By Lawrence G. McMillan
A “modified Bollinger Band” (mBB) buy signal is nearly upon us. It almost occurred today (Thursday, January 13th), but missed by a couple of points. We began to wonder how past sharp market declines lined up with the eventual mBB buy signal. Was the first signal successful, or did it take a number of probes before the market eventually bottomed. Was the mBB buy signal the bottom of the market, or did it continue on downward at a later time? Those are good questions, and we’ll attempt to shed some light on them in this article.
The “mBB” System
For those now familiar with the mBB System – or for those who have forgotten – let’s review the particulars of the system. We use “modified Bollinger Bands” in order to create these signals. A mBB differs from the normal Bollinger Band (as invented by John Bollinger, and as found in many charting services) in the way that volatility is calculated. John Bollinger initially used the standard deviation of the closing prices of the undelrying over the past 20 days in order to calculate volatility. That seems like a logical thing to do, but in the Black-Scholes Model and in many other mathematical approaches to volatility, mathematicians have traditionally defined volatility as the standard deviation of daily closing price changes. So that’s what we use, because it is important that our volatilities line up with Black-Scholes implied volatilities in all of our analyses.
We draw four Bands around the chart of $SPX. The first set of Bands is spaced +/- 3 standard deviations (sigmas – σ) from the 20-day moving average of $SPX. And the second set is spaced +/-4σ. During periods of high volatility, the Bands are quite wide, and during periods of low volatility, they are quite narrow...
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