Saturday, January 28, 2012

A Response to Bob Jarrow's Regulatory Recommendations

This note is prompted by a short technical report written by Robert Jarrow on January 26, 2012 and announced by his company Kamakura in this press release. The press release states that
  
            "life insurance economics and credit default swap economics are essentially identical"

The paper is intended to influence regulators (as are the other responses to the Federal reserve proposal for risk-based capital guidelines). Professor Jarrow's main beef in the paper is the use of credit default swaps as a gauge for company default probabilities. 
“Surprisingly, when discussing corporate or sovereign default probabilities, the common belief is almost the reverse. For some unknown reason, it is believed that implied default probabilities from CDS spreads provide reliable estimates. This paper shows that this common belief regarding implied default probabilities is false.”
The paper shows no such thing and, while it illustrates some important if well known concepts, I shall argue that the financial system will undoubtedly collapse again if regulators accept Professor Jarrow's argument uncritically. Before we get to that, however, a pre-emptive clarification might be in order:

The location of this response (in a frequently flippant, sporadically thrown together blog about pseudoscience in finance) does not in any way suggest a dismissive attitude to Professor Jarrow's issue and certainly not the man or his company. On the contrary I lend support to his more generic point: loose interpretation of probabilistic categories is dangerous and, I will argue below, a major contributor to the financial crisis. Also, I hope it goes without saying that I applaud and respect the author's commercial and intellectual contributions. The fact that I respond in this locale reflects purely on my own time constraints and the fact I don't have a "serious" blog. (As a further aside, I started this blog on a whim because Pablo Triana insulted my entire profession, then me personally and, rather cowardly, didn't allow comments on his page by which I might otherwise have responded). 

                                      A response to Jarrow's argument

I believe those of us in the vendor community should be forthright when talking our book. Your blogger sells real-time market prices for bonds and credit default swaps. Professor Jarrow's company sells probabilities of default that are derived from sources other than credit default swaps and bonds. He has incentive to downplay the importance of credit markets in an assessment of the credit of a company. I have incentive to argue otherwise, and I shall.

Professor Jarrow argues that the use of credit default swaps is "laden with difficulties", and that these difficulties are exposed, in part, using a simple analogy to life insurance premiums. It is absurd, argues Jarrow, to assess life expectancy using only market-implied probabilities inferred from life insurance premiums themselves. To do so ignores self-evident facts ranging from inefficiency of the retail insurance market to capital requirements of the insurance company itself. I agree and it is fair to say there are analogous difficulties in the interpretation of corporate bond insurance. Counterparty risk, risk premia and recovery cloud the picture, as is widely appreciated. My conclusion is the same as former Prime Minister Malcolm Frazer: life wasn't meant to be easy.

Professor Jarrow's conclusion is otherwise:
"Using statistical measures of default probabilities like those in the Kamakura Risk Information Services is the only accurate alternative to ratings and credit default swaps.”  
Professor Jarrow does not appear to be advocating the use of credit default swaps as inputs to default probabilities. A reading of the firm's technical documentation appears to bear this out (I apologize profusely if I'm mistaken) because listed amongst the inputs to the default probabilities provided are firm financial ratios, other firm attributes, industry classification, interest rates and information about firm and market equity price levels and behavior. There is no mention of credit default swaps or corporate bonds.

Generalizing from Kamakura one observes a long standing cottage industry centered around the provision of default probabilities using all inputs except those which might well be the most important: credit default swaps. Historically that was because MarkIt, CMA and BQuotes were the pretty much the only vendors with "access" to the bulge bracket dealers and therefore "owned" the credit default swap data, for all intents and purposes. There is nothing wrong with the complementary data services using equity, structural models and other regressors and again, this is very valuable. Yet it is overreach, and bordering on disingenuous, to suggest that equity and macro numbers are sufficient or in any way obviate the use of credit default swap and bond data. There is a reason people look to the credit markets in order to assess the creditworthiness of a company.

But what of Jarrow's analogy to life insurance? I suggest this merely provides the opportunity to point out important aspects of the credit default swap markets that are very different to life insurance. The relative wealth of historical mortality data immediately strains the analogy to corporate survival. Life is cheap, insofar as there are many data points and a statistician could happily throw half the data away. In contrast a single company attracts a lot more probabilistic scrutiny form the market than any individual's longevity, including scrutiny from individuals who are free to subscribe to Professor Jarrow's excellent service. By definition they may add value over and above what he provides, and that will be reflected in the market prices. 

