Mean Reversion Recast as Measurement Error: Lessons for Finance from Galston's Fallacy
This paper explains why so many real life phenomena generate regression towards the mean or mean reversion results. We start our analysis by revisiting Galton's original paper on the height of children and the height of parents. We then show that the regression towards the mean result also holds for year-to-year performances of children in the L.A. school district, U.S. state unemployment rates, baseball player performances, and mutual fund rankings. To clarify the connection to a measurement error type problem, we relate the high temperature in various U.S. cities to the high in the previous year for randomly selected dates. Finally, we show how this hypothesis may apply to the price earnings ratio (P/E) anomaly and the stock market overreaction hypothesis.
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