## BOLLINGER BAND In a previous post, I have discussed in detail the concept of moving average. I have also demonstrated the concept with the help of examples. Here we will discuss a technical indicator known as the Bollinger Band (BB). It is an indicator which uses the concept of moving average, but combines it with the concept of confidence interval. A confidence interval is a statistical concept which combines descriptive statistics with probability theory. Generally speaking, we say that if X is a random variable and S is the variance, and if X follows a normal distribution, then if we construct an interval equal to X +/- 2S, we can say with 95% confidence that any value of this random variable will lie within this interval. For example, if ri is the daily returns from a stock over a period of time with mean r* and variance s2 , then we can say that in the next 100 trading days, 95 times the daily returns will lie within r* +/- 2s. The concept of Bollinger Band is built around these concepts.

BB is constructed as an envelope around a 20 day moving average, the upper band being +2s away from the moving average and the lower band being -2s away. Since the spacing between the bands is based on the standard deviation, the bands widen when the security becomes more volatile. They band contracts when the security becomes less volatile. Let us straight go to an example. Readers who are visiting my other web site fin-insight.com must be familiar with BB by now as I use it quite extensively.

Figure 1

Consider Figure 1 where we have drawn Bollinger Band for Baja Auto for the period 24.6.2010 till date. It is a band constructed around a 20 day simple moving average at 2s distance from the moving average. 4 observations are in order which makes BB an useful indicator.

1. When the actual price hugs the upper band, prices fall after that, and when it hugs the lower bound, it is time for prices to rise;
2. When the band narrows along a trend, it is time for a reversal; a narrowing of the band implies consolidation and reversal;
3. When the actual prices move outside the band, it implies that the trend will continue;
4. The middle curve, which is the 20 day moving average, should be interpreted as a support and a resistance as the case may be.
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