Mandelbrot – The (Mis)behaviour of Markets
Meine Unterstreichungen:
“We have a good deal of comfort about the capital cushions at these firms at the moment,” said the SEC chairman just six months before the 2008 crash. (S. xii)
According to the text-book market formulae, the September 29 plunge should never have happened. The odds were about one in a billion. Yet it happened. (S. xiii)
Our focus should be on the concentrated bursts of action and the discontinuities in prices, events that common economic wisdom says shouldn’t happen and calls “statistical outliers”. (S. xiii)
Financial economics, as a discipline, is where chemistry was in the sixteenth century: a messy compendium of proven know-how, misty folk wisdom, unexamined assumptions and grandiose speculation. (S. xv)
A bank in which the research department thinks it has discovered something new and useful will not share it with anyone else. Being focused on profit, not knowledge, it is unlikely to fund fundamental research. (S. xv)
Thus reading this volume will not make you rich. But it will make you wiser – and may thereby save you from getting poorer. (S. xix)
the common man is wise in his prejudice that […] markets are risky. But financial theorists are not so wise. (S. 5)
But this is confidence trick: Everybody knows that everybody else knows about the support point, so they place their bets accordingly. It beggars belief that vast sums can change hands on the basis of such financial astrology. (S. 9)
[1900] Louis Bachelier, hat the temerity to study financial markets at a time “real” mathematicians did not touch money. In the very different world from the seventeenth century, Pascal and Fermat invented probability theory to assist some gambling aristocrats. (S. 9)
Alas, the [financial] theory is elegant but flawed, as anyone who lived through the booms and busts of the 1990s, can now see. The old financial orthodoxy was founded on two critical assumptions in Bachelier’s key model: Price changes are statistically independent, and that they are normally distributed. The facts, as I vehemently argued in the 1960s and many economists now acknowledge, show otherwise. (S. 11)
In fact, the bell curve fits reality very poorly. (S. 13)
Truly, a calamitous era that insists on flaunting all predictions. Or, perhaps, our assumptions are wrong. (S. 13)
Warren E. Buffed […] jested that he would like to fund university chairs in the Efficient Market Hypothesis, so that the professors would train even more misguided financiers whose money he could win. He called the orthodox theory “foolish” and plain wrong. (S. 14)
The old methods are easy and convenient. They work fine, it is argued, for most market conditions. (S. 15)
For centuries, shipbuilders have put care into the design of their hulls and sails. They know that, in most cases, the sea is moderate. But they also know that typhoons arise and hurricanes happen. They design not just for the 95 percent of sailing days when the weather is clement, but also for the 5 percent, when storms blow and their skill is tested. The financiers and investors of the world are, at the moment, like mariners who heed no weather warning. (S. 24)
And the subtle distinction, of thinking about prices as if they were governed by chance, has the been dominant, fructifying notion of financial theory for the past one hundred years. (S. 26)
The word comes from the Greek stochastes, a diviner, which in turn comes from stokhos, a pointed stake used as a target by archers. (S. 28)
When temperature rises above a certain critical level called the Curie point, magnetism disappears. (S. 29)
In history modernists argue that the course of human events is shaped by many trends, economic and social, enacted in the lives of millions of forgotten individuals; the historian’s task is to trace these trends. By contrast, traditionalists, now coming back into fashion pretend that history was shaped and dominated by a few great men, Caesar or Napoleon, Newton or Einstein, for example. (S. 39)
In one 1933 paper, [Alfred Cowles II] found what Bachelier would have predicted: Among twenty-four stockmarket forecasters whom Cowles systematically studied, he found “no evidence of skill”. (S. 54)
In fact, in 1976 some economists spotted such a pattern of regular January rallies in the stocks of small companies. Many investors close their losing positions towards the end of the year so they can book the loss as a tax deduction—and the market rebounds when they reinvest early in the new tax year. […] Alas, before you rush out to trade on this trend, you should know that its discovery seems to have killed it. (S. 55f)
Cheaper and safer to ride with the market. Buy a stock index fund. Relax. Be passive. Or as Samuelson at MIT put it: “They also serve who only sit and hold.” His advice then:
“A respect for evidence compels me to incline toward the hypothesis that most portfolio decision makers should go out of business—take up plumbing, teach Greek, or help produce the annual GNP by serving as corporate executives. Even if this advice to drop dead is good advice, it obviously is not counsel that will eagerly followed. Few people will commit suicide without a push.” From The Journal of Portfolio Management 1974. (S. 57)
[Sharpe’s] concept is straight forward. It says the more you risk, the more you expect to get paid. It says the most important risk you face as a stock-market investor is the general state of the economy, reflected in how the market is doing. It says that if you are rational you would nor normally want a stock that is going to die just as a recession arrives and you are about to get laid off; so to buy that stock, you have to be thinking it will rise so far in the good times that it will more than pay its losses in the bad times. (S. 68)
Scholes, Merton and I (Black) and others jumped right in and bought a bunch of these warrants. For a time, it looked as if we had done the right thing. Then a company called American Financial announced a tender offer for National General shares… (That) had the effect of sharply reducing the value of the warrants.
