Models.Behaving.Badly.: Why Confusing Illusion with Reality Can Lead to Disaster, on Wall Street and in Life

著者は元物理学者で後にウォール街の金融理論家、現在は金融工学の大学教授。前作同様、変わった本だ。ほとんどが物理学の話なんだな。くりこみ理論の解説まで出てきて眩暈がしたぞ。そいや以前ポール・ディラク伝を読んだが、ディラクが「くりこみ」に怒って絶望していたのが興味深かった。数式が醜い。神は醜い数式で世界を創造したのではない、と。ワタクシの場合は「くりこみ」が金融理論にどう関係してくるのか目が点になる程度で別に絶望はしないのだが、この本、何気に想定読者のレベルが高過ぎる。スピノザの「エチカ」とディリヴァティブの関係なんかもちょっと迂遠過ぎて辛いんだが、ワタクシの知的レベルの問題なのかなー。しかし「スピノザとディリヴァティブ」の相関図を二頁分のダイアグラムにしてしまう著者の情熱には感心した。本書は物理学の高見からファイナンス理論のダメさを見下す本である。自然は神が創り、金融システムは人間が作った。物理学の世界には燦然と輝く「セオリー」がある。しかしファイナンスにおいて可能なのはせいぜいが「モデル」、或いはアナロジーの提示でしかない、と著者は言う。神の法則を扱う物理学をファイナンスに応用出来ると思うなどとは不敬罪であり邪教だッ、というのが元物理学である著者の本音だろう。という訳で、「そんなの当たり前じゃ〜ん」という方が読むと当たり前過ぎてむしろ面食らう内容なんだが、ファイナンス理論の授業で「This is order in the universe!」とかとか天啓に震える人も中にはいるらしいので（実際そういうエピソードを読んだことがある）、そういう危ない人の為に、「知」なるものの手法と作法から語り起こしている。故国のアパルトヘイト時代回想やユダヤ教徒としての教育、言語学（「言語は全てメタファーである」）から文学から哲学まで、個別の経験と普遍への希求がない交ぜになったカオス的で豊かな一冊だと思う。全ては著者の「人生経験」の中で結晶化しているのだ。読む側の資質が相当に試されるシンドさがあり、且つ、著者の思索の深さが読み物として昇華し切れていない印象もある。しかし人生論と物理学への恋歌とメタ金融論が融合した著者ならではの個性的な一冊。そのユニークさ、そして通奏低音として流れるプラトニズムの旋律に対して、五つ星。

著者の前作を読んでいないのですが、この著作は不思議な著者の情熱の混合物です。結論的なメッセージはしごく当たり前のものです。あまりにも常識て過ぎてはたしてこのような著作の執筆がはたして必要だったのかと思わせるほどです。全編を通して流れるのは、著者のスタートラインでもある物理学への消えることのない執着の念です。金融工学はこの「科学の王様」ともいうべき物理学と多面的に比較されることにより、そしてその本質的な「非科学性」とその論理的な帰結としての限界と危険性がこれでもかというほど明らかにされていきます。この作業は著者にとってもおそらくほろ苦いものだったと思われます。物理学で著者が直面したキャリア上の限界は直接的には語られることはありませんが、著者はいまだに物理学に恋しているのです。むしろ本書の面白さは、前半で著者の南アフリカでの成人するまでの半生の邂逅の部分ではないでしょうか。アパルトヘイトの南アフリカでのユダヤ人としての成長の軌跡は、ある一部のユダヤ人社会の断面を興味深く描いており一読の価値があります。

We live in an "information age" where much of our observable universe --- everything from the climate to the economy ---- is modeled by computer simulations. We attempt to use mathematical models to analyze past trends and interpolate them into the future, thereby trying to determine what we should be doing today to optimize our future outcomes.Emanuel Derman is a mathematician who started his career as a theoretical physicist studying the profoundly elegant models that explain the quantum nature of our universe. Like a few other theoretical physicists before him, he eventually became a "quant" (quantitative financial analyst) hired by the financial firms who trade the stock, bond, and commodity markets. He explains how the "quant" models of financial instruments like mortgage derivatives failed.Derman embarks on a circuitous but fascinating journey through all kinds of modeling philosophies from theology to the Theory of Relativity. After examining the (often flawed) techniques that people use to model the realities they believe in, he gets down to the business of explaining why the analysts' models of the financial system failed. The primary reason, as might be expected, is their failure to account for all the inputs that go into a complex system:===========================A weather model's equations are a limited and partial representation of a limitlessly complex system. One cannot model the physics, chemistry, and biology of all the chemicals in the atmosphere and their effect on every species on Earth. There is always the danger that one has omitted something ostensibly negligible whose tail effects over long times are crucially important. This is what makes the predictions of global warming the subject of legitimate debate.An economic model aims to do for the economy what the weather model does for the weather. It too embodies a set of equations to represent the interactions of people and financial institutions. But an economy is an even more abstract concept than the weather. Supply, demand, and investors' utility, to name just a few of many possible variables in the model, are much harder to define (let alone quantify) than temperature and pressure. When you model "the economy" and "the market" you are modeling high-level abstractions.