COMPARISON BETWEEN ACTUAL PRICE CHANGES AND NORMAL DISTRIBUTION The average weekly natural log changes in the Standard & Poor's 500 index from April 1986 through December 1995 was measured and the standard deviation of these changes calculated. The results show an average weekly log change of 0.19% (annualized to 9.88% by multiplying by 52) and a weekly standard deviation of these changes of 2.0% (annualized to 14.42% by multiplying by the square root of 52). The entire range of price changes was then normalized by creating a series in which the mean is equal to zero and the standard deviation is equal to 1 (by subtracting 0.19% from each weekly change and then dividing the results by 2.0%). Using Excel's frequency function, the number of times these different-sized moves occurred was calculated and then these results divided by 493 (the total number of weeks) to get the actual percentage of times these moves occurred. -L.D.C. |
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