FT.com: The pseudo-science hurting markets by Nassim Nicholas Taleb on October 23, 2007

Last August, The Wall Street Journal published a statement by one Matthew Rothman, financial economist, expressing his surprise that financial markets experienced a string of events that "would happen once in 10,000 years". A portrait of Mr Rothman accompanying the article reveals that he is consider­ably younger than 10,000 years; it is therefore fair to assume he is not drawing his inference from his own empirical experience but from some theoretical model that produces the risk of rare events, or what he perceives to be rare events.

Earthquakes, volcanic eruptions, hurricanes and floods are events that are also often described as "one-hundred-year events" or something to that effect. I believe that in these cases a probability distribution is empirical and descriptive, rather than model-based. I seem to recall that nothing as simple as a normal distribution actually fits the empirical data. Fear not, I will be researching this point with Nomad's help.

The theories Mr Rothman was using to produce his odds of these events were "Nobel-crowned" methods of the so-called modern portfolio theory designed to compute the risks of financial portfolios. MPT is the foundation of works in economics and finance that several times received the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. The prize was created (and funded) by the Swedish central bank and has been progressively confused with the regular Nobel set up by Alfred Nobel; it is now mislabelled the "Nobel Prize for economics".

I'm shocked, shocked, but I am sure this will indeed be shocking news to the MBAs reading the FT's "comment and opinion" pages.

MPT produces measures such as "sigmas", "betas", "Sharpe ratios", "correlation", "value at risk", "optimal portfolios" and "capital asset pricing model" that are incompatible with the possibility of those consequential rare events I call "black swans" (owing to their rarity, as most swans are white). So my problem is that the prize is not just an insult to science; it has been putting the financial system at risk of blow-ups.

To briefly cut through the jargon jungle here: MPT is based on the assumption that stock returns are random variables (so far so good) with well-defined means ("alphas"), standard deviations ("sigmas") and "correlation" coefficients (related to "betas"). Under these assumptions it is relatively straightforward to construct an "optimal portfolio" (for a reasonably convincing value of "optimal"), whose "sharpe ratio" is the ratio of its alpha to its sigma. In a perfect world (efficient, complete markets, etc), one is actually able to write down a formula (the capital asset pricing formula) for the price of an asset in terms of its risk and return characteristics. The problem is that, when calculating all these quantities from historical data, the results are dominated by "extreme events". In order to get estimates that don't depend strongly on any one data point, more or less sophisticated "outlier rejection" techniques are used which basically throw out the extreme events in order to produce "robust" estimates. This is, unfortunately, circular. The extreme events which potentially disprove the hypothesis that well-defined alphas, betas and sigmas do exist are thrown out because they prevent one from estimating the alphas, betas and sigmas that the optimal portfolio construction methods require in order to produce a portfolio. "Value at Risk" is actually worse, because it is normally computed not only assuming that standard deviations and correlations exist, but that the random variables involved are actually "normally distributed".

I was a trader and risk manager for almost 20 years (before experiencing battle fatigue). There is no way my and my colleagues' accumulated knowledge of market risks can be passed on to the next generation. Business schools block the transmission of our practical know-how and empirical tricks and the knowledge dies with us. We learn from crisis to crisis that MPT has the empirical and scientific validity of astrology (without the aesthetics), yet the lessons are ignored in what is taught to 150,000 business school students worldwide.

Since I don't write for the Financial Times I can say that I don't give a flying fuck what Business Schools teach their graduates. I would hazard that an MBA is not the kind of qualification people look for when hiring a risk manager or trader. A serious command of probability and statistics is required and that's not what Business School is about. In my experience, (undergraduate) Business students' reaction to the word "mathematics" would be to run away screaming in the opposite direction were it not for the fact that some of it is required for graduation. Given his fondness for the work of Mandelbrot, one would hope that Taleb would not advocate making multifractal measures a required topic of study in Business Schools. And, of course, nothing prevents Taleb and his colleagues from distilling their accumulated experience into books and other resources, like Taleb himself has presumably done in his three books "Dynamic Hedging", "Fooled by Randomness" and "Black Swans" (well, actually, he himself claims the latter two are only tangentially about finance). It would be the fault of the professors at business schools if they don't recommend reading his books, but if they have practical value they will spread by word of mouth among practitioners anyway.

