Tail Events: SCOPE

What Are Tail Events?

Pascal vander StraetenMarcus Evans Conference – Tail Risk Management; 22 – 23 October 2015 Chicago

Definition of Tail Event• From time to time, something occurs which is outside the

range of what is normally expected. • A tail event is an outcome which, from the perspective of

the frequency of historical events or perhaps only from intuition, should happen only once in a thousand or million or centillion years.

• Momentous tail events were the detonation of the first atomic weapon over Hiroshima in 1945, the sharp rise in oil prices in 1973, the 23 percent fall in stock prices in October 19, 1987, the destruction of the World Trade Towers in 2001, and the collapse of the world financial system in 2007- 08.

Tail events in the statistical world

• Low-probability, high-consequence events can dominate the impacts and societal concerns for many issues, of which climate change is a signal example. This is the problem known as “fat tails.”

• To illustrate the problem of fat tails, it is helpful to first picture a probability distribution such as the common “bell curve” or normal distribution. The normal distribution has most observations clustering around the center, with few showing highly divergent results.

Tail events in literature: Black Swan• The black swan theory or theory of black swan events is a metaphor that

describes an event that comes as a surprise, has a major effect, and is often inappropriately rationalized after the fact with the benefit of hindsight.

• The theory was developed by Nassim Nicholas Taleb to explain:

• The disproportionate role of high-profile, hard-to-predict, and rare events that are beyond the realm of normal expectations in history, science, finance, and technology.

• The non-computability of the probability of the consequential rare events using scientific methods (owing to the very nature of small probabilities).

• The psychological biases that blind people, both individually and collectively, to uncertainty and to a rare event's massive role in historical affairs.

Understanding uncertainty and risk, and industry applications

• Risk: We don’t know what is going to happen next, but we do know what the distribution looks like.

• Uncertainty: We don’t know what is going to happen next, and we do not know what the possible distribution looks like.

• The future is always unknown — but that does not make it “uncertain.” Risk is different from uncertainty where “risk” to describe cases of known probability.

• Uncertainty is when you don’t know the probabilities. John Maynard Keynes used the example of a company considering an investment in a copper smelter which could last years and years. The company has no good idea what the price of copper will be in 20 years, nor is it certain what is the probability of different possible prices.

Confusion between crash, volatility, and tail events

• The study of tail events has become a central preoccupation for academics, investors and policy makers, given the recent financial tur- moil. However, what differentiates a crash from a tail event?

• Defining a tail event is straightforward. Indeed, it corresponds to any return located in the tails of the distribution; an adverse tail event represents an negative extreme return for a long position and a positive extreme return for a short position. In addition, if a crash (anti-crash) corresponds to a negative (positive) extreme return, the reverse is not true. Indeed, the largest negative return during a bullish period will surely not be a crash; for example, the minimal return of the S&P 500 stock index during year 1999 is -2.85%.

Are Tail Events Really Unknown Unknowns

Known unknowns and unknown unknowns

• There are known knowns. There are things we know that we know.

• There are known unknowns. That is to say, there are things that we now know we don't know.

• But there are also unknown unknowns. There are things we do not know we don't know.

• => the discovery of a previously unknown unknown shows us how little we know and leads to the propagation of a family of known unknowns which can then be tackled by traditional hypothesis forming and testing, occasionally throwing-up another unknown unknown, and so the cycle continues.

Causes for tail events

• We look at four of the most standard causes for the occurrence of tail risks:

• 1. The phenomenon of “unknown unknowns” relatively rarely triggers tail risk events. Many events simply are without precedent, undercutting the basis of this type of reasoning altogether. It can only relate to very new financial instruments (e.g. exotic derivatives), of which the behavior could be less known to market participants.

• 2. In many extreme events in different areas of human activity have been triggered by coincidence of multiple non-critical errors. A relatively recent example in the financial world is the failure of RBS’ payment system, which led to around 750,000 bank customers being unable to use their credit and debit cards.

• 3. Reckless behavior was and still remains the source of many extreme events.

• An accident triggered by a deliberate human error, such as the Chernobyl disaster (24 April 1986)

• In other words, the operators understood that they were breaking the operation rules. In the financial industry, the most notorious examples of such extreme event causes are cases of “rogue” trading or large scale frauds (e.g. Nik Leeson and Barings Bank, Bernard Madoff, Jerome Kerviel and SocGen, etc.).

