In December 2015 we published a blog article on technical analysis/charting and more specifically the use of a relative strength index (RSI) as one of many technical tools used to predict potential change in market trend. The purpose of these series of blog articles is to give our readers a more in depth background on a variety of technical analysis tools that can be used as a reference point for readers unfamiliar with charting.

The first article in the series entitled “How to tell if the market is about to change direction” provides a brief description of technical analysis (also known as charting) and explains the logic behind its use in commodity market forecasting. As such, readers that missed this initial blog article may find it useful to familiarise themselves with the first in the series prior to completing this article.

**Bollinger bands and statistics**

The purpose of this instalment is to outline the basics of Bollinger bands and how they relate to the use of percentile/decile tables when comparing current price levels to historical price movements. Before we investigate the link between percentile/decile tables and Bollinger bands it is probably prudent to provide a more detailed background into Bollinger bands and how they are created using statistical mathematics methods.

In essence Bollinger bands are a charting technique designed by John Bollinger in the 1980s that uses a moving average of historical market price and a measure of market volatility in order to generate an upper and lower band around the current price.

The Bollinger band calculation uses standard deviation to determine market volatility. The upper Bollinger band represents two standard deviations above the moving average and the lower band represents two standard deviations below the moving average. (Figure 2.)

Readers that have forgotten their high school mathematics lessons may recall that standard deviation is a statistical measure of variance away from the mean (average) when looking at a set of data, such as market prices. In a graphical format this data can be displayed as the “bell shaped curve” - figure 1.

The bell shaped curve shows the variation in market price measured by the standard deviation, as represented by **σ **on the graph, and provides a measure of the probability that price can vary away from the mean (average).

The bell shaped curve in figure 1 highlights that the distribution of price data can be measured using statistical probability based on historic prices. It shows that using a calculation of the standard deviation (σ) away from the mean (average) price. The blue shaded sections on the bell curve represents the percentage of price movement that can be explained by the standard deviation away from the mean.

For example, one standard deviation above the mean (**1σ**) can explain 34.1% of the historic price movement, Similarly, one standard deviation below the mean (**-1σ**) can account for another 34.1% of historic price movement. Therefore, one standard deviation either side of the mean can explain 68.2% of price movement.

Likewise, two standard deviations either side of the mean **(-2σ **to** 2σ**) can account for 95.4% of the historic price movement (13.6% + 34.1% + 34.1% + 13.6% = 95.4%). In other words, it is most probable that prices will range within two standard deviations of the mean 95.4% of the time.

Using this measure of two standard deviations to create the upper and lower Bollinger bands means that the area in between the two Bollinger bands provides a visual signal of where the current price is in relation to 95.4% of the historic price data.

Figure 2 shows price movements for the Eastern States Trade Lamb Indicator (ESTLI) since 2013

with the upper and lower Bollinger bands applied to the price data. We can see that the majority of variation in price for the period was contained within the Bollinger bands. Furthermore, the graph is able to provide a quick visual signal as to where current price is in comparison to the historic price data.

In simple terms price movements towards the upper (red) band indicate prices nearing historically high levels. In contrast, price movement towards the lower (blue) band signify that current price is nearing historically low levels.

At this point is important to note that Bollinger bands, like all technical analysis tools should not be used in isolation to determine selling or buying levels. Indeed, using price near the upper Bollinger band as a sell signal and price near the lower Bollinger band as a buy signal without any reference to other technical analysis tools can be fraught with danger. This is because there is no guarantee that historical price movements will tell you where the price will be in the future. Rather, they act as a reference point to where current price is when compared to the past.

**So why use Bollinger bands?**

Bollinger bands can be a quick and easy to use visual tool that provide a signal when price movements are nearing historic extremes. If this tool is combined with other technical indicators, such as the Relative Strength Index (RSI) it can help identify a market that is changing direction. This is particularly true for a market that shows the RSI displaying bullish or bearish divergence (see the RSI article here for a more detailed explanation of divergence).

In simple terms bullish divergence is when a market in a down trend shows divergent signals in the RSI consistent with a market that is losing down side momentum and is ripe for a rally higher. Bearish divergence, on the other hand, is an up trending market where the RSI indicates the rally is running out of steam and is ready of a correction lower.

Consider a down trending market that is displaying bullish divergence in the RSI, which signals a bounce may be imminent. If the current price level is also at historically extreme lows, near or below the lower Bollinger band, this would indicate to a technical analyst that the buy signal has a higher degree of reliability and that the bounce is likely to be more aggressive and could potentially be reflective of a market about to change trend. This situation is highlighted in figure 3 where Bollinger bands and RSI bullish divergence combined to signal a change in direction for the ESTLI during the 2014 season.

However, if prices were in the middle or upper area of the Bollinger band the technical analyst is more likely to interpret the bullish divergence as a potential short-term correction higher, before the down trend resumes. It may also prompt the analyst to undertake further investigation using other technical tools before making a final decision on their forecast for price movement.

Bollinger bands can also be used as a visual representation of market volatility as the width between the upper and lower band will widen as volatility increases and will narrow as volatility reduces. To put it simply, if a prices moves around a lot it will have a larger standard deviation (a wide and low bell curve). If the price of a commodity barely moves at all, it will have a smaller standard deviation (a high and narrow bell curve) – see figure 4.

**Bollinger bands and percentile tables**

Regular readers to Mecardo may be familiar with percentile (or decile) tables and there is a similarity between Bollinger bands and these tables in that they are both methods used to display how current price levels compare in statistical terms to the historic price data.

A percentile is a measure of how often, prices have been above or below a particular level. It gives a brief snapshot of whether a market has more upside or downside, and how large this may be. The percentile table in essence is a tabulated matrix that uses statistical measures to section prices into percentage rankings based on the bell shaped curve – figure 5.

In the percentile table these ranking sections are listed as a minimum or lowest price figure (Min), the lowest 10% (10%), the lowest 20% (20%), etc., progressing higher until the lowest 90% (90%) and the maximum or highest price in the data (Max) – see figure 6.

Figure 6 shows a percentile table for national lamb and sheep markets. Looking at the second column that highlights the percentiles for the Eastern States Trade Lamb Indicator (ESTLI) we can see that the current price of 551¢ has a decile (percentile ranking) of 93% which indicates that 93% of historical prices have been below 551¢, while only 7% of historical prices have been above 551¢.

For a more detailed description on how to read percentile tables please refer to the article “What are percentiles and how do I use them?

As is evident from figure 5, the lower Bollinger band, two standard deviations below the mean, represents price levels that are lower than the lowest 5% of historical price movements. Similarly, price levels on the upper Bollinger band, two standard deviations above the mean, represent prices that are higher than more than 95% of the historical price movements.

**Another tool in the technical toolbox**

It is important to note that, while Bollinger bands and percentiles show the time spent above or below particular price levels, they are not a definitive measure of absolute price ranges. They are just one tool in your market information toolbox, and should be considered in conjunction with the other information you use.