Academic economists are no more self-serving than other professions. You should blame those in the real world who give them the means to be taken seriously: those awarding that "Nobel" prize.

Well, clearly the "Nobel" Prize in Economics was created by people with academic degrees in Economics for the purpose of raising the intellectual profile of the discipline among the general public. It's not like the people "in the real world" were not economists to begin with. In fact, Taleb's comparison of Economics with Physics will later allow me to use the Nobel Prize in Physics to argue that, at least in relation with the "Nobel"/Nobel Prizes, academic economists are a tad more self-serving than academic physicists. Yes, I have a degree in Physics myself. So, sue me.

In 1990 William Sharpe and Harry Markowitz won the prize three years after the stock market crash of 1987, an event that, if anything, completely demolished the laureates' ideas on portfolio construction. Further, the crash of 1987 was no exception: the great mathematical scientist Benoit Mandelbrot showed in the 1960s that these wild variations play a cumulative role in markets --- they are "unexpected" only by the fools of economic theories.

The stock market crash of 1987 is the worst such event since the crash of 1929, so let us call it "a 60-year event". If it is, indeed, a sixty-year event it is probably not "unexpected" but it may well be "unpredictable". It is certainly "unaccountable" by the MPT that Sharpe and Markowitz got their "Nobel" prize for. Now, I am not sure that it would be fair to say of a 60-year earthquake [like, for instance, the one in Kobe which was the worst in Japan for over 70 years] that "it completely demolished architects' ideas on building construction". As for the reference to Mandelbrot, I have to admit I don't know quite enough about his work to be able to say what Taleb's vague statement refers to, so I cannot comment. The one thing I know is that Mandelbrot has argued that extreme events are not qualitatively different from the ordinary small-scale movements in the stock market, that they have the same root causes, and that they are described by the same "multifractal probability measure". I hope I am not misrepresenting Mandelbrot and I think Taleb is referring to something along those lines. If I may pursue my geophysics analogy a bit further, I believe it is recognized by seismologists that small and large earthquakes share the same underlying causes and are described by a single probability distribution. The same can be said of meteorology where so-called "scaling laws" ensure that the vortex in a bathtub's drain is essentially the same phenomenon as Hurricane Katrina. This kind of thinking is part of the emerging paradigm of complex, self-organizing systems. It seems to me very likely that financial markets could be described by a variation of the theory of Self-Organised Criticality, which however does not mean that their behaviour should be predictable.

Then, in 1997, the Royal Swedish Academy of Sciences awarded the prize to Robert Merton and Myron Scholes for their option pricing formula. I (and many traders) find the prize offensive: many, such as the mathematician and trader Ed Thorp, used a more realistic approach to the formula years before. What Mr Merton and Mr Scholes did was to make it compatible with financial economic theory, by "re-deriving" it assuming "dynamic hedging", a method of continuous adjustment of portfolios by buying and selling securities in response to price variations.

Presumably the formula is more or less correct (since people Taleb respects used it in practice) so this is just a matter of the experimentalists resenting the theoreticians for awarding one of their number a prize for showing how the empirical formula can be derived within the theory. Apart from decrying that Thorp did not share the prize, I fail to see what exactly Taleb is complaining about.

Dynamic hedging assumes no jumps --- it fails miserably in all markets and did so catastrophically in 1987 (failures textbooks do not like to mention).

