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Critique
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Chapter 4
Copulated Nightmares
⢠Abrupt reform, if not so much prison â˘Modeling death
⢠The 2005 pre-warning â˘Rating us into hell
⢠A disapproving grin â˘
Around mid-July 2008 (with the then one-year-old global credit crisis still fuming on all cylinders, having recently forced U.S. authorities to bail out stricken mortgage giants Fannie Mae and Freddie Mac) the following, rather unshy, ruminations appeared on Nassim Talebâs idiosyncratic web site:
Having a risk number is not trivial. It does lead you to do foolish things, even if you knew that the measure was wrong. If I can show that, many people [who offered quantitative risk measures in finance] will have to be held accountableâand I can show that! One of Fannie Mae directorâs, a quack and proponent of âModern Financeâ charlatanism, kept promoting âscientificâ risk measurement methodologies that do not measure risks adequately, but lead people to TAKE MORE RISK foolishly thinking they know something. [This is the reason I singled out Fannie Mae in The Black Swan as a firm sitting on dynamite and the International Association of Financial Engineers as a society of snake oil vendors harmful to society]. After > 1 trillion in losses I can safely say that my statement that the banking system has been taking more risks than they thought SHOULD HAVE BEEN TAKEN MORE
SERIOUSLY. So I hold that giving someone a bad risk measure was just as CRIMINAL as giving someone the wrong medicine. For a long time nobody sanctioned doctors who poisoned their patients. Why donât we take on the proponents of quantitative risk management, put them in jail so they stop harming us?
It is clear that widespread reliance on quantitative methodologies and constructs was, at least in a large enabling role, behind the mayhem that originated in the summer of 2007, first in an obscure corner of the U.S. residential mortgage market and then spread-out like a virus throughout the worldâs credit and financial markets. It is also clear that previously conventionally accepted (or at least widely sanctioned) quantitative techniques and the âideologiesâ supporting them became unappealingly discredited amidst the chaos.
What should we do about it? We could, as Taleb proposed, imprison all those directly responsible for this âquantitative 9/11,â perhaps make some room for them in Guantanamo Bay, next to Osama Bin Ladenâs henchmen. After all, if we are to fully endorse the arguments of Taleb and similar critics, finance theorists and financial mathematicians have committed criminal acts that are not exactly outside the realm of Taliban-size dimensions.
But such course of action may be impractical, and not just because of human rights or legal process concerns. Short of donning quant types with orange jumpsuits and sending them out to the Caribbean, we could, rather less aggressively and a tad more efficiently, voice the need for unavoidable reform. If the credit crisis (in the words of George Soros, curiously a strong opponent of Guantanamo, the gravest since the 1929 Crash) shows something, it is that the role of quantitative tools in finance must be entirely rethought, reconsidered, and reevaluated.
In this sense, a sensible initial step would be to ask ourselves a very simple question: Why does finance need quantitative tools? Why does finance need theorems? Granted, finance, by its very nature, has always depended and will always depend on a certain amount of math and lemma-like truisms. But these are of a very soft nature. Because there are numbers involved, you need to be able to do some arithmetic (you know, if you buy 1,000 shares and each share is worth $25, you will need $25,000) or at least be able to employ a machine capable of doing the arithmetic for you. And because there are products with predefined payout formulas, it is possible to infer unquestionable relationships (if bond prices go up, yields go down; or when the price of the underlying asset goes up, the price of a regular call option goes up). But do we need extra math and lemmas beyond these simple bedrocks? And, more pointedly, do we need such extras to be as incredibly complex as they have become through the years?
The quantification of finance was a process most likely not dictated by a real, existing, indisputable need on the part of math-challenged ancient pros (if we exclude, naturally, the computer revolution, which unleashed the need for people who could produce software and design interfaces and databases; but here we are focusing on the modeling-forecasting-theorizing aspects of quant finance, not on the more habitual technical plumbing activities of those deemed quants), but rather was a need artificially (and forcibly) imposed on insiders by a mass of outsiders, with the aid of a smallish fifth column of insiders who (either out of pure belief in the value-adding capabilities of the tools or as means to enhance their own internal relevance) eagerly engaged in active pulling.