============================Then there is the bias caused by preconceived opinions. Once someone develops a theory to explain an observation, their subconscious mind becomes a "prisoner" of the theory and constantly forces the theory back into the conscious mind. People operating in any field are extremely reluctant to recant a theory once they have developed it. They are said to have invested "ego capital" in defending their pet theory and have closed their minds to accepting any new information that would tend to refute the theory.Derman goes on to explain the phenomenon that many sick people have experienced, in which a physical malady is misdiagnosed by specialists. Each specialist is predisposed to believe that the malady must result from some failure of bodily function within his/her narrow area of expertise. Sometimes it is a generalist who "sees the big picture" who finally makes the correct diagnosis, even though the generalist's knowledge of medicine is less than the total of all the specialists. Models created by specialists may fail because they are modeled at a complex level in one dimension while failing to see the many other dimensions that affect the outcome.I also wonder if financial markets (stocks, bonds, and commodities) CAN'T be modeled, no matter how complete the inputs are. If they could be modeled the price movements would become predictable and all future values of a stock or commodity would become known. The current price would instantly adjust so as to anticipate the future values. The volatility of the markets would then go to zero. Conversely, the fact that volatility can't be zero explains why the markets can't be modeled. This is akin to the Heisenberg Uncertainty Principle: the effect of measuring a market (by modeling it) makes it unpredictable and therefore IMPOSSIBLE to model. If this is true and financial markets CAN'T be modeled, it follows that a stock with expanding earnings that is at $10 today MUST go to $6 (or some other irrational price) before it can go to $20.We have an example this very day (December 15, 2011) of gold crashing down a couple hundred bucks, wiping out months of upward price movement. All the "gold bugs" who model the price of gold lost many months of gains in a single day. I didn't hear any one of them predict the price collapse until after it happened.I've also wondered about the peculiar way that stock market capitalizations are valued. Conventional inventory is valued on either a FIFO/LIFO or an average cost basis. If you own a store and buy a thousand widgets to put on your shelf at a total price of a thousand dollars, the total value of each widget is a dollar. If for some reason you decided to buy a single widget tomorrow at a price of $2.00 the value of the other 1,000 widgets doesn't change. You'd either keep them on your books at a dollar a piece, or else you'd revalue the entire inventory on an average cost basis of ($1,000 + $2) / 1000 = $1.002 per widget. Either way, the value of your inventory is $1,002 dollars. Your last buy did not disproportionately affect the value of your inventory. If you asked a bank to loan you money using the inventory as collateral, $1,002 is the most you'd get.However, when you buy or sell a stock THE LAST SALE REVALUES THE ENTIRE INVENTORY. If you bought a thousand shares of stock for a thousand dollars the value of that stock is $1.00 a share. If tomorrow you happen to pay $2.00 for one share, then the MARKET VALUE OF ALL the shares you already own rises to $2.00. Yesterday you had a thousand shares worth a thousand bucks. Today you have a thousand shares worth $2,000 all because you (or somebody else) was willing to pay $2.00 to buy ONE share on the market. If you asked your bank for a loan using the stock as security you might get $2,000, whereas yesterday you would only have received $1,000. A $2.00 transaction created $1,000 of new purchasing power. This highly leveraged expansion and contraction of purchasing power based on "last transaction value" is how financial booms and the inevitable crashes that follow them are created.It would seem that any system that revalues all of its components any time one of them changes would be very difficult to model.Reading Derman's book encouraged me to think about these topics that make the market appear to be random. This book is rich in thought-provoking discussions. Derman not only dissects the idea that markets are extremely difficult (perhaps impossible) to model, but also expands the idea into some very interesting philosophical dimensions. He takes us through a most interesting journey of the theory of modeling, especially in making us aware of why so many models fail to correlate with reality.