For life insurance economics and credit default economics to be "essentially identical" one would require a vast number of insurance companies taking a keen interest in the idiosyncrasies of every person. They would be reading our facebook pages to see what social circles we might be falling in with (motorcycle riding friends), checking the drain outside our house for cigarette butts, peering through the window during our medical checkups and so on and so forth. Perhaps that time will come but for now, the credit default swap markets are vastly larger per bet than life insurance markets are and vastly more efficient. To think otherwise requires a "colossal error of scale."  

True seekers of timely probabilistic truth will go out of their way to assimilate all relevant information, and subscribe to the only real time default probabilities inferred from both bond and credit default swap prices at great expense using leading edge analytics, detailed modeling of market microstructure, state of the art high performance pricing libraries and large scale data assimilation techniques by Benchmark Solutions. They are free to combine this information, gleaned from the most relevant market, with other services.

Oh I'm sorry, does this sound mildly commercial? With respect, I suggest that Jarrow is trying out the method of false dichotomy on his potential customers and consequently, my response is firm. I have seen this one too many times in the context of ratings and regulation. The method of false dichotomy is quite common when it comes to market-implied and empirical probabilities, because any perceived difficulty is taken as an excuse to throw out obviously relevant information. For example, the vagaries of the bond market, tax effects, coupon effects, cash flows, size effects and so forth are often cited as a reason to eschew bond prices. They are not not good reasons, merely excuses. 

The presentation of risk-neutral probability as the only "alternative" implies we are obligated to choose between market-implied and market-ignoring (or most-relevant-market ignoring) probabilities. The world is not black and white. Our only obligation to civilization, while it miraculously survives, is to carefully critique both extremes and if possible, delineate a sensible middle ground.

                         In defense of Kamakura: the timeliness of probabilities

This does not prevent us from borrowing Professor Jarrow's analogy and prodding a few sore points, especially amongst those vendors who, unlike Kamakura, don't use any market prices whatsoever. In defense of Professor Jarrow and his company the use of equity prices provides a mechanism whereby changes to default probabilities can change in timely fashion. And surely they do change rapidly, even for the entire population. Consider the invention of penicillin or the outbreak of influenza in 1918. We must believe this led to an instantaneous change in survival probabilities, and incidentally we see the the variety of "global" dependence we find also in the corporate markets (and distinct from my grandparents dying on the same day). We might sharpen the analogy to credit by considering the mortality of certain sections of the community, like religious heretics, and how it might change quickly in response to policy decisions.

Thus even in a seeming stronghold for the actuarial profession, life insurance, I wonder if anyone will seriously defend backward looking estimates of probability and the slow aggregation of requisite data as the only means by which probabilistic information can be assimilated. Moving back to credit markets, I wonder if anyone will seriously defend this in the presence of events and decisions that are obviously interpreted by the market. Those of us who watch the credit markets react to information every day require no thought experiments, but let us indulge anyway, in the hope of putting this to bed.

The gedunken: a fleet of space craft streaming menacingly towards Earth. Perhaps the fleet will destroy civilization. Perhaps it will merely give it a good shake and take a severe human toll, analogous to the railroad credit crisis of the late nineteenth century that wiped out a third of all bonds. Alternatively, and with belated apologies to Douglas Adams, the fleet might be swallowed in its entirety by a yawning dog (due to the original, colossal, "error in scale"). In that last scenario the actuaries will be leading the parade. You see, they might cry, our probabilities were right all along!

Of course one is entitled to ask how quickly, and by how much, our true mortality probabilities really did change. Surely they spiked when the lonely astronomer played by Jeff Goldblum noticed a flight formation in the corner of his screen. Surely the probabilities collapsed back most of the way to where they had laid when he recognized said formation from his favorite eighties arcade game (and noticed the fat nerd sniggering in the corner). Surely the probability of our collective destruction spiked once again when the sighting was confirmed by other stations, and so forth.

Not to downplay the fact that life insurance companies are rife with actuaries and their culture strong, I suggest an imminent attack might have even have nudged those life insurance premiums - at least while the threat was considered real - and therefore the market implied probabilities. I suggest this is a genuine aggregation of information.

I apologize profusely for the banality of this point, incidentally, but it is clear that not everyone advising regulators is taking the same side. It has been suggested that we can't trust market implied prices because they vary from time to time, for example, and we frequently hear the ridiculous phrase "through the cycle ratings" that is intended to provide a warm feeling of "reliable" probabilities. This is, of course, utter drivel. 

          A second comment in defense of Jarrow's more general point

This seems like a reasonable place to consider the real probabilistic blunders made in finance. But I've moved this into part two at the behest of a kind reader.                  

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.