Earlier this week, Andrew Haldane, the Bank of England’s director for financial stability gave a speech to the Marcus-Evans Conference on stress testing.
While that doesn’t exactly sound particularly enticing, it was. And we’d recommend that you read this – the paper Haldane has authored based on his speech. It’s entertaining and fascinating – and what it really very clearly shows is just what a blinkered world modern finance operates in.
Risk managers are of course known for their pessimistic streak. Back in August 2007, the Chief Financial Officer of Goldman Sachs, David Viniar, commented to the Financial Times:
“We are seeing things that were 25-standard deviation moves, several days in a row”
To provide some context, assuming a normal distribution, a 7.26-sigma daily loss would be expected to occur once every 13.7 billion or so years. That is roughly the estimated age of the universe. A 25-sigma event would be expected to occur once every 6 x 10124 lives of the universe. That is quite a lot of human histories.
When I tried to calculate the probability of a 25-sigma event occurring on several successive days, the lights visibly dimmed over London and, in a scene reminiscent of that Little Britain sketch, the computer said “No”.
As Haldane notes, there is a simpler, non-space-time judged, explanation. Those standard deviation models were wrong. “They failed Keynes’ test”, says Haldane. That is, it’s better to be roughly right, than precisely wrong.
And so - probably wittingly, but without mentioning it - Haldane turns to another Keynes trope: the long run. (In which, pace Keynes, we are all dead).
How does the current “golden decade” compare to the historical performance of the economy? Here’s the GDP variance:
And here’s unemployment:
Ahistorical times, we have been living in.
And to put that in financial market terms:
For financial time-series, small sample problems are even more acute, especially for events in the tail of the distribution. Measures of kurtosis – the fatness of the tails – of UK house price inflation are 6 times larger over the full sample than over the Golden Decade; for UK bond yields 10 times larger; and for UK equity returns 16 times larger. If we assumed the Golden Era distribution was the true one, the three worst monthly returns in history – the bursting of the South Sea bubble in September and October 1720, and Black Monday in October 1987 – would have been respectively 12.7, 6.9 and 6.5-sigma events. All three would have appeared to be once in a lifetime – of the universe – events.
In other words, is it any wonder that any model, which takes historical data from the past ten years only – or as a great part of its time series – is deeply, deeply flawed. Little wonder than that almost all credit models are very very susceptible to black swan events: they are based on time series that are simply too short.
Take the CDS markets – historical data on CDS indices only exists in any relaible form for the past five years or so. And while modellers have sought (imperfect) proxies, such as broader, broker-calculated bond indices, even those only have 20 year historical timeframes, in the best cases.
Francis Fukuyama pronounced in 1992 that we had reached “the end of history“. While he was talking in a political-sociological sense, what’s astounding is that markets seemed to believe the same too. For the past 10 – if not more – years, the world’s developed economies have too been labouring under the delusion that history was dead.
Turns out, surprisingly, it’s not.