How to lose $10m a second

Bell curves are everywhere in the analysis of data but the system is fundamentally flawed - as stock-market investors find to their cost, Robert Matthews writes.

Hanergy Holding Group boss Li Hejun losing half of his wealth in a day. Song Fan / Image China

At sunrise one day last month, solar energy magnate Li Hejun was the richest man in China, worth an estimated US$30 billion (Dh110bn). By the time the Sun had set that day, he had a less desirable title: the biggest and fastest loser in history.

In the final 30 minutes of trading on the Hong Kong stock exchange, confidence in one of his companies – Hanergy Thin Film Power Group – collapsed, taking almost half his personal fortune with it.

Mr Li’s net worth that day vanished at the rate of about $10m a second.

He wasn’t alone. Kowloon property and electronics tycoon Pan Sutong lost a similar amount last month.

Both billionaires have seen their wealth skyrocket in recent months, only to collapse with even greater alacrity.

Welcome to the terrifying rollercoaster of the Chinese financial markets.

These latest white-knuckle rides have been described using the standard gambling metaphors. One commentator described investing in Chinese enterprises as “a crap-shoot”, while another claimed “it’s as unpredictable as a casino”.

The same response greets such gyrations across the world, from bursting market bubbles to “flash crashes” where computer algorithms set off plunges and surges in stock prices. Yet they are all hopelessly wide of the mark. Financial markets are not remotely like casinos. History has shown repeatedly that they are far riskier than that.

Indeed, the gambling metaphors are symptomatic of a delusion that’s persisted for decades – one underpinned by one of the most potent discoveries yet made about chance events.

Known as the Central Limit Theorem, it rarely attracts attention outside the academic world. Yet it has led to a much better-known concept worming its way into a host of fields where it has wreaked untold harm: the bell curve.

The origins of both lie in the first efforts by mathematicians to get to grips with the workings of blind luck. During the 17th century, they found themselves being asked for advice by professional gamblers about when to accept a bet.

This demanded careful study of the outcomes of dice and card games and spawned one of the most useful branches of maths: probability theory.

The sums involved were often subtle and complex and sometimes defeated even the ablest mathematicians. Fortunately, one of them – French-born Abraham de Moivre – found a formula that spat out results for large numbers of random events all working together.

When plotted out on graph paper, de Moivre’s formula gave a beautiful, bell-shaped curve, with a central peak and graceful slopes to either side.

The eponymous curve reflected the fact that collections of random events – such as coin tosses – have a “most likely” outcome (in this case, half of the tosses producing heads or tails). The slopes, meanwhile, gave the progressively less likely outcomes, culminating in every toss giving only heads, or only tails.

All this was immensely useful but in 1812 mathematician Pierre-Simon de Laplace unveiled an astonishing discovery about the bell curve: it didn’t just

apply to things such as coin tosses or dice throws. The Frenchman proved that any phenomenon that is the sum total of many random influences acting independently will follow a bell curve.

The idea that even a vestige of order can emerge from a grab bag of random influences defied belief, and not even Laplace recognised the significance of his discovery. Even today its bland title of “the Central Limit Theorem” belies its power. Yet when researchers began looking for bell curves in real-life data, they found them everywhere.

Its ubiquity led to researchers calling the bell curve “the normal distribution”. Its ability to bring mathematical precision to so many phenomena overwhelmed qualms about its validity.

Yet like all mathematical results, the curve came with terms and conditions crystallised in Laplace’s Central Limit Theorem. If breached, these insights based on the bell curve might prove hopelessly misleading.

For example, it seems reasonable to assume human height is the cumulative effect of lots of influences. Can the same be said of other phenomena claimed to follow a bell curve – like stock price movements?

The idea that stock prices follow the normal distribution has been around for decades. It is widely used in calculations of financial risk and underpins the pricing of all kinds of assets.

It’s also long been known to be fundamentally flawed.

The reason is obvious to anyone who has lived through a financial crash. Once market confidence is shaken, prices move en masse. This flies in the face of the fundamental assumption of the Central Limit Theorem: that the underlying influences act independently – any risk estimate based on bell curves will be hopelessly unreliable.

This is not just a theoretical possibility. Ever since the credit crunch of 2007, bell curve estimates of market risks have repeatedly proved far too optimistic. Price movements predicted to occur every few billion years have struck several times in a matter of days.

Yet, incredibly, the bell curve continues to be used by everyone to estimate risks.

Warnings about the dangers of assuming everything is “normal” have been sounded ever since the term first started to emerge more than a century ago but, still, the disconnect with reality persists – reflected in the constant refrain that stock markets “are like casinos”.

Whether the two Chinese billionaires will ever recoup their fortunes remains to be seen. Whatever happens, the lesson for every investor is clear: the terms and conditions in Laplace’s dangerous discovery are at least as important as those buried in the prospectus.

Robert Matthews is Visiting Reader in Science at Aston University, Birmingham