Tuesday, September 04, 2007

Blindsided by our expectations

kw: book reviews, nonfiction, finance, philosophy

There is no closed system. Those who try to understand, or worse, forecast (predict), what is going on, all base their conclusions on closed-system thinking. Moreso, we all model the world around us (as we perceive it), simply so we can grab the tools we need to cope with it from our "kit" of experience: "This is like that, so I need to do thus..." The amazing thing is, it often works.

What to do when it doesn't? People today talk of "paradigm shifts." They happen more often than we realize. When I was a child, mountains were "explained" as wrinkles on the earth like those seen on the skin of an apple that is drying out; the earth was shrinking as it cooled. By the time I got to college, there was "The New View of the Earth" (a textbook title), based on continental drift and "plate tectonics".

The opening scene of The Black Swan: the Impact of the Highly Improbable portrays the discovery of black swans in Australia more than a century ago. Before then, whiteness was part of the definition of "swan". Until one was seen, nobody dreamed swans could be non-white. The author, Nassim Nicholas Taleb, uses the Black Swan as a metaphor for a (comparatively) rare, unexpected event that changes everything. But in the course of the book, he brings out that these highly significant events are more common than we suppose.

In 1972 Rapid City, SD suffered a massive flood. One foot (30cm) of rain fell in half a day, just downstream from a "flood control" earthen dam. One side canyon to the Rapid Creek canyon had a bridge crossing a stream that is usually a half meter wide and about ankle deep. After the flood, engineers could see that rocky streambed sediment had been washed out and replaced. They dug down with a backhoe to see how deep the scouring had been. They never found out.

The bridge is (was?) supported by large pillars that had been placed on a footing dug 6 meters below the streambed. The engineers found, another meter deeper yet, a pickup truck in the sediment, washed in during the flood. They didn't dig much further. I remember the awe in their voices as their "gradualist" paradigm began falling apart. They realized that most of the sediment movement in streambeds occurs during large, rare floods. Hydrologic theory applied to the Rapid City flood of '72 indicated it was a 500-year flood. But historical evidence indicated it might not be quite such a scarce event.

Not twenty miles away, along the east side of the Black Hills, a fellow student of mine studied boulders ranging in size from a meter to four meters; masses from a tonne to 30 tonnes or more. They are fanned out on the plain below a narrow canyon that hosts a modest stream. By measuring the size of lichen patches (lichen grows very slowly), he was able to determine that there had been twenty events in the past 5,000 years that emplaced such boulders as much as two miles from the canyon mouth. They occurred about every 250 years.

After calculating the flow needed to move these boulders, he showed that such floods were in the realm of "1000-year floods", and that there "should" have been between four and seven such floods, not twenty. Historical climatology indicates the climate over the past 5,000 years has seen little change. Rare events are not quite so rare.

Dr. Taleb has worked primarily in financial markets. He has seen the surprises that occur, and what they can do. The entire industry had its past century of profits swallowed up in the foreign banking crisis of fifteen years ago. Everyone, absolutely everyone, was taken totally unawares. What gives?

He writes of "The triplet of opacity":
  • the illusion of understanding, or how everyone thinks he knows what is going on in a world that is more complicated (or random) than they realize;
  • the retrospective distortion, or how we can assess matters only after the fact, as if they were in a rearview mirror (history seems clearer and more organized in history books than in empirical reality); and
  • the overvaluation of factual information and the handicap of authoritative and learned people, particularly when they create categories—when they "Platonify."
He devotes a section of the book to each sort of error. But he devotes particular spleen (in part 3, but spilling over throughout) at the "normal" curve of error, usually called the Gaussian Distribution, the famous "bell curve". Things that can't vary a whole lot (people's heights: 3m or less; scatter of measurements with a meter stick: a few mm) often do follow mathematical rules based on the Gaussian.

But many, probably most, natural phenomena follow tendencies that have much greater variability (rainfall from a single storm: usually a cm or two, but can be meters; payoff from a new invention: usually little or none, but might be billions).

I have to tell him, there is a trace of good news out there. The risking methodology used in the oil industry is based on lognormal distributions. If the expected field area is between one and twenty sq km (not unusual), the oil-bearing layer thickness between 0.5 and 12 m, and the porosity expected to range from 10-60%, one multiplies the limits, applies a scaling factor to reset the "sideboards", and computes an expected production from 120,000 to 30 million barrels.

The "most likely" value is a bit under 2 million barrels, and if drilling the hole costs more than the profit from one million barrels, you have a 75% chance of losing money on the hole...but a 15% chance of making enough to drill ten or more "dry holes" (and the 10% left over is an "ordinary" level of profit). How many bankers would bet on odds like that?

Yet such risking strategies still assume a closed system. It takes another set of ideas (futures markets or political machinations, for example) to better assess the entire risk. Yet Taleb writes, "...to understand the future to the point of being able to predict it, you need to incorporate elements from this future itself." Simply: you have to know the future already to predict it. No can do. Thus the prevalence of hedging.

In such arenas, how can we even claim expertise? We are experts at sounding expert, but those who survive are actually lucky. Oil men have a cogent saying, "It is better to be lucky than good." Exxon, Shell, BP, Conoco and others were built more on luck. E.W. Marland, founder of Conoco, said in the 1930s, "We know how to find oil now. We have the right science, the right methods, the right engineering," not knowing he'd already found his last barrel of oil.

But we wish to believe in expertise: "We have a natural tendency to listen to the experts, even in a field where there may be no experts." And where are the loudest "experts" today? In finance and investing. I get a weekly update from Motley Fool, that I seldom read. They are but one contrarian voice among dozens, each with a totally different set of "hot tips." They are expert at sounding expert. Look at this chart; it is the distribution of the daily percent change of the NASDAQ over the past 35 years or so (~9,200 data points), analyzed as a Gaussian Distribution:

It is easy to see there is no meaningful "fit". Yes, about 98% of the days are rather close to the "fitting" line, but look at the top and bottom 1%. 9,200 points cover a range of a bit less than -4 to +4 sigmas. Yet, there are plenty of days (about a hundred!) that the excursion, either plus or minus, exceeded 5 or 6 sigmas. Such curves for single stocks are even wilder; 15- and 20-sigma excursions occur millions of times more frequently than a "Normal" bell curve would predict.

Being a compulsive analyst, I took a look at each side (the pluses and minuses) separately, and applied lognormal and power law analyses. Dr. Taleb likes fractal (power law) math, I like lognormal math. I have in thirty years seen only one trend that genuinely followed a power law rule. Even the chart on page 327 that shows two power law regimes, with a transition from one to the other is actually diagnostic of a single lognormal trend.

So I applied both kinds of statistic...close, but no cigar. Then I found a way to generate a "symmetrical" lognormal analysis. I applied the appropriate distortion to the numbers and let Minitab have a whack at the new values. The result is this chart:

That's much better! Minitab, of course, concentrates its fitting where most of the data are. A properly weighted analysis, putting higher relevancy to the outer realms, where you can get helped or hurt much more, would tilt the blue "fitting" line a little more shallowly, raising the "standard deviation", which is here actually a "root log variance".

In this analysis, the formerly "extreme" events are seen to be part of the expected distribution. Thus, a rise or fall of 20% is about a 3.5-sigma event, not a 15-sigma event. More to the point, about a dozen 10% (up or down) days occured in the 35-year period, so one ought to be prepared for such days in any portfolio, every few years, per equity holding.

I am just beginning to get Dr. Taleb's point. I don't plan to stop. I think his book is the best treatment of uncertainty (or whatever you might prefer to call it) to be had today.

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