— “How we came up with the option formula.” Black 1989
In other words, they lost their shirts. But they did not care. The fact that their formula had correctly spotted the anomalous warrants suggested that their math was sound, even if their market intelligence was not. (S. 74)
In that sense, the formula puts a price on risk. (S. 75)
The whole edifice hung together—provided you assume Bachelier and his latter-day disciples are correct. (S. 77)
The old models are still taught, refined retailed, and used, but they are no longer viewed with quite the same degree of respect. As will be seen, that is just as well. (S. 77)
Seated at one row of desks, a pair of analysts spend their days studying the orders of the bank’s own customers. They are looking for broad patterns they can report back to the clients in regular newsletters. Theirs is the sort of market-insider information that, one form of the Efficient Market Hypothesis says, should not be useful; any profitable insights into trading data should already be reflected in prices. But thy do not buy that notion: “The biggest edge you can have is the private information of who’s buying what,” says one of the analysts. “We do not believe in the market is efficient.” (S. 80f)
By the Black-Scholes formula, there should be nothing of interest in such a [volatility] surface; it should be flat as a pancake. In fact it is a wild, complex shape. (S. 81)
None of this would exist if the original Black-Scholes formula were accurate. (S. 81)
Now, by orthodox theory, there should be no research department. You cannot beat the market, so all you need are a few traders and computers to stay even with it. (S. 81)
As James notes, there is a big difference between spotting veins of gold in old price charts and minting real gold in live markets. Those 7.97 percent average returns include some periods of hair-raising loss, when sticking to the strategy would have required steel nerves and deep pockets. (S. 82)
So how to explain so stark a discrepancy between theory and reality? Start looking at the assumptions underpinning the theory. (S. 82)
Discontinuity, far from being an anomaly best ignored, is an essential ingredient of markets that helps set finance apart from the natural sciences. (S. 87)
Big price changes, of more than five standard deviations from the average were far more common than the standard model allowed. Large changes, of more than five standard deviations from the average, happened two thousand time more often than expected. (S. 96)
But such ad hoc fixes are medieval. They work around, rather than build from and explain, the contradictory evidence. (S. 104)
The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight – as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out non-Euclidean geometry. Something similar is required today in economics. – John Maynard Keynes (S. 109)
But the variety of natural phenomena is boundless while, despite all appearances to the contrary, the number of really distinct mathematical concepts and tools at our disposal is surprisingly small. […] When a man has hammer, all he sees around him are nails to hit. So it should be no great surprise that, with our small number of effective mathematical tools, we can find analogies between a wind tunnel and a Reuters screen. (S. 116)
But the sensation of roughness had almost entirely been ignored by scientists. Euclid, the Greek geometer whose Elements is the world’s oldest treatise with near-modern mathematical reasoning, focused on its opposite, smoothness. (S. 123)
My contribution was, foremost, to recognize that in turbulent and much else in the real world, roughness is no mere imperfection from some ideal, not just a details from a gross plan. It is of the very essence of many naturals objects–and of economic ones. (S. 125)
Zipf, independently wealthy, was a university lecturer at Havard in a self-invented field called statistical human ecology. His Book, Human Behaviour and the Principles of Least Effort, saw power laws as an omnipresent pattern in social sciences. (S. 151)
If the time a modern scientist must lavish on publicity were redirected to discovery, what marvels would we see? (S. 189)
Well, the Efficient Market Hypothesis is no more than that, a hypothesis. Many grand theory has died under the onslaught of real data. (S. 193)
Two forms of wildness remain: abrupt change, and almost-trends. These are the two basic facts of a financial market, the facts that any model must accommodate. (S. 200)
Given the profits he and Pharaoh must have made, one might call Joseph the first international arbitrageur. (S. 201)
To say much with little: Such is the goal of good science. But most established financial models say little with much. They input endless data, require many parameters, take long calculation. When they fail by loosing money, they are seldom thrown away as a bad start. Rather they are “fixed”. They are amended, qualified, particularized, expanded, and complicated. Bit by bit, from a bad seed a big but sickly tree is built, with glue, nails, screws, and scaffolding. That people still lose money on these models should come as no great surprise. (S. 222)
To drive a car you do not need to know how it goes; similarly, to invest in markets, you do not need to know why they behave the way they do. (S. 229)
But these papers miss the point. They assume that the “average” stock-market profit means something to a real person; in fact, it is the extremes of profit or loss that matter most. […] In this light, there is no puzzle to the equity premium. Real investors know better than the economists. (S. 231)