Taleb is, in fact, arguing that Merton and Scholes used the wrong method (dynamic hedging) within the wrong theory (MPT) to arrive at the right (Thorp's) conclusion. What is puzzling about this is that Taleb himself wrote what is essentially a practical textbook on Dynamic Hedging, and he did so after 1987.
But is the formula right or wrong, in Taleb's view? It is a fact that the formula is now used to deduce, from derivative prices, an "implied volatility" (one of Taleb's hated "sigmas") which is a parameter of the Black-Scholes equation. The implied volatility is not a single number, as the pricing formula appears to require, but rather when plotted in a particular fashion it produces a curve called a "volatility smile" that derivatives traders use as a diagnostic tool.

Later, Robert Engle received the prize for "Arch", a complicated method of prediction of volatility that does not predict better than simple rules --- it was "successful" academically, even though it underperformed simple volatility forecasts that my colleagues and I used to make a living.

I don't have any expertise in this area so I'll pass no comment.

The environment in financial economics is reminiscent of medieval medicine, which refused to incorporate the observations and experiences of the plebeian barbers and surgeons. Medicine used to kill more patients than it saved --- just as financial economics endangers the system by creating, not reducing, risk. But how did financial economics take on the appearance of a science? Not by experiments (perhaps the only true scientist who got the prize was Daniel Kahneman, who happens to be a psychologist, not an economist). It did so by drowning us in mathematics with abstract "theorems". Prof Merton's book Continuous Time Finance contains 339 mentions of the word "theorem" (or equivalent). An average physics book of the same length has 25 such mentions. Yet while economic models, it has been shown, work hardly better than random guesses or the intuition of cab drivers, physics can predict a wide range of phenomena with a tenth decimal precision.

Now for the promised argument purporting to show that Academic Physicists are less self-serving than Academic Economists. In 1971 't Hooft and Veltman laid down the theoretical keystone of the Standard Model of Elementary Particle Physics, namely a proof of the renormalizability of non-abelian gauge quantum field theories. However, they had to wait for 28 years before they got their Nobel Prize because, until then, no known experimental result actually required renormalization. Technically, experimental results could be matched with "tree-level" calculations until there was finally one experiment requiring renormalized "one-loop" calculations. For those nearly 30 years nobody had any doubt that 't Hooft and Veltman's work was correct, yet experimental verification (or a first explanation of an experimental result) is required for a Nobel Prize in Physics. It would appear that Economists award each other "Nobel" Prizes without experimental support. Mathematization doesn't make Economics any more of a science, and Mathematical Economics is rather contemptuous of empirical verification. In that it is in good company, as Einstein once said "if observations had not confirmed General Relativity I would have been sorry for Nature, because the theory is correct". Needless to say, Einstein did not receive the Nobel Prize for Relativity, General or Special.

Every time I have questioned these methods I have been abruptly countered with: "they have the Nobel", which I have found impossible to argue with. There are even practitioner associations such as the International Association of Financial Engineers partaking of the cover-up and promoting this pseudo-science among financial intitutions. The knowledge and risk awareness we are accumulating from the current subprime crisis and its aftermath will most certainly not make it to business schools. The previous dozen crises and experiences did not do so. It will be dying with us, unless we discredit that absurd Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel commonly called the "Nobel Prize".

I suppose the reason Taleb insists on referring to Business Schools as if they were the be-all and end-all is that he's writing for the FT and he needs to make his audience, who presumably has been to Business School, feel important. "Read my books" he says "if you want to received the accumulated wisdom gained from the previous dozen crises". He has gotten Colman to buy "Black Swans" and I'll probably get ahold of a copy of "Dynamic Hedging" soon, so his FT sales pitch has achieved some of its objectives. And we don't even have an MBA!

The writer is author of 'The Black Swan: The Impact of the Highly Improbable', shortlisted for the FT/Goldman Sachs Business Book of the Year Award. The winner will be announced at a dinner in London on Wednesday night

The diarist is a professional smartass.

Copyright The Financial Times Limited 2007

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