Emanuel Derman is a "quant" of illustrious pedigree: not only a 20-year veteran of Goldman Sachs (say what you like about the Vampire Squid but over the last couple of decades Goldman's financial analysts have consistently been the smartest guys in the room), but also a close colleague of nobel laureate Fischer Black, co-inventor with Myron Scholes of the (in)famous Black Scholes option pricing model.Given that the motion before the house concerns misbehaving financial models you might expect some fairly keen insights on this topic: It has already been well documented that Black Scholes doesn't work awfully well when the market is in a state of extreme stress - that is, precisely when you want it working awfully well. In fact, in those situations Black Scholes can create havoc, and memorably did during the Russian Crisis of 1998, during which Myron Scholes' pioneering hedge fund Long Term Capital Management catastrophically failed.But this isn't Emanuel Derman's interest: the specific inadequacy of Black-Scholes (that it assumes that market events occur in isolation of each other and are therefore arranged according to a "normal" probability distribution) rates barely a mention. Derman's view is that reliance on *any* financial model will end in tears, simply because models are poor metaphors which are not grounded in the same reality as the sciences whose language they mimic.Hmm.Benoit Mandelbrot, whose excellent book  The (Mis)Behaviour of Markets  clearly outlines the "tail risk" inadequacy of Black Scholes, recognises that it is the market, not the model, that tends to misbehave. A model can't be blamed for failing to work when misapplied. Guns don't kill; the people holding them do.This is a narrow example of a broader principle which (counterintuitively) is true of all scientific theories: they only work within pre-defined conditions in carefully controlled experimental environments. Even Newton's basic laws of mechanics only hold true where there is zero friction, zero gravity, infinite elasticity, infinite regularity and a total vacuum, conditions that in real life never prevail. "Real life" experiments are thus indulged with a margin of error: that a heartily-struck cricket ball does not prescribe precisely the trajectory Newton says it ought is not evidence that his fundamental laws are wrong, but the simply that the pure experimental requirements for its true operation are not present.All scientific - and, for that matter, any other linguistic - theories benefit from this "get out of jail" card: they are what philosopher  Nancy Cartwright  calls "nomological machines", explicitly pre-defined to be "true" only in tightly circumscribed (and often practically impossible) conditions. The looseness or tightness of those constraining conditions and the consequences of marginal variations to them determine how useful the theory, or metaphor, is in practice. F=MA will be a better guide for a flying cricket ball than for the proverbial crisp packet blowing across St. Mark's Square.Emanuel Derman thinks science really speaks truths, while models peddle something less worthwhile. He sees a qualitative difference and not merely one of degree. Models he treats as broadly analogous with metaphors, which he says depend for their validity on comparison with an unrelated scenario. Theorems and laws, on the other hand, need empirical validation but once they have it stand rooted to the ground of reality by their own two feet.I'm not sure the distinction is as sharp as Derman thinks it is. Nevertheless, this talk of metaphors cheered me because the vital role of metaphor in constructing meaning is overlooked even by linguists, and is completely ignored by most scientists and mathematicians. But Derman makes less of it that I hoped he might.What Derman means by metaphor is really a simile: the ability to reason by analogy with something already well understood. A model, under this reading, makes its prediction by reference to what would happen in an analogous situation. "Resemblance is always partial, and so models necessarily simplify things and reduce the dimensions of the world". But metaphors are far more powerful, expansionary operators in scientfic and literal discourse than that.In Derman's world there is a clear line between fact and metaphor and he has trouble being patient with people who confuse it. That would include me, because I have trouble seeing the boundary between metaphorical models and theoretical (or even literal) reality: each is an abstraction, each a simplification, each a "nomological machine" which only has value within a set of parameters. Literal meaning is really a species of metaphor. The difference between a model and a theory is one of scope and degree: a model is a heuristic; a theory more of an algorithm. Models are less worked out; more rules of thumb. If so treated, both have reat practical uses provided their output is treated with an appropriately sized pinch of salt. LTCM's folly was to suppose their model could solve for something it manifestly could not. Scientists in recent times have been just as guilty of ontological overreach, so I'm not enormously sympathetic with the bee in Derman's bonnet.There are plenty of better grounds to take umbrage at Investment Bankers at the moment, in other words.What we are left with is really a low level, idiosyncratic grumble. There are better books written on this and similar subjects: Mandelbrot's The (Mis)behaviour of Markets remains the technical classic, and Nassim Taleb's  The Black Swan: The Impact of the Highly Improbable  a more entertaining popular entry. Not quite sure where this fits between.Olly Buxton The (Mis)Behaviour of MarketsNancy CartwrightThe Black Swan: The Impact of the Highly Improbable