Common sense and folk wisdom are often wrong, of course, but must never be ignored. (S. 231)
From 1986 to 2003, the dollar traced a long, bumpy decent against the Japanese yen. But nearly half that decline occurred in just ten out of those 4,695 trading days. (S. 234)
Suppose big news has inflated a stock price by 40 percent in a week, more than twice it normal volatility, What are the odds that, anytime soon, yet another 40 percent run will occur? Not impossible, of course, but certainly not large. A prudent investor would do as the Wall Street pros: Take a profit. (S. 235)
Continuity is a fundamental assumption of conventional finance. […] Without that, their formulae simply do not work. […] Alas the assumption is false and so the math is wrong. (S. 237)
Once upon a time, there was a country called the Land of Ten Thousand Lakes. Its first and largest lake was a veritable sea 1,600 miles wide. The next biggest lake was 919 miles across; the third 614; and so on down to the last and smallest at on mile across. An esteemed mathematician for the government, the Kingdom of Inference and Probable Value, noticed that the diameters scaled downwards according to a tidy, power-law formula. Now, just beyond this peculiar land lay the Foggy Bottoms, a largely uninhabited country shrouded in dense, confusing mists and fogs through which one could barely see a mile. The Kingdom resolved to chart its neighbor; and so the surveyors and cartographers set out. Soon, they arrived at a lake. The mists barred their sight of the far shore. How broad was it? Before embarking on it, should they provision for a day or a month? Like most people, they worked with what they knew: They assumed this new land was much like their own and that the size of the lakes followed the same distribution. So, as they set off blindly, they assumed, they had at least a mile to go and, on average five miles. But they rowed and rowed and found no shore. Five miles passed, and they recalculated the odds of how far they had to travel. Again the probability suggested: five miles to go. So they rowed further–and still no shore in sight. They despaired. Har they embarked upon a sea, without enough provisions for the journey? Had the spirits of these fogs moved the shore? (S. 242f)
First is the so-called martingale condition: that your best guess of tomorrow’s price is today’s price. Second is a declaration of independence: that tomorrow’s price is independent of past prices. Third is a statement of normality: that all the price changes taken together, from small to large, vary in accordance with the mild, bell-curve distribution. In my view, that is two claims too many. The first, though not proven by the data, is at least not (much) contradicted by it; and it certainly helps, in an intuitive way, to explain why we so often guess the market wrong. But the others are simply false. (S. 247)
The turbulent markets of the past few decades should have taught us, at least, that value is a slippery concept, and one whose usefulness is vastly over-rated. […] prime mover in a financial market is not value or price, but price differences; not averaging, but arbitraging. (S. 252)
But a full understanding of multifractal markets begins with the realization that the mean is not golden. (S. 252)
“I have this terrible sense of frustration,” says Olsen. “We send space shuttles into orbit; we send probes to Mars; but we haven’t studied the financial markets. We literally know nothing about how economics works.” (S. 254)
modern portfolio theory bases everything on the conventional market assumptions that prices vary mildly, independently, and smoothly from one moment to the next. If those assumptions are wrong, everything falls apart: Rather than a carefully tuned profit engine, your portfolio may actually be a dangerous, careering rattletrap. (S. 265)
“Despite results that are inherently inaccurate and unreliable for this purpose”, groused Intel CEO Craig Barrett recently. “Black-Scholes is the only method available.” (S. 271)
To safeguard against bankruptcy, most banks in the world are obliged by law to keep a certain amount of cash on hand–a capital reserve. It can be tapped in extremis, but its main purpose is to assure the rest of the world that all is safe, and the bank that it is a safe partner with which to do business. (S. 272)
Assume the market cracks and you land in the unlucky 5 percent portion of the probability curve: How much do you lose? Well, 12 percent, you say. Wrong. Even the VAR model recognizes that the actual loss could be greater; the amount the theoretical 12 percent is the “overhang”. […] But if price-changes scale, the overhang can be catastrophic. […] There is no limit to how bad it could get for the bank. (S. 273)
“Planning for crisis is more important than VAR analysis.” (S. 274)
Wassily Leontief: “In no field of empirical enquiry has so massive and sophisticated a statistical machinery been used with such indifferent results.” (S. 275)
They are like a shipbuilder who assumes that gales are rare and hurricanes myth; so he builds his vessel for speed, capacity, and comfort–giving little thought to stability and strength. To launch such a ship across the ocean in typhoon season is to do serious harm. Like the weather, markets are turbulent. We must learn to recognize that, and better cope. (S. 276)
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