra that ‘if you can’t measure it, you can’t manage it’. I suspect that this really originates from Lord Kelvin, who once write that:

When you can measure what you are talking about and can express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.

Ah, Kelvin. The man who used the latest thinking in physics to prove that Darwinism was impossible. But what is wrong with his emphasis on measurement? Well, as John Maynard Keynes put it:

Am I right in thinking that ... the statistical method ... essentially depends on ... having furnished, not merely a list of the significant causes, which is correct so far as it goes, but a complete list?

For example, suppose three factors are taken into account, it is not enough that these should be in fact verae causae; there must be no other significant factor. If there is a further factor, not taken account of, then the method is not able to discover the relative quantitative importance of the first three.

If so, this means that the method is only applicable where [one] is able to provide beforehand a correct and indubitably complete analysis of the significant factors. The method is neither one of discovery nor of criticism.

In other words, Kelvin is assuming what he should be proving, namely that he knows what he is measuring, rather than using measurement to decide what he is looking at. And that is exactly the fallacy of “If you can’t measure it, you can’t manage it” – the view that we already know how things work, and measurement will only add to the precision of our knowledge. And indeed it will – but it won’t add anything to its accuracy unless we understand the things we are measuring. Which is precisely what we think we are using measurement to do...