The Black Swan of Leicester

Last summer, London bookmakers were updating their odds list for the most outlandish possibilities. Cantankerous TV personality Simon Cowell to become Prime Minister: 500/1. The Loch Ness monster to be discovered: 500/1. Her Majesty the Queen to release a chart-topping hit that Christmas: 1000/1. Kim Kardashian to become US president: 2000/1. Elvis to be found alive and well: 2000/1.

But then the bookies took a more preposterous step; they offered 5000/1 odds that humble soccer team Leicester City, having barely escaped being relegated (i.e. unceremoniously dumped to the lower leagues) the season before, would win the English Premier League.

Now the English top-flight soccer league constitutes a pure plutocracy – the wealthiest clubs buy all the best players, and with neither annual draft nor salary cap to restore some semblance of parity, the top five teams won every title from 1996 to 2015. (To highlight the massive spending disparities at play, Sporting Intelligence notes that Manchester United spent more money on new players in the last two years than Leicester City did during its entire 132-year existence!) The club’s best goalscorer was playing non-league soccer and making medical splints to support himself three years earlier, and their journeyman coach faced derision in Italy as the man with “zero tituli” – no titles.

Then the unthinkable happened. Leicester City won or drew 92% of its games en route to claiming the Premier League title, as its far richer and more experienced competitors underperformed or wilted under the pressure. One commentator called their victory the “most unlikely feat in sports history,” and a Hollywood screenwriter is already at work to capture the fairy tale surrounding their striker’s meteoric rise. Of course, it’s not a happy ending for the bookmakers who lost about £10 million, the largest such sum in Premier League history.

As we lived through the Leicester City miracle this season, from 5000/1 odds back in August to their glorious victory this month, we couldn’t help thinking about black swans, the low-probability/high-impact events of the finance world. Just as bookmakers grossly underestimated the chances of Leicester City’s capturing the Premier League title – an analogue, Ipswich Town, had climbed just as quickly from third-division ignominy to top-division victory in 1962, making this miracle not without precedent — traditional financial models systemically under-predict the chances of extreme market moves across asset classes. This is because

(1) Models assuming normal distributions of events greatly underestimate extreme possibilities. We are all familiar with a normal distribution’s bell curve shape, comprised of a tall center to capture greater frequency of observations around the mean, and extrema rapidly tapering off to signify the relative improbability of events far from the mean. But financial market data, such as equity or foreign exchange rates, do not adhere to this shape – the bell curve shape overstates mean-proximate events and understates extreme events. Andrew Haldane, the Chief Economist of the Bank of England, said last year that “a four-standard deviation event – a true catastrophe – would under a normal distribution be expected to occur roughly every 15,000 years. Under the [best-fit] distributions for economic and financial systems, such an event would occur every 10 to 15 years.” No wonder massive financial swings happen so often and surprise so many!

(2) Models assuming normal distributions of events ignore the skew between upside and downside moves. While some asset classes demonstrate roughly equal sample populations of upside and downside extreme moves – e.g. monthly equity returns over the last three hundred years – others have significant skew. For instance, coffee has experienced 2-standard-deviation upward price shocks with measurably greater frequency than 2-standard-deviation downward price shocks, perhaps because both worsened growing conditions (falling supply) and increased popularity (rising demand) have caused sharp price increases much more regularly than their opposites have caused sharp declines. When pricing derivatives for this and other analogous assets, a normal distribution would assume that downward price shocks are just as severe and frequent as upward price shocks – this can be an extremely costly mistake.

(3) Models assuming static dependencies neglect the changing correlative relationships among assets across time. Hedgers with dozens of currency or commodity exposures should certainly consider cross-asset correlations in determining optimal hedges. However, models that assume static dependency among assets don’t precisely reflect the dynamic nature of correlative relationships. For instance, in the two-year period between the beginning of 2013 and the end of 2014, the historical correlation between the euro and the Brazilian real swung from +0.3 to -0.3. Analysis from the beginning of the period, assuming the two currencies moved together, would almost certainly recommend different hedges from analysis at the end of the period, which would assume they moved in opposition.

Traditional risk models based on a normal distribution of rates and static correlations can greatly underestimate extreme events. While not all of us have to decide the likelihood of Elvis showing up alive and well, or of a Kardashian redecorating the White House, we do have low-probability/high-impact events we need to understand, assess, and quantify. If you’d like to discuss the extreme disrupters pertinent to you, please give us a call.