ANALYTICAL TOOLBOX: Bollinger Bands and %b
November 23, 2006
In addition to statistical volatility, Bollinger Bands provide a nice visual for relative volatility levels. This is accomplished with contracting and expanding standard deviation bands around a simple moving average, usually based upon the closing price for a set period. A second volatility measure created by John Bollinger is %b, a tool used to quantify the price relative to band width [BW] of a Bollinger Band.
Why introduce these two tools while exploring option volatility? There are two reasons: 1) implied volatility, a component of option pricing is partially determined by the past volatility for the underlying, and 2) it represents a different view of past volatility for the underlying to provide the trader with a better insight on relative levels of volatility for the underlying.
Bollinger Bands and Statistical Volatility
One standard setting for Bollinger Bands includes the use of a 20-period simple moving average [SMA] with 2 standard deviations used to construct the upper and lower band. An Optionetics article search for “Bollinger Bands” in the Title/Text should provide more basic indicator usage, if needed. Cisco Systems (CSCO), the stock reviewed last week, will be used again here. Figure 1 provides a daily chart for CSCO with the standard Bollinger Band [BB] described, along with the 20-day statistical volatility [SV], to coincide with the 20-day SMA used to construct the bands. 
Figure 1: Daily CSCO Chart with Bollinger Bands and 20-day Statistical Volatility
Recall that SV is calculated by annualizing the standard deviation of price movement (not price) over a set period of time. ProfitSource uses 252 days for the number of trading days in one year. You can see that both volatility-based measures display strong moves in early August and early November when CSCO gapped upward. The second move actually includes two gaps upward and is the reason CSCO was included on the stock ranking performed last week.
Since two standard deviations are used to construct the bands, we expect closing prices to remain predominantly with the bands. BBs do a great job of incorporating relative price information along with relative movement for the stock over a certain period of time. In terms of price, we can quickly see that the initial gap upward in August caused price to close above the upper band and represented atypical price action relative to the previous 20 days. Additionally, this move was not mean-reverting; the price moved aggressively right through the 20-day moving average. From mid-August through late October price would periodically touch the 20-day mean price (mean-reverting) then head back upward towards the upper band.
SV on the other hand does not give you information about where price is relative to previous movement. However, it is easier to gauge increasing, decreasing and steady periods of relative volatility for the stock. While it’s easy to detect more extreme band expansion or continuous band contraction, it is more difficult to note subtle changes. Two bands, a moving average and price can slightly distort the view. SV displays a more straightforward view of changes in the volatility environment.
%b
This indicator (%b) provides information about where price is relative to the upper and lower band and is based on George Lane’s Stochastic indicator (see bolingerbands.com for more information). This is accomplished by calculating %b as follows:
%b = 100 X (Lastest Stock Close – Lower BB) / (Upper BB – Lower BB),
where (Upper BB – Lower BB) is the total band width.
Using the following data points:
Upper BB = 28.14
Lower BB = 22.76
Close Price = 26.80
Average = 25.44
%b = 100 X (26.80 – 22.76) / (28.14 – 22.76) = 75.09
Since the equation’s denominator includes closing and lower band data, we note that the value 75.09 reflects price that is within the bands [greater than 0, but less than 100] and approximately three quarters away from the lower band from a total bandwidth standpoint.
Information about price relative to the two bands is provided by %b. The manner in which it is calculated allows the trader to make an apples-to-apples comparison of different stocks. The benefit of this is that it can then be used as a ranking tool to find trades.
Stock Ranker
One Optionetics Platinum Stock Ranker makes use of %b and Relative Strength Index [RSI] data to rank stocks in a variety of different ways. The tool represents a stock query that uses volatility and price momentum to yield a sequence of stocks by the following:
1) Breakout Hi Using Short BB (%b)
Stocks are ranked by highest %b using the 20-day SMA Bollinger Band.
2) Breakout Low Using Short BB (%b)
Stocks are ranked by lowest %b using the 20-day SMA Bollinger Band.
3) Lowest Short BB Bandwidth* (possible Squeeze)
Stocks are ranked by lowest 20-day SMA Bollinger Band Bandwidth.
4) Lowest Short BW / Long BW (Squeeze)
Stocks are ranked by lowest of the
20-day SMA** BB BW / Long BB BW.**
5) RSI = Relative Strength Index in percent.
Stocks are ranked by lowest days or highest days inside an RSI range.
* Bandwidth (BW) = (Upper BB – Lower BB) / Average
** Actual short values range from 20-30 days for this calculation and long values range from 100-120.
If you have access to this ranker, take some time to play around with the tool to see what types of price charts result. Add BB and SV to chart to gain more of an intuitive sense of the results returned. When using rankers that identify quiet stocks from a volatility standpoint, it’s very important to also review stock news to determine if the underlying price consolidation is occurring for a particular reason.
When a stock is holding steady at one level due to a pending corporate action such as a stock buyout at a pre-determined price, the stock will appear in your results. You want to be sure not to establish a directional trade for such a stock. One step you can take to reduce the stock news review time for your results is to bring up a chart for the underlying and check for large one day price moves. Note the date of the move and target your news search for that period of time.
Summary
Bollinger Bands provide option traders with a second visual display of volatility levels. When using this tool for trading, be sure to thoroughly understand BB application before making assumptions about what signifies an alert and what does not. According to John Bollinger, the indicators are most powerful when used in combination with other technical tools that are derived using different measurements (i.e., a price indicator and a volume indicator). By incorporating %b in the analysis, this volatility measure can be used to rank stocks. This will be completed next week.
To see the other articles by this author, please click here.
Clare White, CMT
Contributing Writer and Options Strategist
Optionetics.com ~ Your Options Education Site
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