Fat-tailed statements

Goldman deviates back to bad old standard

Goldman Sachs is deviating back to a bad old standard. On January 16, Finance Chief Harvey Schwartz described the Swiss currency mess as "something like a 20-plus standard deviation move." That's a daft assessment devoid of any practical use. He's not the first Wall Street executive to trip up on such a statement. In fact, his own predecessor, David Viniar, was similarly soft-headed when describing the storm in the markets in 2007.

Viniar talked of "25 standard deviation events, several days in a row." Let's put that in context. A seven standard deviation event is only supposed to occur once every 3.1 billion years, according to the 2008 research paper "How Unlucky is 25-Sigma?" written by several British and Irish academics.

A 20 standard deviation event, meanwhile, explain academics Kevin Dowd, John Cotter, Chris Humphrey and Margaret Woods, "corresponds to an expected occurrence period measured in years that is 10 times larger than the higher of the estimates of the number of particles in the Universe." As for Viniar's assertion, it would require that the "decimal point moved 52 places to the left!"

Using such terms to describe market movements might sound clever. But it actually exposes wrong-headed thinking on risk management. Schwartz, for example, was basing his 20-plus standard deviation estimate on the overall volatility of the Swiss franc being around 2 per cent during the three-plus year life of the peg. Last Thursday's 30 per cent shift in the value of the franc against the euro may well fit that.

But the franc was far more volatile before the peg was introduced. Granted, the Swiss National Bank had called the peg a cornerstone of its policy days before ditching it. Risk managers, though, should be looking beyond three years of supine stats: the chance of the peg ending may have been low, but the pre-2011 numbers showed that the event risk was high.

It's a similar story with other measures like value-at-risk. This relies on data either from the past one, three or five years, depending on the whim of the firm. In any event, it means that the more stable the environment becomes over time, the less the model is going to expect a problem. That path can lead to taking excessive risks - an impression Schwartz and other executives would be wise to avoid giving.