BANK OF ENGLAND
Speech
Tails of the unexpected
Paper by Andrew G Haldane (and) Benjamin Nelson
Given at “The Credit Crisis Five Years On: Unpacking the Crisis”, conference held at the University of Edinburg Business School, 8-9 June
8 June 2012
...
But as Nassim Taleb reminded us, it is possible to be Fooled by Randomness (Taleb, 2001). For Taleb, the origin of this mistake was the ubiquity in economics and finance of a particular way of describing the distribution of possible real world outcomes. For non-nerds, this distribution is often called the bell-curve. For nerds, it is the normal distribution. For nerds who like to show-off, the distribution is Gaussian.
The normal distribution provides a beguilingly simple description of the world. Outcomes lie symmetrically around the mean, with a probability that steadily decays. It is well-known that repeated games of chance deliver random outcomes in line with this disbribution: tosses of a fair coin, sampling of coloured balls from a jam-jar, bets on a lottery number, games of paper/scissors/stone. Or have you been fooled by randomness?
In 2005, Takashi Hashiyama faced a dilemma. As CEO of Japanese electronics corporation Maspro Denkoh, he was selling the company's collection of Impressionist paintings, including pieces by Cézanne and van Gogh. But he was undecided between the two leading houses vying to host the aution, Christie's and Sotheby's. He left the decision to chance: the two houses would engage in a winner-take-all game of paper/scissors/stone.
Recognising it as a game of chance, Sotheby's randomly played “paper”. Christie's took a different tack. They employed two strategic game-theorists -- the 11-year old twin daughters of their international director Nicholas Maclean. The girls played “scissors”. This was no random choice. Knowing “stone” was the most obvious move, the girls expected their opponents to play “paper”. “Scissors” earned Christie's millions of dollars in commission.
As the girls recognised, paper/scissors/stone is no game of chance. Played repeatedly, its outcomes are far from normal. That is why many hundreds of complex algorithms have been developed by nerds (who like to show off) over the past 20 years. They aim to capture regularities in strategic decision-making, just like the twins. It is why, since 2002, there has been an annual international world championship organised by the World Rock-Paper-Scissors Society.
The interactions which generate non-normalities in children's games repeat themselves in real world systems -- natural, social, economic, financial. Where there is interaction, there is non-normality. But risks in real-world systems are no game. They can wreak havoc, from earthquakes and power outages, to depressions and financial crises. Failing to recognise those tail events -- being fooled by randomness -- risks catastrophic policy error.
So is economics and finance being fooled by randomness? And if so, how did that happened? That requires a little history.
(a) normality in physical systems
(b) normality in social systems
(c) normality in economic and financial systems
p.3
He [Galileo 17th century physical experiments] found that random errors were inevitable in instrumental observations. But these errors exhibited a distinctive pattern, a statistical regularity: small errors were more likely than large and were symmetric around the rule value.
p.3
This “reversion to the mean” was formalised in 1713 by Jacob Bernoulli based on a hypothetical experiment involving drawing coloured pebbles from a jam-jar.1
p.4
Gaussian world
It suggested regularities in random real-world data. Moreover, these patterns could be fully described by two simple metrics -- mean and variance.
p.5
English statistician Francis Galton
Galton's study of hereditary characteristics provided a human example of Bernoulli's reversion to the mean.
p.5
This semanic shift was significant.
p.5
In the 18th century, normality had been formalised. In the 19th century, it was socialised. The normal distribution was so-named because it had become the new norm.
pp.6-7
shifting from models of Classical determinism to statistical laws.
Evgeny Slutsky (1927) and Regnar Frisch (1933)
They divided the dynamics of the economy into two elements: an irregular random element or IMPULSE and a regular systematic element or PROPAGATION mechanism. This impulse/propagation paradigm remains the centerpiece of macro-economics to this day.
p.6
Tellingly, these tests were used as a diagnostic check on the adequacy of the model.
p.6
As in the natural sciences in the 19th century, far from being a convenient statistical assumption, normality had become an article of faith. Normality had been socialised.
p.6
Kenneth Arrow and Gerard Debreu (1954)
the world were assumed to have knownable probabilities.
Agents' behaviour was also assumed to be known.
allowed an explicit price to be put on risk, while ignoring uncertainty.
Risky (Arrow) securities could now be priced with statistical precision.
These contingent securities became the basic unit of today's asset pricing models.
p.7
Black and Scholes (1973) options-pricing formula, itself borrowed from statistical physics, is firmly rooted in normality.
p.7
finance theorists and practitioners had by the end of the 20th century evolved into fully paid-up members of the Gaussian sect.
p.7
1870s, German statistician Wilhelm Lexis
The natural world suddenly began to feel a little less normal.
p.8
In consequence, Laplace's central limit theorem may not apply to power law-distributed variables. There can be no “regression to the mean” if the mean is ill-defined and the variance unbounded. Indeed, means and variances may then tell us rather little about the statistical future. As a window on the world, they are broken. With fail tails, the future is subject to large unpredictable lurches -- what statistician call kurtosis.
p.8
Assuming the physical world is normal would lead to a massive under-estimation of natural catastrophe risk.
p.8
The central limit theorem is predicated on the assumption of independence of observations.
p.8
A comparably self-similar pattern is also found in the distribution of names, wealth, words, wars and book sales, among many other things (Gabaix, 2009).