A model is a simplified representation of reality which tries to mirror a system by idealizing certain details and leaving others out. It is not a theory and it is certainly not reality itself. Yet many financial modelers who built models assumed their models to be real and contributed significantly to a financial crisis which will likely play out for decades. In this book Emanuel Derman, a modeler and quant par excellence, provides a refreshing and balanced outlook on the flaws in financial models and how these models are quite different from their exact theoretical counterparts in physics.Derman would know better than almost anyone else since he is a both a veteran financial modeler and an accomplished theoretical physicist. Before pioneering the art of quantitative finance on Wall Street he was an expert in the rarefied domain of particle physics, a discipline which has produced theories agreeing with experiment to an almost unbelievable degree of accuracy. Thus Derman begins by discussing the difference between models and theories and why the former are much more approximate, uncertain and tentative than the latter. The trouble starts when we start confusing the two and expecting models in finance to be as precise as theories in physics.In the first part of the book, Derman has elegant definitions of models, theories and intuition and pens substantial chapters on the history of physics culminating with his chapter on quantum electrodynamics, the most dazzlingly accurate theory of nature that we have uncovered. In Derman's words, a theory is something that stands on its own two feet without justification while a model is a framework that describes only a part of reality and cannot be a unique description of the world. There is also a curious digression on Spinoza's "Ethics" and why Derman thinks that Spinoza's constructs came closest to being a bonafide theory of human behavior and emotions. Derman also sprinkles these chapters with personal recollections of apartheid in Africa and a bout with an eye disorder. I thought these parts of the book were a little meandering and unclear, but Derman essentially seems to be making a point that imposing the wrong model (in these cases, assumptions behind apartheid or the diagnosis of his eye disease) on reality can lead to disaster and pain.The second part of the book contrasts models in physics with those in finance. Unlike physics, the fickle world of human beings precludes having any kind of real theories or axioms about financial markets. Even the models in the financial world try to mirror moving targets whose complexity keeps on changing and whose parameters are hard to define in the first place. Yet as Derman describes, modelers on Wall Street believed in rather absurd entities such as a "fundamental theorem of finance" akin to the fundamental theorem of arithmetic. In an illuminating and fairly detailed chapter, Derman points out the flaws in the efficient market model (EMM) which tries to distill down the complex variables contributing to the value of a stock or company to a few simple numbers (drift and volatility in this case). But the real "value" of a company depends on unpredictable and constantly changing human decisions which cannot be captured in an incomplete quantitative model. As Derman makes clear, models like the EMM fail to predict or even explain sudden changes arising during crises akin to the present one and therefore do a rather poor job of guiding our economic choices. The basic problem of course is in trying to fit human behavior to a set of mathematical equations.Derman concludes by summarizing the problems inherent in modeling financial markets which are systems engineered and manipulated by flawed, volatile and complex human beings. To prevent future modelers from getting carried away by their models, Derman reprints a modeling "manifesto" which he penned in 2009. The manifesto exhorts financial engineers to not get dazzled by fancy mathematics, to not assume that the complexities of human behavior could ever be boiled down to pithy equations, axioms or theories and to honestly state and evaluate the parts of reality left out from their models (even if they are sweeping these under the rug in practice).And Derman's most important piece of advice? To always remember that financial modeling is not physics, and that models don't equal reality.