Drowning by numbers

Was the banking crisis caused by an over-reliance on risk models based on inherently unknowable future events? John Kay analyses the probability that Keynes was on the money.

Keynes is best remembered today for the economic policies derived from the General Theory, which are widely thought the most relevant to the resolution of our current crisis. But another group of Keynesian ideas are central to understanding the origins of that crisis.

Keynes’ fellowship dissertation at King’s College, Cambridge, was submitted in 1909 but published as A Treatise on Probability only in 1921. Keynes defined an approach to risk and uncertainty that put him in opposition to another, younger Cambridge scholar – Frank Ramsey, whose brilliant career was cut short by his death at the age of 26. Keynes and Ramsey each, coincidentally, had seconders from the University of Chicago. The Keynesian position was similar to that taken by Frank Knight in a book that appeared in the same year. Jimmie Savage extensively developed Ramsey’s ideas.

Ramsey and Savage won the debate. The structure they proposed, which we would now describe as the theory of subjective expected utility (SEU), is the basis of virtually all quantitative modelling in financial markets today. That theory assumes that we can describe uncertainty with the aid of attaching probabilities to all possible outcomes, updated as new information becomes available. We value alternative outcomes by multiplying our subjective assessment of their value by these probabilities. Extended at the University of Chicago in the 1950s, this approach paved the way for a systematic study of financial economics. The growth of markets for derivatives – the first exchange was established in Chicago – was made possible by the development of scientific models for valuing these new constructs. The same approach informs the risk models used in almost all financial institutions. The most widely used template in the banking industry was elaborated by J P Morgan, which published the details and subsequently hived off a business, RiskMetrics, which promotes it still.

These risk models are based on analysis of the volatility of individual assets or asset classes and – crucially – on correlations, the relationships between the behaviour of different assets. Some risks are inversely related – an umbrella shop makes money if it rains and an ice cream stand makes money if it shines. In these situations individually risky assets can be combined to create a portfolio with low overall risk. This textbook example is too good to be true, but as long as different risks are less than perfectly correlated, the process of aggregation will reduce overall.

The standard assumption of both valuation and risk models is that the dispersion of returns follows the normal distribution, the bell curve that characterises so many natural and social phenomena. If so, the whole problem can be encapsulated in what is called the variance–co-variance matrix. Fed with such data, a computer can assess any asset distribution and calculate, day by day, the distribution of expected overall gains and losses.

The most common way of describing this distribution is the value at risk – the size of loss that will be exceeded only with very low probability, like one in 1,000. A CEO can sleep soundly at night knowing that this value at risk is the largest likely loss in a tenure of 1,000 working days. If he (or she – but the new bosses of the failed Icelandic banks are almost the first women to occupy such positions) is risk averse, he can ask his people to tweak the model by setting an even higher hurdle, for the probability of unacceptable loss, say one in 10,000. But models are only as good as the correspondence between the model and the world. The assumption of normal distribution of returns seems to work well in times that are – well, normal. But what of abnormal times?

More sophisticated institutions test their own risk models against their own historic experience. But that experience is necessarily drawn from a time when the institution was not experiencing the problems that the models are meant to anticipate.
The one thing we know with certainty about the banks, insurance companies and hedge funds that compete for our funds is that they did not go bust in the period from which their historic data is drawn. The calculated variances and co-variances prove inapplicable in times of stress – as when apparently uncorrelated asset prices move together. The US hedge fund Long-Term Capital Management failed in 1997 because, when the effects of the Asian crisis spread to all emerging economies, apparently uncorrelated assets all moved in the same direction. The risk models financial institutions use ensure that it is very unlikely that these institutions will fail for the reasons that are incorporated into these models. That does not mean that they will not fail, only that if they fail it will be for different reasons.

Round the corner are what Nassim Nicholas Taleb calls ‘black swans’: events that no one predicted, or could have predicted. These events are not in the models because they aren’t, and can’t be, in the data. That doesn’t mean they aren’t going to happen. And, in 2007/08, they did.

Keynes and Knight emphasised the uncertainty that arose from the necessarily imperfect nature of human knowledge. The future was not just unknown, but unknowable. Donald Rumsfeld expressed the difference between risk and uncertainty with uncharacteristic clarity. He famously distinguished “known unknowns – the things we do not know” from “unknown unknowns – the things we do not know we do not know”. Risk describes the things we know we do not know; uncertainty describes the things we do not know we do not know. The imperfect state of human knowledge means that widespread uncertainty is inescapable.

The claim made by the SEU school is that their analytic tools enable us to cut through much of this uncertainty with probabilistic reasoning and formal modelling. Keynes was sceptical. Between completion of his work on probability and its publication, the great economist had become famous for his polemical denunciation of the Versailles Treaty that ended the First World War. In a celebrated passage, he described the confidence of the pre-war mood, in which the English upper middle class viewed its comfortable, stable environment as a permanent condition. Government stocks reached an all-time high in 1897, as Queen Victoria celebrated her diamond jubilee and the British Empire extended round the world. Even in July 1914, with the end of dreams only weeks away, the bond market held steady.

