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Updated: September 6, 2010 13:17 IST

Undone by unsound assumptions

D. Murali
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How to put capitalism back on its feet? By looking to the past, say Kevin Dowd and Martin Hutchinson in ‘Alchemists of Loss: How modern finance and government intervention crashed the financial system’ (www.wiley.com). Past, meaning not the twentieth century, but the eighteenth and nineteenth centuries, the authors add. For, a good starting point, in their view, is to reconsider the demerits of the joint-stock form and the merits of the old partnerships in the financial sector, and think seriously about restricting or even repealing the limited liability statutes.

After studying three centuries of financial history, the authors aver that modern financial theory rests on unsound assumptions and should largely be ditched. Some of its main pillars – such as the efficient market hypothesis, the assumption that returns are Gaussian, the belief that financial market risks are predictable, the belief that financial innovation is a good thing that helps make financial markets more stable, and so on have been pretty much exploded, they note.

Flawed risk management

Failure is evident in the related sphere of ‘financial risk management,’ the book outlines, by citing the problems with fat tails and even the most moderate of extreme events. “It is senselessly wedded to the VaR risk measure, which peers myopically away from ‘bad days’ and only works when risks are not particularly risky, and to correlation-based risk management strategies that break down when most needed… Most of modern quantitative risk management is in fact no more than an arcane cult that has helped to disguise risk-taking on a huge scale while pretending to do the opposite.”

The assumption of Gaussianity appears first in a chapter titled ‘modern financial theory’s hideous flaws.’ For starters, the assumption is that financial returns could be adequately described by the Gaussian or normal probability distribution, often known as the bell curve.

“The distribution is centred around the mean, implying that the most likely values are those clustered around the mean. The degree of dispersion, or uncertainty, is determined by the distribution’s standard deviation (or sigma).” As the authors explain, outcomes further away from the mean are less likely than outcomes closer to it, and the distinctive feature of the Gaussian is the way in which the ‘tails’ slope off rapidly, making extreme outcomes very unlikely.

Gaussian probabilities

For instance, the probability of a 5-sigma loss on any given day (0.000029 per cent) can translate to a waiting time of 3.5 million days or about 14,000 years (of 250 trading days a year) before the loss can occur. In the case of a 10-sigma event, we are talking of ‘a period that is vastly bigger than the age of the universe itself. And the waiting period associated with a 20-sigma event is a number, in years, that considerably exceeds recent estimates of the number of particles in the known universe.’

Losses such as the 22- or 23-sigma event of October 19, 1987 (‘Black Monday,’ when stock markets around the world crashed), are thus to all intents and purposes impossible under the Gaussian, remind Dowd and Hutchinson. The fact that even a single loss of this magnitude occurred at all – and, in fact, these sorts of events seem to occur at least every few years – conclusively proves that the Gaussian distribution does not provide an adequate model of financial returns, they argue.

Conceding that there is still a need for quantitative methods, the authors emphasise on the focus that tail events demand, because that is where the real damage occurs. Alternative approaches they suggest include the use of stable Paretian distributions, Bayesian statistics and fan charts.

“We also suggest that ‘litmus’ risk pathology tests become standard practice. These might be based on fuzzy logic (which would catch ‘fat’ tailed risks such as collateralised debt obligations), and Cauchy analysis (which would catch ‘long’ tailed risks such as credit default swaps. In addition, genuinely stressful stress tests should be carried out. All of these would give us worst-case estimates on which good risk management needs to be based.”

Cauchy approach

To those who find that discussion tough, here is a helpful snatch to elucidate the Cauchy approach: Imagine a rifleman with an infinitely powerful rifle, poised on a turntable ten feet from a wall of infinite length, the authors begin. Every minute his turntable is rotated and he fires a shot in a random direction, they continue. “Naturally, half the shots miss the wall altogether. The other half hit the wall, mostly close to the spot opposite the rifleman, but some are far away, and a few almost infinitely far away. After many shots, the probability distribution of bullet marks on the wall approaches a Cauchy distribution.”

What is striking about the Cauchy, as Dowd and Hutchinson instruct, is its long drawn out tails, implying that extreme losses are much more likely than under the Gaussian. Another property they highlight is that Cauchy could result not from a random walk but from a ‘random warp,’ with each step consisting of a jump through a science-fiction warp drive that could take you infinitely far across the universe but generally doesn’t. “Those with knowledge of stock market behaviour in turbulent periods can see that a ‘random warp’ is in many respects a better description of it in those periods than the conventional ‘random walk’ – the price jumps are not of approximately equal size but can be arbitrarily large.”

No stable laws

Assumption of ‘stable underlying laws’ is another hideous flaw in modern finance, the authors rue. Because, any social system is changing all the time, and the processes governing the operation of financial markets (and more generally, any social systems) are not immutable ‘laws’ comparable, say, to the laws of physics. “Indeed, in contrast to the hundreds of ‘laws’ that operate in the natural sciences, the only real quantitative law in quantitative finance is the law of one price – the ‘law’ that two securities or portfolios with the same payoffs should have the same value – and even this is often violated and holds only as a rough approximation.”

The act of modelling a financial process over time – such as the movement of a stock price – will often lead observers to react in ways that affect the process itself, Dowd and Hutchinson caution. An example they mention is that, if enough risk managers adopt a risk management strategy such as portfolio insurance, then that strategy will affect the stock price dynamics and so undermine the strategy itself. They warn, therefore, of the great danger of identifying spurious but superficially plausible patterns that are little more than accidental and have no serious predictive value.

‘Chartist’ professionals are not going to relish the opinion of the authors that “one of the many scams in finance is the cottage industry of self-described ‘technical analysts’ who claim to be able to detect the patterns in stock prices and profit from them.” Read on: “They treat the charts as some kind of Ouija board that magically reveals the secrets of the market. The trick is to identify the pattern – a ‘head and shoulders,’ a ‘reverse duck tail and pheasant,’ or whatever – and then use it to predict where prices are going. The patterns might be there, temporarily, but they are at best frustratingly ephemeral and, more often than not, exist only in the eye of the beholder…”

Behavioural obstacles

One other flaw of modern finance is the whole set of behavioural and institutional obstacles. Rather than being rational as economists would want to believe, we humans have a number of hard-wired brain impulses that override economic rationality, because of biological reasons and ‘because of our millennia hunting woolly mammoths and fending off attacks by sabre-toothed cats,’ the authors fret.

Examples of our internal hurdles include ‘confirmation bias’ (which causes us to overweight information that confirms our viewpoint), ‘availability bias’ (which causes the most recent information to be heaviest weighted), and ‘hindsight bias’ (by which we rewrite history to convince ourselves that ‘we always knew that’).

Human propensity to overconfidence can be major obstacle, too. Our natural state is to imagine ourselves more capable than we really are, imminently about to make the big breakthrough in our careers, able to forecast with more than usual accuracy which investments will do best for us, the authors describe. “While it is notoriously the case that most institutional investors fail to beat the averages over the very long term, it is inescapably the fact that most private investors do even worse, buying high, selling low, being absurdly prone to following fashion, and missing the performance of the stock averages by a substantial margin.”

In the authors’ reckoning, the only thing that prevents us from falling into terminal depression is that most of us are too lazy or poor at record-keeping to benchmark our performance properly against the indices.

Eminently educative read for the finance-avid.

**

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