Tales of the unexpected: understanding risk at the extremes

Business as usual is the normal state affairs, and the world that managers and policymakers operate within most of the time. Occasionally, however, that world is shaken by unforeseen extreme events, from stock market crashes to earthquakes.

Valérie Chavez-Demoulin’s work helps to provide a better understanding of these extreme events, and in doing so brings more certainty to the apparently improbable.

Extremes are important in business and society. Most of the time events fall within a reasonably predictable margin – the bulge on the Bell curve – and the normal rules apply. Retailers have sufficient inventory to meet demand, the weather is benign enough for people to pursue their daily routines, markets trade, businesses operate, and societies function as usual.

Helping to make the unlikely more predictable

Occasionally, however, the unexpected happens, an event at the tail of the normal distribution, an outlier at the margins of probability. Due to their unpredictability these extreme events have the potential to cause significant damage and loss, to business and society. That is why Valérie Chavez-Demoulin has spent over a decade researching these extreme events, adding to our knowledge of Extreme Value Theory (EVT), modelling the risk of these extremes occurring, and helping to make the unlikely more predictable, the unknown more certain, the extremes less unexpected.

While isolated extreme events may be discounted by executives making business decisions, they have not been ignored by researchers. A specialized field of research focuses on events in the tail and has led to two established approaches for identifying and evaluating the risk of extreme events occurring using probability distributions with names like generalized extreme value, and generalized Pareto.

One approach looks at blocks of data and, in particular, the isolated maximum values within that data. Another, Peaks-over Threshold, sets a threshold – high or low – and examines the data points that lie above or below the threshold assessing both frequency and size of the extreme events outside the threshold.

Seasonality, trends, dependence on external factors, and regime changes are the rule

Neither method is ideal in practice, however. One drawback is that they are based on the principle that the statistical properties of the data – the time series – being assessed are constant, or stationary, over time. But this stationary element is absent in many data time series. Instead seasonality, trends, dependence on external factors, and regime changes where there is a switch from one prevailing context or state to another, such as pre and post corporate merger, are the rule, rather than the exception, and must be taken into account when modelling extremes.

Take product demand. The weather may affect product demand; a spike in demand for soup during a period of very cold weather, or for ice cream on hot days. Furthermore, there may be other variables that affect the incidence of extreme events –in the case of ice cream demand, holidays or public events, for example.

Chavez-Demoulin has taken the classic approach to considering extreme values in EVT and adapted it. She demonstrates through backtesting – applying her methodology to a known set of data – that her approach can provide a more accurate perspective on a number of extreme value related topics. These are discussed in several of her papers.

Finance is one sector where Chavez-Demoulin’s methodology has obvious application. In banking, the Basel Accord’s regulatory framework requires banks to calculate minimum capital requirements as a buffer to protect the bank and its stakeholders in the event of an extreme loss. The banks use the risk measure concept of Value-at-Risk (VaR) in estimating the probability and size of any extreme loss. However, using a backtesting study for the UBS share price over the subprime crisis, Chavez-Demoulin shows how her Extreme Value Theory methodology estimates these risk measures more accurately. She also shows how her approach to EVT can be used to predict the probability of extreme movements in share price and corporate failure, using the example of Swissair.

Elsewhere, Chavez-Demoulin has investigated the application of EVT to operations. Take supply chain management, for example. Supply chain managers tend to assume everything will work within the normal range of outcomes, and tend not to allow for extremes when making supply chain decisions. However, Chavez-Demoulin demonstrates that a good understanding of extreme value probabilities can improve operations.

Catastrophic response to excess inventory is predictable

We know, for example, that supply chain glitches, such as excess inventory announcements, may normally be expected to cause a five to ten per cent knock-on reduction in share price. Yet, when mobiles firm Nokia suffered an excess inventory problem in 1995, subsequent associated profit warnings led to share price falls of 28 per cent and 50 per cent in the space of a few weeks. As Chavez-Demoulin demonstrates, albeit rare, catastrophic response to excess inventory is predictable by EVT and should be considered by managers assessing the potential impact of supply chain problems on share price.

In another example Chavez-Demoulin highlights how, on closer examination, intuitive expectations about peak demand can turn out to be misplaced. For instance, the general assumption is that standard products have a more manageable demand distribution, whereas demand for customized products is difficult to forecast. Chavez-Demoulin uses a case involving standard and tailor made messenger bags to confound our expectations, demonstrating that domestic demand may be far from normally distributed, with existing production and stocking strategies not allowing the firm in question to meet potentially profitable demand spikes. Whereas predicted demand peaks for tailor made products may be catered for by existing production and stocking strategies.

Chavez-Demoulin’s methodology is useful in any area where risk matters

Chavez-Demoulin’s work on EVT is game changing. It allows risk managers to identify changes in context that create clusters of extreme events. By analysing the past it can predict the probability of extreme events happening in the future, even if those specific events have not been observed in the past. For practitioners and policymakers, Chavez-Demoulin’s methodology is useful in any area where risk matters. It can be applied to finance, climatology, atmospheric chemistry, medicine, used to look at share price movements, flood heights, earthquake incidence, product demand, and many, many, other risks and events.

Perhaps most importantly, however, Chavez-Demoulin’s work teaches us that where we believe, intuitively or otherwise, that we have accounted for and mitigated the potential impact of significant adverse events, this is often not the case. We are laboring under a false sense of security. The world is a lot more uncertain than it appears – that is something we really can be certain of.

Read some significant research papers on this topic:

  • Chavez-Demoulin V., Embrechts P. & Sardy S. (2014). Extreme-quantile tracking for financial time series. Journal of Econometrics, 181(1), 44-52
  • Chavez-Demoulin V. & Davison A. C. (2012). Modelling time series extremes. REVSTAT – Statistical Journal, 10(1), 109-133
  • Chavez-Demoulin V. Embrechts P. Hofert M. (in press). An extreme value approach for modeling Operational Risk losses depending on covariates. Journal of Risk and Insurance.

Featured image by P K / Flickr CC (recolored and zoomed in)