If the world of the English middle class was transformed by the war that followed, the world of the central European middle class was shattered. Wealthy families whose lifestyle had seemed secure lost everything: from the default of Russian bonds; as a result of hyperinflation in Germany and central Europe; in consequence of the expropriation of Jewish property.

The future has not become more certain. The collapse of the Twin Towers was a major event for financial markets, as for international politics. No one, on 10 September 2001, could sensibly have framed or answered the question ‘What is the probability that the World Trade Center will be destroyed tomorrow by a terrorist attack?’

Keynes claimed that there could be no scientific basis for an assessment of probabilities in the face of this kind of uncertainty. He asserted that the right response to the question ‘What will interest rates be in 20 years’ time?’ was ‘We simply do not know’. A question about the level of interest rates seems to be one that might be answered probabilistically. But his agnosticism about what interest rates would be 20 years after his statement appeared was prescient. A holder of British government bonds in 1941 could not have been certain whether he would be repaid in sterling, in reichsmarks, or at all.

Investors are vulnerable to defined, identifiable risks such as interest rate risk or currency fluctuations. But the business and financial environment is vulnerable to fundamental uncertainty. Questions like ‘What will be the outcome of the Iraq war?’, ‘What will be the economic consequences of China’s rise?’ or ‘How will economic and political systems deal with climate change?’ are open-ended. We cannot fully describe the range of outcomes, and decades from now there will still be disagreement over what the outcomes proved to be.

We may attempt to transform these open-ended questions into more narrowly defined ones like ‘How many US troops will be in Iraq in 2010?’ or ‘What will be China’s GDP, or the average world temperature, in 2025?’ But even if it were possible to make such predictions – and it is not – the numbers would not tell people what they really want to know. A time traveller from the 19th century, asking us about the world in which we live would not understand enough about our world to be able to frame sensible questions. We suffer, not just from ignorance of the future, but from a limited capacity to imagine what the future might be. People who are today concerned about the Iraq war, China’s rise or climate change would not have been worrying about these issues 20 years ago. They would have been worrying about the Cold War, Japan’s economic pre-eminence and the effects of Aids.

These earlier uncertainties have largely been resolved, and in ways that few people expected. But the key point is not that we mostly fail to anticipate the answers, rather that we mostly fail to anticipate the relevant questions. No one predicted the catastrophes of the 20th century – the stalemate of the First World War, the influenza pandemic, the murder of millions of people by deranged dictators. The same was true of transforming political and economic developments – the rise and fall of communism in Russia, decolonisation, the development of information technology, the changed role of women in society.

Such failure of imagination is inevitable. If you could anticipate the functions and uses of the personal computer, you would already have taken the main steps towards inventing it. To describe a future political movement or economic theory or line of philosophical thought is to bring it into existence.

We usually deal with uncertainties through stories rather than probabilities. Thinking about probabilities does not come easily to the human mind. Constructing narratives does. We weave stories and fit events and expectations into them. Our ability to tell stories is a valuable asset, the means by which we make sense of disconnected information. 

Yet in financial markets this skill often misleads. Financial mathematics teaches us that, in securities markets, purposive and directed behaviour can produce outcomes with the appearance, and mathematical properties, of randomness. But we resist randomness. The search for patterns in randomly generated data warms the heart as it hurts the wallet. Our abilities in pattern detection often lead us to observe systematic relationships that do not exist, or to confuse underlying causes with statistical noise. Hopes and dreams become confused with expectations.

The antidote to errors of interpretation is general knowledge, what many people call common sense: the disparate facts about the world that we apprehend but do not articulate systematically, and that inform every decision we make. Keynes was a successful investor, as well as a man who achieved success in many other fields, in part because he brought to all his activities a range of experience and knowledge of both ideas and affairs probably unparalleled in the 20th century.

The common mistake is to believe that the uncertainty described by Keynes and Knight can, through diligent research or analytic sophistication, be transformed into the well-defined quantifiable risk that responds to the techniques developed by the successors of Ramsey and Savage. Keynes correctly observed that the only justified answer to many questions about the future is ‘We simply do not know’, but no one is rewarded for saying that. Many people in the financial services sector profess knowledge of the future they do not have, and cannot have.

We need probabilities to help us assess risks and narratives to guide us through uncertainties – and the general knowledge and judgment to know how to approach each particular situation. It is that general knowledge and judgment that has been so lacking in the financial follies of the past decade.

Leading economist John Kay is a columnist for the Financial Times.

Finance: a guide for uncertain times
Join us at the RSA on 22 January 2009 or listen live as John Kay offers his expert guidance on the modern financial system and how we can take control of our own finances.