Michel Pireu Columnist

From Peter Bernstein in Against the Gods: The Remarkable story of Risk: Mathematics tells us that the variance — a measure of how observations tend to distribute themselves around their average level — of a series of random numbers should increase precisely as the length of the series grows. Observations over three-year periods should show triple the variance of observations over one year, and observations over a decade should show 10 times the variance of annual observations. If the numbers are not random, because regression to the mean is at work, the ratio of the change variance to the time period will be less than one. Baylor University professors William Reichenstein and Dovalee Dorsett studied the S&P 500 from 1926 to 1993 and found that the variance of three-year returns was only 2.7 times the variance of annual returns; the variance of eight-year returns was only 5.6 times the variance of annual returns. When they assembled realistic portfolios containing a mixture of stocks...

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