Daily Speculations
April 2003
But as for certain truth, no man has known it,
Nor will he know it; neither of the gods,
Nor yet of all the things of which I speak.
And even if by chance he were to utter
The perfect truth, he would himself not know it:
For all is but a woven web of guesses.
Xenophanes
Statistics is often defined as the process of uncovering large-scale regularities in the face of individual variabilities. There is natural variability in all experiments. We are sampling from a characteristic of the phenomena being studied. There is much uncertainty in using any sample to represent this characteristic. Almost all characteristics show individual variability.
A good book that documents this variability in humans is “You Are Extraordinary,” by Roger Williams. It is to be expected that when taking repeated from any population, including stock returns, that there will be differences relating to the instrument used to measure, the definition of the variable, and—most important of all—the variability of the characteristic in the population.
In short, there is a distribution of the characteristic from which we are sampling. Each sample is expected to be different, and it is the task of the statistician to measure the parameters of that distribution, including variability, and to estimate the uncertainty of conclusions about these estimates.
If you'd like to add a comment to those below, please e-mail ltkenner@bloomberg.net.
Stephen Stigler, professor of statistics, University of Chicago:
Uncertainty is always a tough topic, but I like Laplace's statements from his “Essai Philosophique”:
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1) Laplace’s famous statement of determinism:
If an intelligence, at a given instant, knew all the forces that animate nature and the position of each constituent being; if, moreover, this intelligence were sufficiently great to submit these data to analysis, it could embrace in the same formula the movements of the greatest bodies of the universe and those of the smallest atoms: to this intelligence nothing would be uncertain, and the future, as the past, would be present to its eyes.
2) This statement, reconciling probability with determinism, first appeared
in Laplace’s 1795 lectures at the Ecoles Normales:
The regularity which astronomy shows us in the movements of the comets doubtless occurs in all phenomena. The curve described by a simple molecule of air or water vapor is regulated in a manner just as certain as the orbits of the planets; the only difference between these is that introduced by our ignorance.
Probability is relative in part to this ignorance, and in part to our knowledge.
Pete La Corte:
I notice there are huge philosophical implications in the subject of uncertainty versus variability: The eternal underlying question about this matter is: Is it possible to predict the future of market movements by means of statistical sampling?
I wrote in “Theory and Practice of Speculation “ (unpublished work):
Werner Heisenberg's Principle of Uncertainty has had deep implications in science because it has put an end to the pretension that we live in a deterministic universe. The truth about the entire cosmos is we cannot ever be certain about anything; we only may pretend for a timid approximation to sureness, a real setback for prognosticators. This principle is ingrained in the very intimate nature of reality and of course, markets are not the exception.
Fortunately in our business we are not soothsayers.
Leonard Kreicas, trader:
The wonderful thing about anomalies is they lead to finding
new paradigms. If an anomaly don't fit with the present order there probably is
a new set of rules out there the markets have not taken into consideration.
The orbits of planets were anomalies that could not be totally reconciled with a
geocentric theory of the universe. It took a heliocentric view of the planets to
abolish planetary anomalies. Then the anomalous behavior of the planetary orbits
disappeared.
The discovery of market anomalies leads to challenging many of today's market
rules and norms because the anomalies tell us there is something not quite
kosher in these accepted truths. The geocentric view lasted for thousands of
years because it was good enough for those times. However when telescopes and
other precision instruments became available the shortcomings of this view were
exposed.
Today's market structure has evolved from roots established hundreds of years
ago. Anomalies are popping up all over the place as technologies expose the
limitations of the present norms. Accepting new norms require the overthrow of
old ones but the power brokers have too much capital at stake to simply walk
away from their trillion dollar investments. The new norms begotten from
anomalies will eventually reap their just rewards at the expense of the old
rules.
Adam Robinson, aka "The Lucubrator":
Date: 03/20/2003 8:57:53
I agree with everything Leonard says, but I'd like to point out a
terminological inexactitude (to borrow Alexander Haig's brilliant dodge).
I think it no mere semantic quibble to say that anomalies should NOT be viewed
as departures from the norm, unless we mean by departure a 4 or 6 or whatever
big number you choose sigma event.
Normal variation is a departure from the norm, is it not? (I was about to say
n'est-ce pas, but I caught myself.)
Nor is it merely unexpected departures from the norm that qualify as an anomaly.
It's gotta be unexplained by a law to qualify as an anomaly (anomaly, without a
law/rule, comes from the same root as astronomy, rule/law of stars).
So being a departure from the norm is necessary but not sufficient to qualify
an event as an anomaly, the event in question cannot be subsumed under the
rubric of the law, causal or otherwise, in question.
But these are mere quibbles,
Leonard Kreicas replies:
Quite correct about anomalies versus normal noise. In
"Reinventing the Bazaar,"
McMillan talks about price dispersion: "Despite the ease of comparison shopping
on the internet, however, it has not eliminated the dispersion of prices....More
systematic studies find the same thing: the ready availability of price
information has not driven prices of identical items into alignment."(p49)
This is similar to stock prices since one share of stock is the same as another,
yet prices can vary second by second. Interesting how price dispersion seems to
be a natural feature of markets. As you point out though, when does dispersion
end and anomaly begin? Difficult question to answer.
"The secret of business," the shipping tycoon Aristotle Onassis remarked, "is to
know something that nobody else knows." (ibid, p52)