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Kim Zussman

12/03/2005
Risky Regression, by Kim Zussman

The Stigler paper on regression to the mean (kindly offered by Doc) describes the repeating exam analogy:

"Verbally, we may consider a stochastic time-varying phenomenon, where two correlated measurements are taken of the same person or object at two different times. For example, we might consider the scores recorded on two examinations taken by the same individual at two separated times. Suppose the first score is exceptionally high near the top of the class. How well do we expect the individual to do on the second test? The answer, regression teaches us, is 'less well', relative to the class's performance. And the reasoning is clear: there is a selection effect. The high score on the first occasion is surely due to some mixture of successes in two components, to a high degree of skill (a permanent component) and to a high degree of luck (a transient component). The relative bearings of the two components of skill and luck on the first time score would require measurement to pin down, but the fact that we expect both to have, on average, contributed to the exceptional first outcome is intuitively plausible, even obvious. And on the second occasion we expect the permanent component of skill to persist (for that is the meaning of permanent) while the transient component of luck will, on average, not be present (for that is the meaning of transient)."

So a student taking numerous equivalent exams should have a mean score which approaches measurement of skill, since luck is a random component averaging zero over many tests.

In a changing-cycle paradigm of trading, investors weigh various parameters to continuously change their position. Success (and failure) in such trading over various time periods should also attribute both to a luck and skill component. Over time, the luck component converges to zero and skill is demonstrated. However the problem with markets would seem to be sticky luck. Persistence of various regimes favor certain "skills": momentum/growth in the 90's, value/small stocks in the 00's, bullish bias 1946-69, 82-00, and bearish 1929-50, etc., as well as the un-announced change in regimes which are obvious only in retrospect.

Was Mr. Hill, who bought VL1's from 1970's-00 and sold out with millions, a skillful trader, or was 20 years too short to eliminate luck from the test? To him and his family, during an investment lifetime, he was genius. Perhaps the persistence of luck in markets, coupled with useable investment lifespan, makes it less an SAT than a game of chicken with risk.

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