What I mean by all this is that finance is, in itself, not a fiendishly complex activity, even after products and markets have become incredibly more sophisticated. You really donât need much beyond the basic elements highlighted earlier (provided, again, that you can count on technical computational support). You donât absolutely need advanced mathematical theorems in order to run a modern-day financial institution. Scientific prowess is not a requirement in order to be successful as a hedge fund, an asset manager, or an investment bank. Nothing in the markets or the products dictates that you must have mastered econometrics or numerical methods prior to being allowed and able to play. Even 20 years deep into the derivatives revolution, elementary arithmetic and solid practical market knowledge remain the only true requirements. Until someone designs a financial market where payouts are determined by the solution to a stochastic differential equation or a multivariate regression model, things will remain so.
This is not to supinely argue that advanced quantitative methods canât be of help, simply to underline that, whatever their potential benefits, they are not irrefutably needed. The same markets and the same products would have emerged without the development and presence of the fields of mathematical finance and financial economics (but surely not without the advent of the computer, at least at the same level of activity). There was no extreme, unavoidable urgency on the part of players to be equipped with funky forecasting and valuation tools. If they are available and they can help, great for the traders, punters, and deal makers. But if they are not, no irreparable harm would be inflicted, no innovation would be prevented, no solution would be lost. If consenting adults want to make a market in whatever asset or to take an existing asset market to the next level, they can and would do that without waiting for mathematical authorization. The history of derivatives (perhaps the most sophisticated financial arena) shows us that professionals are more than willing and capable of creating new stuff long before the technical paper has been published.
Much more urgency would be urged, in contrast, by those endowed with the skills to design and implement the tools, and who desire to join the financial industry or to multiply their relative relevance within it. You are likelier to praise the contributions of financial econometrics and to peddle its solutions as God-sent if you are a financial econometrician. You are likelier to argue for the utter necessity of modeling if you are a modeler. And, throughout history (though less markedly today than yesterday), modelers and theoreticians have been overwhelmingly outsiders.
What motivates quanty outsiders (academics, scientists) to want to colonize the financial planet? Well, the rewards are potentially very tasty and the sales pitch has a more than decent chance of working. By rewards I donât just mean monetary ones. Quantitative finance can be a very exciting intellectual adventure, full of challenging potential discoveries. Who wouldnât want to try his hand at unlocking the mysteries of the market through fancy ultrasmart mathematical manipulations? Who wouldnât want to be the first to obtain a (purportedly fair) price for a new hot product? The markets are also tailor-made for those with a disproportionate taste for research and analytics in one very important sense, namely the availability of tons of reliable data to play with. Finally, there is also fame and power. Finance promises more of both to those scientists unsure of their Nobel prospects.
Having a chance at achieving all those rewards (i.e., having a chance of being hired by a financial institution) is appealingly not impossible. These days, and continuing with a process that was kick-started some 30 years ago, investment banks and hedge funds hire a substantial number of quantitatively trained individuals. If you are a nerdy type who wishes to go into finance and have the patience to do a numerate PhD or the money to enroll in one of the increasingly prevalent specialist Masterâs programs, it is indeed quite possible to achieve your dream. In spite of the nonabsolute necessity for mathematical wizardry exposed earlier, there is little doubt as to the habit of financial institutions to let mathematical wizards in. And while (as has been detailed earlier in the book) most of these brainiacs spend most of their time doing no mathematical modeling or undecipherable forecasting, instead becoming highly skilled technical assistants who provide the computational support essential for any financial organization, it is likely that such reality would not prevent finance from appearing insurmountably superior to other alternative occupations in the eyes of many scientists.
