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The odds of financial ruin in a free, global-market economy have been grossly underestimated.
Thus, my research could help people avoid losing as much money as they do, through foolhardy underestimation of the risk of ruin.
If prices take a big leap up or down now, there is a measurably greater likelihood that they will move just as violently the next day.
If the side doubles, the area quadruples;
My principal objections—that prices do not follow the bell curve and are not independent—were heeded,
Extreme price swings are the norm in financial markets—not
A sound trading strategy or portfolio metric would build this cold, hard fact into its foundations.
It can be—and increasingly is—used in computer simulations to “stress-test” a portfolio, to play a wider and darker range of “what-if?”
Rule II. Trouble runs in streaks.
Market turbulence tends to cluster.
they also know that it is in those wildest moments—the rare but recurring crises of the financial world—that the biggest fortunes of Wall Street are made and lost.
To use the economists’ terms: In substantial part, prices are determined by endogenous effects peculiar to the inner workings of the markets themselves, rather than solely
The power of chance suffices to create spurious patterns and pseudo-cycles that, for all the world, appear predictable and bankable.
Likewise, bubbles and crashes are inherent to markets. They are the inevitable consequence of the human need to find patterns in the patternless.
This trading time speeds up the clock in periods of high volatility, and slows it down in periods of stability. Mathematically, I can write an equation showing how one time frame relates to the other and use it to generate the same kind of jagged price series that we observe in real life. This
Professional traders often speak of a “fast” market or a “slow” one, depending on how they judge the volatility at that moment. They
small example: “stop-loss” orders are imperfect, to put it mildly.
But as many have learned to their grief, when prices are really flying, they typically whiz past the target so fast that even the most attentive
the H exponent of price dependence, and the α parameter characterizing volatility. A
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 other 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 warnings. This book is such a warning.
that subtle distinction, of thinking about prices as if they were governed by chance, has been the dominant, fructifying notion of financial theory for the past one hundred years. On
When temperature rises above a certain critical level called the Curie point, magnetism disappears.
Fortunately, how and why each individual particle interacts with the next happens to matter less than one may think.
We can think of financial prices in much the same way: not predictable, not controllable. Under such circumstances, the best we can do is evaluate the odds for or against some outcome: a stock rising a certain
So, what kind of variability generator will you use? If mild, the resulting price charts will vary within a certain well-defined range;
For the most part, this way of drawing the Dow makes it appear as if history did not begin until about the 1980s, when the index finally left the 1,000-mark behind.
magnitude of the index fluctuations increased towards the end of the twentieth century,
Logarithms rescale everything, so that a 1 percent change in 1900 will look about the same on our charts as a 1 percent change in 2000.
The strip alternately narrows and widens, in some apparently haphazard cycle of thin and broad. Also, the spikes
seem most likely to cluster together when the strip is wide. Now we
Next look at the Dow variations. The spikes are huge. Some are 10σ; one, in 1987, is 22σ. The
The very big changes, plus or minus, are shown at the right end of the chart; the
A perfect, unseasoned bell curve has a kurtosis of three. A hot, fat-tailed curve of the sort we have been finding would have a higher spice number, while a curve that had been boiled into a dull paste would have a lower number.
Just the opposite appears to happen in the medium term, three to eight years. A stock that was rising over one multi-year stretch has slightly greater odds of falling in the next.
One, the prices bounce around a lot; and, two, they appear to move in irregular trends.
The size of the price changes clearly cluster together. Big changes often come together in rapid succession, like a fusillade of cannon fire; then come long stretches of minor changes, like the pop of toy guns.
If the price changes start to cluster, or the prices themselves start to rise, they have a slight tendency to keep doing so for a while—and then, without warning, they stop.
abrupt change, and almost-trends.
The flood came and went—catastrophic, but transient. Market crashes are like that. The 29.2 percent collapse of October 19, 1987, arrived without warning or convincing reason;
The market’s second wild trait—almost-cycles—is prefigured in the story of Joseph.
Seven years of famine would follow seven years of prosperity.
He advised Pharaoh to stockpile grain for bad times to come.
Noah Effect and the Joseph Effect.
A low-α market would be risky, prone to wild price swings. A market with higher α differs less from the classic coin-tossing market.
An H of one half implies each price change is independent of the last. A larger H suggests the data are “persistent,” trending in the same direction. A smaller H implies “anti-persistence,” a tendency to double back on themselves.
the name is short for range divided by standard deviation.
The idea is simple: The Joseph Effect depends on the precise order of events, while the Noah Effect depends on the relative size of each event.
To complete the test, just compare the deck before and after shuffling. If there is a difference, it must be due to the long-term dependence in the original data; the precise sequence must have been important in the original data, and the degree of that importance can be measured.