p.9
for equities once every 8 years.
pp.9-10
Systems are systems precisely because they are INTERdependent.
p.10
(a) Non-Linear Dynamics
p.10
In 1963, American meteorologist Edward Lorenz was simulating runs of weather predictions on his computer. Returning from his coffee break, he discovered the new run looked completely different than the old one. He traced the difference to tiny rounding errors in the initial conditions. From this he concluded that non-linear dynamic systems, such as weather systems, exhibited an acute sensitivity to initial conditions. Chaos was born (Gleick, 1987).
p.10
Lorenz himself used this chaotic finding to reach a rather gloomy conclusion: forecasts of weather systems beyond a horizon of around two weeks were essentially worthless.
p.10
Reversion to the mean is a poor guide to the future, often because there may be no such thing as a fixed mean.
p.11
The accumulation of leverage was a key feature of the pre-crisis boom and subsequent bust. Leverage generates highly non-linear system-wide responses to changes in income and net worth (Thurner et al, 2010), the like of which would have been familiar to Lorenz.
p.11
(b) Self-Organised Criticality
p.12
(c) preferential attachment
p.12
Keynes viewed the process of forming expectations as more beauty pageant than super-computer (Keynes, 1936). Agents form their guess not on an objective evaluation of quality (Stephen Fry) but according to whom they think others might like (Kim Kardashian).
p.13
The classic example in finance is the Diamond and Dybvig (1983) bank run. If depositors believe others will run, so will they. Financial unpopularity then becomes infectious.
p.13
(d) Highly-Optimised Tolerance
p.13
features -- non-linearity, criticality [man-made, self-organized, hybrid], contagion
This is particularly so during crises [self-organized critical state?].
p.14
(a) non-normality in economics and finance
p.14
tell-tale signs of intellectual infatuation
p.14
Tipping points and phase transitions have been the name of the game. The disconnect between theory and reality has been stark.
p.14
In 1921, Frank Knight drew an important distinction between risk on the one hand and uncertainty on the other (Knight, 1921). Risk arises when the statistical distribution of the future can be calculated or is known. Uncertainty arises when this distribution is incalculable, perhaps unknown.
p.14
Hayek criticised economics in general, and economic policymakers in particular, for labouring under a “pretense of knowledge” (Hayek, 1974).
p.15
(b) non-normality and risk management
p.17
Now ask what happens if the actual, fat-tailed distribution of GDP over the past three centures [300-years] is used. Under the baseline calibration, this raises the required capital buffer four-fold to around 12%.
p.18
(c) non-normality and systemic risk
p.18
systemic oversight agency
able to monitor and potentially model the moving pieces of the financial system.
Financial System Oversight Council (FSOC) in the US,
European Systemic Risk Board (ESRB) in Europe,
Financial Policy Committee (FPC) in the UK
p.18
This map could provide a basis for risk management planning by individual financial firms. As in weather forecasting, the systemic risk regulator could provide early risk warnings to enable defensive actions to be taken.
p.18
And as in weather forecasting, it is important these data are captured in a common financial language to enable genuinely global maps to be drawn (Ali, Haldane and Nahai-Williamson, 2012).
p.19
Economics does not have the benefit of meteorologists' well-defined physical laws. But by combining empirically-motivated behavioural rules of thumb, and balance sheets constraints, it should be possible to begin constructing fledging models of system risk.13
p.19
Regulatory rules of the future will need to seek to reflect uncertainty.
p.19
Less is more (Gigerenzer and Brighton, 2008)
p.19
The reason less can be more is that complex rules are less robust to mistakes in specification. They are inherently fragile ([complex rules --> complex system --> subsystems are interdependent --> errors show up within interaction between the different specialized subsystems --> error prone (not if there is error, but when will the error show up, given the self-organising critical condition) --> ... --> fragility is baked into the cake ??? --> how-to do rescue & recovery planning when systems crash (refer to as After the crash, what to do) ]).
p.19
In retirement, [Harry] Markowitz instead used a much simpler equally-weighted asset approach. This, Markowitz believed, was a more robust way of navigating the fat-tailed uncertainties of investing returns (Benartzi and Thaler, 2001).
p.20
fail-safe against the risk of critical states emerging in complex systems, either in a self-organised manner or because of man-made intervention.
p.20
structural separation solutions
p.20
Under uncertainty, however, that is precisely the point. In a complex, uncertain environment, the only fail-safe way of protecting against systemic collapse is to act on the structure of the overall system, rather than the behaviour of each individual within it.
p.21
Until then, normal service is unlikely to resume.
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Mark Buchanan, book, “Ubiquity”
What Buchanan says is that many events in nature and the financial markets have event patterns defined more by power law probability distributions than by standard Gaussian bell curve distributions. This is what produces so-called fat tails. The way he describes it in the book is that fingers of instability build that individually could end in a market dislocation. If you think of a forest of trees, then the instability could lead to a forest fire. In markets, it leads to a market hiccup or melt-up. Now, when enough fingers of instability build up in nature, what happens is a catastrophe of unpredictable size and scope, an earthquake of 5.0 or 6.0 or 7.0 on the Richter scale or a forest fire of 100 acres or 1000 acres or 10,000 acres. The key here is that the fingers of instability come together to form a potentially catastrophic outcome that cannot be predicted in time or size but that varies in an exponential magnitude that is not consistent with a Gaussian distribution.
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