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Strategies & Market Trends : The Rational Analyst

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To: HeyRainier who wrote (206)	1/16/1998 12:44:00 AM
From: ftth	Read Replies (4) of 1720

Rainier: Great call on EK! Still looks like there's more to come. On your Bollinger band observations, I think the standard deviation / volatility measure used in Bollinger bands is based on the regular statistical definition of standard deviation of an arbitrary data set. Option pricing models (Black-Scholes) uses lognormal volatility. Regular standard deviation doesn't give the correct result if used as the volatility measure in B/S because there's an underlying assumption that stock prices follow a log-normal distribution (a normal distribution (regular standard deviation) would allow negative prices; other option pricing models use weird empirical distributions, but in any case there is always an effort to skew the distribution so that negative prices aren't allowed). I just wonder if a lack of fit to the underlying assumed distribution has any relation to how well Bollinger bands perform as indicators (not to mention the observation interval). Maybe Peg could address this too. I'm diggin' deep here in the old brain, but I think there's a t-statistic that can be used to validate or invalidate the underlying premise of a normal distribution. I'm pretty sure this is part of the reason why Bollinger himself says never use periods less than 10. Also, isn't there only about a 16% chance that the price will move by more than a standard deviation in one direction over the time period of interest, meaning there is always a tendency to cluster about the moving average, and to swiftly move inward toward the MA if its statistics get out of line. Large cap issues may more closely approximate a normal distribution, with smaller, more consistent swings and less tendancy to gap. My point is (yes there was a point to this rambling) perhaps a measurement of "Bollinger efficiency" could be attached to the indicator so you have a gauge of how much faith to put in the signal??? dh

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