Standard Deviation Bands
Bollinger bands are a very popular application of price distributions. They do not detrend price, but calculate the standard desiation of prices over a period of 20 days and form a band of 2 standard deviations around the trendline. It is common for traders to vary both the period and the number of standard deviations used to construct the band. Once calculated, Bollinger bands can be displayed on any price chart and used to generate buy and sell signals, much the same as any other channel breakout system. Using a smaller Bollinger band, for example, 1 standard deviation, will give many more signals than using one of 3 standard deviations. At the same time, a band of 3 standard deviations translates into risk that is 3 times greater than 1 standard deviation. Signals produced with a larger band tend to be more reliable, but have greater risk.
USING THE STANDARD DEVIATION
The data used to determine the standard deviation is very important. Because it is a statistical measure, it is most accurate when a large amount of data is applied. For example. you might find that 1 standard deviation of the crude oil daily price move is only SO.25 per barrel when measured over the past 10 years, but during the 6 months of the Gulf War the same measurement yielded $.50, twice as large.
Most trading applications using the standard deviation tend to apply short data intervals to its calculation, such as 20 days. This short period is not likely to represent the same price distribution as a 10-year calculation; therefore, the probabilities given by the resulting standard deviation value must be interpreted differently. While it is less likely that the price will make a move of 3 standard deviations compared with 1 standard deviation, the probabilities can be misleading. Statistics tell us that there is only a 1% chance that prices will move a distance of 3 standard deviations higher or lower; however. that value is reliable only when measured over a long data period. If you selected 20 days of unusually low volatility, the chance of a 3standard deviation move Would be very high.
The frequency distribution is another very practical approach to measuring price distributions. It has the advantage of having a much clearer visual interpretation. While the standard deviation gives us what appears to be a highly mathematical probability, the large error factor that is caused by small amounts of data may make its usefulness about the same as the frequency distribution.