Leonard Tippet, an English statistician who worked for the British Cotton Industry Research Association. Whilst there, in the 1920’s and 1930’s, he clarified and worked on making cotton thread stronger, noting how a thread’s strength was controlled by its weakest fibres. Further work with the noted statistician Sir Ronald Fisher Tippett, saw Tippett describing the distributions of extremes assuming independent variables. This was codified into a Theory in 1958 by the eminent German mathematician Emil Gumbel.
In more modern times, the book ‘Extreme Value Theory: An introduction’ by Lauren de Haan & Ana Ferreira is not just an introduction but also a focus on theoretical results and applications. This is where the phrase ‘In Cauda Venenum’ popped out as it is the first sentence of the book. In case you Google it, it IS NOT the 13th studio album by Swedish progressive metal band Opeth, but the Latin for ‘…Poison in the Tail…’, aptly describing where the threat lies in assessing the markets using EVT as compared to VaR.
So…we know where it came from and have an idea of its meaning, though I would urge you to do more of your own independent study to learn further details. However, let’s now look at how it can be used, assuming that you’re not using it.
Well, in trying to study the data and impact of potential large market losses and the probability of their occurrence. Normal distribution, as laid out under VaR, does not happen. The issue is the fat-tail distribution in some extreme moves which affects all VaR assumptions. Now, EVT can be used to supplement VaR, not replace it, as VaR uses all the data for estimation…and most are central, falling short of the extremes because of scarcity. EVT allows techniques to concentrate on the behaviour of these extremes and the risks involved.
Yet with all this, EVT is seemingly still only a stepping stone, if a large one, towards further refinements or even jumps. One important issue, as outlined again by Younes Bensalah, was how ‘…these results apply well to the univariate case, the multivariate one seems to define the limits of this theory.’.
Thus, EVT can be seen as robust, using fewer strong assumptions, is justified by a body of mathematical theory and honestly reflects many of the uncertainties seen in rare events. It is also relatively quick and straightforward when applied to data compared to other methods. Yet it does not work well if you have limited datasets as it is dataset heavy. That is because it has been designed to deal with difficult questions, ones where information may be sparse…or non-existent!
I’ll finish with the words of Professor Jonathan Tawn, Professor of Statistics at Lancaster University and a leading researcher in EVT. He said ‘The key message is that EVT cannot do magic – but it can do a whole lot better than empirical curve-fitting and guesswork. My answer to the sceptics is that if people aren’t given well-founded methods like EVT, they’ll just use dubious ones instead.’.
Eddie Tofpik E:
eddie.tofpik@
admisi.com T: +44(0) 20 7716 8201
23 | ADMISI - The Ghost In The Machine | Q3 Edition 2021
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