The ubiquitously numerous presence of quanty types around trading floors (many times reported by mass media) may give the impression that fourth-generation analytical tools (those, again, beyond computer power) are indispensable if you want to make a buck in the markets. All these quantitative people certainly have a strong vested interest in having the world believe that finance does need advanced quantitative tools (though we must highlight the admirable honesty displayed by many top quants when they loudly voice their skepticism as to our ability to mathematically tame the markets). Sometimes, no-nonsense nonquant pros contribute to that story line, for self-serving reasons of their own. These impressions are mainly illusions, but they also rightly convey the message that certain mathematical and statistical constructs have indeed become mainstream elements of the financial industry, a revolutionary development that sharply differentiates modern market practice from its historical predecessors.
While, it must be again emphasized, impressions are not quite reality in this case (the undeniable presence of scientists does not imply that finance is a science, and not just because those former scientists donât really perform much science in their new financial environment), there is no doubt that the quantitative and theoretical invasion unremittingly launched in the late 1970s and early 1980s has established very solid beachhead in financeland. Mathematical models are (partly at least) routinely embraced, statistical measures are (rather more profoundly) followed, econometric guidelines are (not exorbitantly frequently) sought. Existing markets, products, and practices may have emerged in a math-deprived environment anyway, but that does not negate the fact that advanced math has, for the past few decades, been used. Possibly not as intensely and religiously as conventionally believed, but used nonetheless.
The financial markets of May 2007 were faithful adherents to that three-decades-old legacy. The financial order prevalent just as the horrendous credit crisis began to rear its ugly head was one where theoretical models and quantitatively charged dictums enjoyed a privileged existence. Far from being widely shunned, many of them were adoringly abided by and wholeheartedly accepted as backbones of the system. A few skeptical outsiders had been crying wolf for a while, but those who matter (the practitioners, the rating agencies, the regulators) had overwhelmingly decided not to entirely ban the math from the premises. The financial Titanic that hit the iceberg in the summer of 2007 and then began a painfully lengthy descent into total darkness was, in modern fashion, inescapably inhabited by quantitative machinations. As we shall see, such machinations not only failed to forewarn of the iceberg in advance, or may have actually directed the ship towards it. They helped create the iceberg themselves.
There is reason to believe that May 2007 could represent the high-water mark for the application of quantitative tools in finance. A backlash against theoretical devices seems to be in the works. Simply stated, the crisis has highlighted too many failings at the same time. Models did not work, guiding measures failed horribly, sacred assumptions broke down. The math did not forewarn, afforded excess complacency and misguided confidence, and justified lethal business practices. Above all, the mayhem has helped confirm what many had always known or at least suspected: Markets are not quantitatively tamable, and efforts in that direction can destroy us.
It is difficult to see how something that is not really necessary for the evolution of finance, whose success is quite improbable, and which can contribute to generating untold pain, could continue to play a prominent role in the markets. It is one thing for academics and maybe a few insiders to spend their time thinking big mathematical finance thoughts (not much downside, maybe some significant upside if someone does come up with valuable insights), but quite another to allow such ideas to unfilteredly affect practice. Perhaps it is time to turn back the clock 30 years and return to a world in which theoretical âcertaintiesâ were not an ingrained part of the financial industry.
When asked about the reasons behind the credit crisis, pundits, analysts, politicians, and other assorted outsiders would be overwhelmingly expected to cite the myriad of oft-cited usual suspects: horrendously lax mortgage lending policies, unsustainable housing bubbles, securitization run amok, asleep-at-the-wheel regulatory practices, untold investor greed, retold bankersâ greed, and so on. But few (if any) would be expected to show rebellious originality and point towards the direction of something called Gaussian Copulas. Before you let your imagination run wild with visions of Germanic sexual activities, it may be prudent to clarify that a Gaussian Copula is a mathematical model, broadly used to probabilistically quantify and predict the interdependence of different individual variables. Such constructs, originally the obscure preserve of statisticians, made their way into finance some 10 years ago, becoming endorsed with particular ardor in the credit derivatives arena, both by quants and academics. The valuation and rating of many of the complex structures that unraveled during the crisis drew from the dictates of Gaussian Copula models, which, naturally, suddenly appeared as less than perfect. Simply put, what the models had been theoretically crowning as highly valuable and highly trustworthy became downgraded by real life to the status of worthless and unreliable.
