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When Tim Harford published a second edition last year of his splendid book, The undercover economist, he added a chapter on the GFC. This week he’s made the chapter, Rotten eggs and rotten investments, available for free via download.

I’m always interested in the mis-use of statistics. I was struck by these paras (page 9) where he explains how investments that were thought to be ridiculously safe turned out to be incredibly dangerous.

To give you a sense of just how badly wrong the sums of the financial mathematicians became in reality, ponder the words of David Viniar, the Chief Financial Officer of Goldman Sachs. At the beginning of the credit crunch, he explained the sudden loss of 30 per cent of the value of a Goldman Sachs spin-off fund by saying, ‘We were seeing things that were 25-standard deviation moves, several days in a row.’

Viniar meant that Goldman Sachs had been unlucky. But just how unlucky, exactly? The financial economist Kevin Dowd has calculated that (given some reasonable assumptions) we’d expect to see three 25-standard deviation days in a row roughly once every

28,900,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000 000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000 years.

For reference, the universe is about 13,000,000,000 years old. Bad luck is not really an explanation. Somewhere, somehow, Goldman Sachs had got its sums wrong and then the inexorable complexity of the financial instruments it was dealing with magnified the error almost beyond comprehension.