• 4. Strategic mistakes are often the primary causes of tail risk events, yet it is difficult to spot this error and for many years they remained under cover until by unfortunate coincidence these mistakes became apparent.

• The Fukushima Daiichi nuclear disaster (Ōkuma, Fukushima, Japan), the second largest nuclear accident after Chernobyl (also level 7 on the International Nuclear Event Scale), revealed a case of when a strategic mistake triggered a failure of crucial systems which in turn led to an extreme disaster.

• On 11 March 2011, the plant was hit by a tsunami and the subsequent failure of the emergency cooling system caused the explosion. The fundamental cause of the accident was a string of strategic mistakes in both the plant location and its design.

• Interestingly, strategic mistakes are the most common cause of extreme events in the financial sector. Many remarkable banks’ failures came as a direct result of strategic mistakes made by the banks’ bosses (e.g. UBS, AIG, Northern Rock, HBOS, RBS, Dexia, Wachovia, etc.).

• This classification of the four key underlying causes of extreme risk events not only helps to better understand the nature of tail risk, but also gives us clues on how we can prevent extreme risk events going forward. Only the first category – cases stemming from unknown unknowns – is entirely unavoidable. We cannot fully protect ourselves from threats that we do not know. It will always remain an unavoidable evil.

• Yet, the other three categories can be preventable. Errors and failures of different elements of the system (isolated or simultaneous) are definitely preventable. Human reckless behaviour and the violation of the existing rules and common sense can also and must be preventable via the strict governance and comprehensive control of all key activities that have extreme risk-linked exposure.

• Strategic mistakes, albeit representing possibly the largest challenge, still remain preventable in theory. While this category is also linked to human errors, these errors are not as obvious as those in the previous category when people knowingly violate regulation requirements, internal instructions or safety rules.

• The problem with strategic failures is that it can take many years before these mistakes surface and become apparent. Moreover, quite often an inherently dangerous strategy, once accepted by the organisation, starts shaping the employees’ behaviour.

• This risky strategy translates to firm’s instructions, business plans, employees’ incentives and business culture. That is why for people inside the organisation, it is almost impossible to spot the strategic error well before it triggers the extreme event.

Tail events and (un)expected losses• The typical loss profile from financial risk contains occasional

extreme losses among frequent events of low loss severity. Hence, firms categorize operational risk losses into expected losses (EL), which are absorbed by net profit, and unexpected losses (UL), which are covered by risk reserves through core capital and/or hedging.

• The expected loss represents a loss that arises from the daily business, while the unexpected loss is the number of standard deviations away from the expected loss (the tail of the distribution). Expected losses are typically covered through ratings (PD) as well as LGD (provisions), while unexpected losses are merely covered by capital.

• While firms should generate enough expected revenues to support a net margin after accounting for the expected component of financial risk from predictable failures & defaults, they also need to provision sufficient economic capital to cover the unexpected component.

• the unexpected loss is calibrated at the 99.95% confidence level, which corresponds to an 'AA' rating, meaning that this is variously expressed as a risk of defaulting once in 2,000 years or, alternatively, as one in 2,000 AA rated banks defaulting in any given year. Obviously, this is based on statistics, and by definition that are mirror-based looking and not forward looking. Therefore, banks calibrate their economic capital models according to the managements risk appetite, which is usually in line with the bank's target rating.

• Now, where the banks still get it wrong on unexpected losses is the fact that first of all the confidence interval is based on a normal distribution, whereas extreme (tail risk) events are NOT based on a normal distribution.

• Secondly, and subsequently, they use that system to calibrate their business model in such a way to reach a let's say AA rating (still under a normal distribution with a couple of standard deviations from the average). Economic capital is set based on high probability events, while it should also encompass low probability (high severity) events mirrored by the recent GFC, or the upcoming deflation scenario in Europe, or collapse of China's house of cards.

• Under the current existing economic capital rules, unexpected losses measure the variability around expected losses. And, the level of economic capital implies a probability of capital exhaustion and an associated debt rating. Given the portfolio loss distribution and a target debt rating, the required economic capital may be inferred.

How to deal with unknowns?

• The known unknowns and unknown unknowns in your organization differ from person to person. Getting people together to share information and make joint decisions is the best way to deal with the unknown.

• Thus, the key is to identify tail events as a specific risk domain, collect and share information about it, and come up with collective decisions and actions.