Quantitative models should be added to the list of guilty parties when discussing the crisis, perhaps displayed prominently atop the rankings, just a few notches below NINJA loans. Without the model-based confident assessments of traders, quants, and rating agencies, the vast securitization of less-than-salubrious credit and its spreading throughout the far corners of the financial universe might not have taken place. Or it might have been that much less carefree and trigger-happy. Those mathematically sanctioned AAA ratings made everyone feel safe and secure, decisively aiding business. Pricing tools that purported to be able to summarize Ăźberly complex trades into one neat number and that ruled out the possibility of such number being zero (or, more to the point, of not being at all) convinced bank executives and trading floor honchos that restraint would be a wasteful course of action. Without the misplaced certainty afforded by elegantly sophisticated analytics, the mayhem may have been no more significant than a mild hiccup.
A Copula (in a statistical sense) is a way to obtain multivariate, or joint, probability distributions that, technicians affirm, is particularly simple and convenient. Once we know the marginal (i.e., individual) probability distributions of each of the concerned variables together with the correlation structure (how closely the variables move in tandem; this idea obviously implies nonindependence), the copula function can be used to marry those univariate marginals to their full multivariate distribution. Roughly, we would be trying to model the likelihood of various different events taking place jointly, with those events depending in some way on each other. That is, you are not simply interested in the chances of X and Y taking place together; you want to know how often X and Y take place together once you know that X can cause Y, or vice versa.
An obvious financial application of this wizardry is the modeling of dependence between defaults, which, naturally, happens to be at the heart of those modern multiname credit derivatives structures which, certainly, happen to be at the heart of the 2007 crisis. Why would default probabilities of many single bonds or loans be assumed to be interdependent? Or, to put it technically, why would copulas be needed to model products where the default probabilities of many different assets matter? Wouldnât the single, marginal distributions be enough on their own? The answer is no. Or at least, the theoreticians, quants, traders, and rating agencies said that the answer is no. And they appear to have a point. The alternative assumption of independent credit risks may seem unrealistic.
As the pioneer of the application of copula methodology to credit derivatives put it, âThe default rate for a group of credits tends to be higher in a recession and lower when the economy is booming. This implies that each credit is subject to the same macroeconomic environment, and that there exists some form of positive dependence among the credits.â If one or more companies default on their obligations, this could trigger further defaults as the original devastation breeds further destruction through several plausible channels (tighter credit, disruption of supplies, loss of customers, enhanced general economic malaise). Needless to say, such interconnectedness would be deeply enhanced if the companies belonged to the same industry sector.
Creepily paradoxically for the mathematics behind tools that caused so much financial obliteration, the original modeling efforts were inspired by work done on the correlation of (human) death rates. There is a concept in actuarial science known as the âbroken heartâ: People tend to die faster after the death of a beloved spouse. Cracking such co-dependence can be quite useful to life insurers. Believing that âDefault is like the death of a company, so we should model this the same way we model human life,â quant David Li borrowed from his death-modeling academic friends, who first gave him the idea of using the technology of copulas. When he published his path-breaking paper in 1999, Li and his One-Factor Gaussian Copula (the âone-factorâ refers to the fact that the performance of each individual asset is linked to a common additional factor, typically economic variables; the âGaussianâ part implies that the modelâs architecture is influenced heavily by the Normal probability distribution) concoction contributed to opening up the floodgates of the complex credit derivatives explosion, by providing a simplicity-embracing way to calculate joint default probabilities and default correlations for a bunch of fixed-income securities pooled together.
This model became the standard ever since. It borrows from the marketâs assessment of the default probability for each loan or bond, runs those individualistic projections (together with correlation estimates, which are assumed to be stable in time and structurally flat) through the copula function, and out comes the theoretical probability mapping the joint default behavior of all the assets (i.e., how likely are assets to default if others default, or to remain solvent if others do so). This number has direct implications for the value and returns of derivatives based on the contingency that a credit event would affect more than one security. If the churned out likelihood is low (a small theoretical chance that all credits survive or default), the model would be ...
