Predicting the next crisis: what don’t we know we don’t know?

 

At next week’s World Economic Forum at Davos, a subject up for discussion at one of the many “interactive sessions” involving leaders from business and government is titled: Managing Fat Tails. Just as “shadow banking” evokes an aura of mystery and mirage, fat tails call to mind squat, repulsive geckos crouching in the naked white glare of a tube-light. And this horrid phrase is everywhere! Fat tails are the definitive answer to everything that went wrong in the financial world in 2007 (no doubt it feeds well into the current favoured view of the investment banker), and have even found favour among climatologists, political theorists, and wannabe philosophers. Everyone loves to talk fat tails.  

Fat tails refer to a phenomenon most of us studied in introductory statistics: positive excess kurtosis or leptokurtosis (not much prettier, evoking some sort of advanced arthritis). The entire set of possible outcomes of any scenario can be arranged by the probability with which each outcome can occur in the form of a probability distribution. The extreme ends of this distribution - representing events that are extremely unlikely – are referred to as tails. In a normal bell-shaped distribution – the kind that characterizes most outcomes, such as the toss of a coin (when Dhoni isn’t involved) or the adult height that a child will grow to – the tails are narrow and thin. The striking feature of the thin-tailed normal distribution is that the probability of an extreme event falls rapidly with respect to the actual magnitude of the event.  

Think about this as an example: the probability that a runner will break Usain Bolt’s 100 metre world record of 9.58 seconds is pretty low, making this an extreme event. However, if someone does manage to break the record, the margin by which he would break the record would be tiny, a fraction of a second – maybe 9.57. So the unlikely event is actually very marginally different from the more likely event. This is a feature of the normal distribution.  

In a fat-tailed distribution, by contrast, the tails are long and, well, fat. Neutrally described as leptokurtic, more casually as heavier-tailed and downright insultingly as fat-tailed: these distributions have become a catch-all explanation for the financial crisis. In such a distribution, the probability of an extreme event, or a tail event, falls slowly relative to the magnitude of the event. An extreme event will be just as unlikely to occur as earlier, but when it does, it has an enormous impact. With a fat-tailed distribution of world record sprint timings, for instance, the next person to break Usain Bolt’s record might snap it by 6 seconds. Impossible? Of course. Until it actually happens.  

The reason fat tails are so much in fashion these days is that it is now widely accepted that the financial crisis was an extreme event in a fat-tailed distribution of possible outcomes. It was so extreme so as to be barely possible, but when it did happen, it was huge. Former options trader-turned-modern day philosopher, Nassim Nicholas Taleb, argues in his best-selling book “The Black Swan: The Impact of the Highly Improbable”, that people, in general, are not equipped to comprehend very extreme events – until they happen. As such, financial system regulators, risk managers, traders and other finance professionals are never able to adequately prepare for what he refers to as black swan events – large events of near-impossible scale. Taleb reserves particularly colourful language for risk managers at large banks, referring to them, among other things, as imbeciles on his rather amateurish website.  

What he essentially tears into is the modern risk management system widely used in the financial sector for the last fifteen years. Most risk managers use a measure of risk called Value-at-Risk, or VaR, to capture the inherent riskiness of a portfolio or a trading desk or even an entire financial institution. The VaR is a seemingly elegant measure that uses historical data to capture risk in a single figure denominated in a currency. An investment portfolio with a VaR of $10million at a 99 per cent confidence level specifies that 99 per cent of the time, the portfolio will not lose more than $10million. So the VaR is another way of capping probable losses in non-extreme events.  

What the VaR doesn’t do, of course, is tell you how much you will actually end up losing in an extreme event. Another way of reading the above example is that $10million is the least you can lose on this portfolio in an extreme event of less than 1 per cent probability. If the extreme event does occur, you could lose $10billion. Or $100billion. Or $1trillion. With a less than 1 per cent probability, of course.  

In the last three years, plenty of holes have been poked into the VaR model: the use of non-representative historical data to build the model, the fact that traders learned how to game the system and so on. Yet, even if VaR is executed to the best of its ability, isn’t the use of the retrospective normal as a benchmark for the future blinding the world to the universe of adverse possibilities that can and do (and did) take place? Taleb certainly thinks so: he calls it “future-blindness”. His language is cringe-worthy: he refers to the world we normally live in as “Mediocristan”, whereas the extreme events that can take place inhabit “Extremistan”. Yet, there is a point in there somewhere: the average human is strikingly unfamiliar with the unprecedented.  

Oddly enough, a rather more scholarly post-financial crisis tome suggests that perhaps crises aren’t quite so unprecedented after all. Kenneth Rogoff and Carmen Reinhart, formerly of the IMF, have produced a minutely-detailed and intensely researched book – “This Time is Different: Eight Centuries of Financial Folly” – which looks at over eight hundred years of data on financial sector crises and the default of sovereigns on their debt. They seek to establish patterns leading to large sovereign default and they arrive at quite a few: serial default by countries takes place in waves, sometimes with individual episodes separated by years, even decades. Default often follows the rapid build-up of sovereign debt – whether domestic or foreign – and episodes of default are accompanied by high inflation and currency crashes. Finally, a high level of international capital mobility has historically led to a large number of private bank failures. In short, a crisis announces its impending arrival well before it actually shows up.  

So where does that leave us? According to Rogoff and Reinhart, governments can certainly do a better job of tracking warning signs in financial sector and macroeconomic indicators, and can also find the will to act preemptively. Yet, the extreme event may fundamentally be unpredictable: whether it’s the size of the next earthquake or the collapse of the global financial system. One of the more recent expositions of this dilemma came from that famed intellectual dynamo, Donald Rumsfeld. He got a lot of stick for this quote, but I think he captured the heart of a very real problem.  

“There are known knowns: there are things we know we know. We also know there are known unknowns: that is to say we know there are some things we do not know. But there are also unknown unknowns: the ones we don’t know we don’t know.  

How do you predict or even prepare for something you don’t know that you don’t know?