Stocks & Commodities V. 24:1 (10-11): Letters To S&C by Technical Analysis, Inc.
The editors of S&C invite readers to submit their opinions and information on subjects relating to technical analysis and this magazine. This column is our means of communication with our readers. Is there something you would like to know more (or less) about? Tell us about it. Without a source of new ideas and subjects coming from our readers, this magazine would not exist.
Had Neil Jon Harrington contacted me prior to writing his article (“The Link Between Bollinger Bands And The
Commodity Channel index,” October 2005 S&C), I could have saved him some trouble, for the relationship between the commodity channel index and Bollinger Bands is well known and has been widely explored. If the same input data is used and the constants equalized, it is true that the main difference in logic between the two approaches comes down to the difference between standard deviation and mean absolute deviation. However, that is not a trivial difference; it is a significant and crucial difference. When prices are close to the average, there is little
difference between the calculations, but when prices move away from the average, the differences become dramatic.
This is due to the squaring of the deviations from the mean in standard deviation, a calculation that accentuates large deviations. Mean absolute deviation has no such magnifying mechanism. This difference is most critical when it is the greatest — that is, at the extremes — because it allows our definition of relatively high and low — the Bollinger Bands — to remain germane to the rapidly evolving price structure. Please note that these two series cannot be made to correspond by adjusting the constants involved, since the difference is nonlinear. This nonlinearity arises from the squaring of the differences in the calculation of standard deviation.
For a normally distributed series, series, MAD is approximately equal to 0.7979 standard deviation; however, security prices are not normally distributed,
so we can expect the difference to be somewhat greater. Though Mr. Harrington did “uncover” the facts, he missed the worth. Traders should not consider %b — that is, the oscillator derived from Bollinger Bands
— and the commodity channel index to be interchangeable. Donald Lambert and I created different tools for different purposes; each has its unique characteristics and utility.
Thanks again for your fine publication, which I read religiously.
JOHN BOLLINGER, CFA, CMT
Readers: See also the explanatory article on Bollinger Bands called “Bollinger Bands Vs. Trading Bands”
in the December 2005 S&C.—Editor