By Jerry Wagner I visited New York City a few years ago. I sat for over an hour as the plane was prepared and de-iced in the middle of what seemed to be unending snowfall. As I watched the snowflakes dance about outside my window, I was struck by their quick and random movements. Although a part of the same storm, each individual snowflake seemed to have a mind of its own. The great composer Tchaikovsky captured this sense of randomness well in the “Waltz of the Snowflakes,” part of his monumental score for “The Nutcracker.” The seemingly haphazard sounds of various instruments invoke a lightness and surreal quality, as runs of harps, flutes, bells, and violins dart in and out of the listener’s ears. In the more modern world we live in, a popular screen saver features a winter scene with a gentle snowfall. If one looks behind the scene to the coding of these visual masterpieces, the heart and soul of the imagery is a simple random-number generator. Each new number thrown out by the device sends the snowflakes darting in unpredictable directions, reinforcing the illusion. For most of my 50-plus-year career as a financial analyst, I have been told that stock prices follow this same random behavior. When I started in 1969, the die was already cast. Randomness was already an underlying rationale for Professor Harry Markowitz’s 17-year-old mean-variance passive-allocation methodology that still holds sway over most financial advisers. It held that since stock price direction was not determinable, the best result could be accomplished by mathematically achieved diversification between asset classes. Backup for this way of thinking arrived from others in academia. Professor Paul Cootner released a book called “The Random Character of Stock Market Prices” in 1964, followed by Eugene F. Fama’s 1965 paper “Random Walks in Stock Market Prices.