Sunday, January 1, 2012

Value Put at Risk by Severe Math-Phobia: A Review of "The Number That Killed Us" by Pablo Triana



Walking past Zuccotti Park the other week I was thrilled to see a placard reading "End Regulatory Capture". At last, I thought to myself, the academic research and its verbiage has made its way into the public consciousness. I was inspired by the power of language. Any passerby could see that sign and within fifteen minutes of Googling on their phone, unearth roughly as much dirt on the financial sector, and its regulation, as Pablo Triana has presented in his new book "The Number that Killed Us".

Of course that sign was mere fantasy on my part so, whatever the flaws of this latest effort, kudos to Triana for choosing a catchy title and keeping cosy financial regulation in the headlines. In fact one of the most sympathetic parts of the book is Triana's recounting of an oversight hearing held for the House Committee on Science and Technology on the topic of Value at Risk. Triana bemoans the empty chairs at this would be rock concert, a testament to waning public interest in even his anti-VAR super-hero Nassim Taleb. Does anyone care anymore?

What taints The Number That Killed Us however is a new kind of anti-mathematical slant, one championed by Triana's mentor Taleb and taken to extremes in Triana's previous book. Wearing 1-d anti-Platonic glasses doesn't help distinguish methodology from policy or history from causality so, for example, while VAR requirements could certainly be more stringent, ad-hoc rules can also be more lenient ... and in another world we might be talking how their arbitrariness caused a crisis. Triana makes a case for better capitalized financial institutions and that section of the book is the most readable, but Triana's real beef is not collusion or policy but a language he is largely unfamiliar with, mathematics. The link is strained and it makes for some odd suppositions (to a practitioner) like the fact that bankers are prone to worshiping the arcane, or inclined to bend on one knee in the presence of a mathematical formula. The weight of this accusation rests, it would seem, on some research by a Berkeley Ph.D. candidate as yet unpublished. I await further details with interest.
 
Value at Risk can mean different things. Taken literally it is a mere definition: a single number representing, or rather failing to represent, a distribution of potential losses. That distribution might arise as the output of a probabilistic model, or it might be a naive empirical estimate based on historical profit and loss fluctuations. Either way, a single threshold number (such as $130 million) is said to be the Value at Risk for a specified probability (say 5% for illustration) if there is a 95% chance, according to the model, that losses will not exceed said threshold. 


To save you looking up Wikipedia ...
Courtesy of Wikipedia

One can take issue with the information loss implicit in this definition, but how upper management chooses to consume summary data is beside the point. The real controversy surrounds the means by which the distribution of losses is modeled. In caricature pop-finance, of the variety peddled by Taleb, this amounts to choosing a univariate distribution from the shelf and - oops - the wrong one. I trust it is evident from the definition of Value at Risk, however, that the Normal distribution need have nothing to do with it. The Value at Risk/Bell Curve conflation is the most successful confusion of terms since 'Iraq' and '9/11'.

To his credit Triana cleans that up a little too, attempting an explanation of how Value at Risk was computed for some people using the RiskMetrics framework. Therein a multivariate Gaussian assumption can be made, and often is, so we expect it hides the weapons of mass destruction. Thing is though, a little more digging in the technical documentation provided by the very same vendor would have revealed stern warnings about the limitation and interpretation of the results, including suggestions for dealing with non-linear payoffs and non-gaussian distributions. It was evidently not the propeller heads who failed to notice fat tails, and what Triana misses is the real story of the crisis: the extremely limited bandwidth for communicating technical information to upper management, and a scornful, impatient attitude toward anything remotely theoretical.

The calculation of firmwide Value at Risk was a complicated undertaking in several respects, influenced by front office/back office politics and, at least in this reviewers's experience, a contempt for mathematical tools extending to the valuation of what were, in reality, complex options. Trading desks who lost the most during the crisis were claiming to manage risk in mortgage backed securities but many eschewed any kind of probabilistic approach, preferring to use a small number of scenarios and their famous 'gut instinct'. So the numbers feeding into firmwide risk were not coming from a mathematical model at all, and even if they involved historical estimates of profit and loss fluctuations, those very same estimates were never honestly attempted. That reality, which many quants fought hard to change, makes a mockery of Triana's underlying thesis: that the language in which we communicate probabilistic information is to blame.

To Triana mathematics is complex and life (including global finance) is simple. One doesn't fit the other, therefore, and you couldn't hope for a more populist, simplistic argument outside of a Republican primary debate.  "Before VAR showed up", Triana writes, "financial risk management was a simple affair." It is an opinion the author states many times, with gusto, but is it true that "the rules respected the simplicity of it all"? Did those good old rules see "reality for what it was, not for what it should be"? It is a tough argument to make, not that Triana feels any obligation to do so. Save for some crass categorical distinctions the "good old rules" assign the very same capital to a risky loan as a safe one.

For the author, winding back the clock is the only solution but was there ever a golden era for risk management, or finance? There were certainly periods where the financial sector was smaller, as Triana is right to point out, but demographics of companies were different. The fact that more companies have access to finance than they once did (provided they can argue for potential future earnings) is not a bad thing.  Distortion of retail lending via housing policy is another matter, granted, but that has little to do with VAR. There are many hidden costs to keeping financial regulation brain-dead simple just for the sake of it, just as there are many games created by overly simple rating procedures that eschew the quantitative tools used by banks.

The notion that finance is trivial is ultimately a contemptible position, almost as contemptible as pronouncements on the inability of other people to solve difficult problems. Life is, one dares to suggest, complex. The challenges of risk transfer, capital allocation and investment are complex. Mathematics on the other hand, is neither complex nor simple, any more than the attribute might be assigned to English. It is tool for building relatively simple calculators and metrics, and can also be used to build more sophisticated technology threatening the margins of Wall Street.  How technology is used is a matter of education, culture and respect for careful, rational inquiry devoid of 1950's style, anti-intellectual overtones.

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