Introduction to Bollinger Bands®
Bollinger Bands®, created by legendary money manager and researcher John Bollinger, are one of the most popular trading indicators in use today. Nearly all commercial charting applications include the ability to plot Bollinger Bands®, which allow traders to quickly assess how overbought or oversold a security is.
While there has been an abundance of information published on how to trade with Bollinger Bands®, the majority is discretionary in nature rather than quantitative. Thus, the trader is left to interpret what the security’s price is doing relative to its Bands, and more importantly, what it is likely to do next.
In contrast, the ETF Trading with Bollinger Bands® Strategy is a precise, quantified approach to Bollinger Bands® trading. It allows a trader to identify the entry and exit signals that have produced the best results over the past 7+ years. We will also show how different levels of intraday pullbacks can increase the edges for this strategy. All of this will be accompanied by historical return data that allows you to select the rule variations that best complement your current trading plan.
Before describing the strategy, let’s look at exactly what Bollinger Bands® are and also what we consider to be the genius within the Bollinger Bands® theory: the %b calculation, which is the centerpiece of our trading strategy.
What Are Bollinger Bands®?
Bollinger Bands® are a measure of volatility. When volatility is low, the bands contract around the security price. The bands expand as volatility rises. Furthermore, a security whose price is approaching the lower band is considered oversold, while a security whose price is near the upper band is considered overbought. So how are these bands calculated?
The Bollinger Bands® calculation begins with a simple moving average of the security price. In our research and throughout this article, we use the daily closing price for this calculation. We have found that a 5-period moving average, or MA(5), is an excellent basis for the Bollinger Bands® trading strategy.
Next, we determine the standard deviation of the price over the same number of periods used for the moving average, which in our case is five. We can refer to this value as SD(5).
Finally, the Bollinger Bands® are calculated by adding (for the upper band) or subtracting (for the lower band) some multiple of SD(5) to the MA(5) value. Our Bollinger Bands® trading strategies always use a multiple of one.
In summary, that gives us:
Upper Band = MA(5) + SD(5)
Lower Band = MA(5) – SD(5)
The %b Calculation
%b is an indicator derived from Bollinger Bands®. The %b value quantifies a security’s price relative to the upper and lower Bollinger Bands®. In our opinion, backed by statistical results, the %b component of Bollinger Bands® allows you to better pinpoint proper entry and exit triggers.
%b = (Price – Lower Band) / (Upper Band – Lower Band)
Note the following qualities of %b:
- %b equals 1 when price is at the upper band
- %b equals 0 when price is at the lower band
- %b is greater than 1 when price is above the upper band
- %b is less than 0 when price is below the lower band
- %b is greater than 0.50 when price is above MA(5), i.e. the middle band
- %b is less than 0.50 when price is below MA(5)
Ideally, when buying a security we want the %b reading to be below 0.3 for multiple days in a row. The lower the %b reading and the more days in a row below that reading, the more oversold the security is and the greater the edges have been. This is the key to trading with Bollinger Bands®, and by applying a few additional filters we can build strategies with high average gains per trade and high success rates over the past 7+ years.
Entry & Exit Rules
The key to success when using the Bollinger Bands® strategy to trade ETF’s is to diligently follow a set of well-defined, quantifiable rules. Let’s begin with the rules that are used to define a Setup condition:
1. The closing price of the ETF must be above its 200-day simple moving average.
2. The ETF’s average daily volume over the past 21 days (one trading month) must be at least 125,000 shares per day, and the lowest daily volume over the past 21 days must be at least 50,000 shares.
3. The %b value of the ETF must be under X (where X=-0.2, -0.1, 0, 0.1, 0.2, or 0.3) for Y days in a row (where Y = 2, 3, or 4).
Rule 1 signifies that the ETF is in a longer-term uptrend. Our research has consistently shown that when an ETF’s price is greater than its MA(200), the price is more likely to rise on any given day than when the price is below the MA(200).
Rule 2 assures that the ETF is sufficiently liquid to enter and exit trades quickly at favorable fill prices.
Rule 3 identifies the oversold condition, or pullback. An ETF that closes with a %b value of 0.3 or less for multiple days in a row is a good short-term pullback. The lower the %b value, the more oversold the ETF is and the greater its returns have been over the next one to two weeks.
Once the Setup conditions have been satisfied, we wait for a further intraday pullback to occur on the next trading day, as defined by Rule 4:
4. If Rules 1-3 are met today, buy the ETF tomorrow using a limit order Z% below today’s closing price (where Z= 1%, 2%, or 3%).
Of course, it’s not enough to have good entry rules. We make money when we complete the trade, so it’s important to have quantified exit rules in place. We typically test a variety of exit rules, but for this article we will present just the one that has historically produced the largest gains. Rule 5 states:
5. Sell the ETF at the close when the %b value is greater than 1.0.
Now let’s see how a typical trade looks on a chart. We’ll use a strategy variation that requires %b to be less than 0.1 for three days (i.e. X = 0.1 and Y = 3 for Rule 3), and an intraday limit (Z) of 2% for Rule 4.
Figure 1: Trade Example
The price chart above is for the Guggenheim China Small Cap ETF, ticker symbol HAO. The gray vertical bar highlights the data for Thursday, April 4, 2013. The green lines are the upper and lower Bollinger Bands®, and the aqua blue line is the 5-day moving average (the midpoint of the Bollinger Bands®).
Let’s verify that all of our rules have been satisfied.
The bright blue line in the upper pane of the chart above shows the 200-day moving average. We can see that the closing price of $22.85 on April 4th is well above the MA(200) value of $21.68, and thus Rule 1 is satisfied.
Rule 2 quantifies our liquidity requirement. Although the chart above does not show a full 21 days of history, there were no days with a volume below 50,000 shares during the past month. In addition, we can see that the 21-day average daily volume is over 325,000 shares, which exceeds our criteria of 125,000 shares.
Note that the %b values for the three days prior to April 4th, (April 1st, 2nd and 3rd) are all below zero, i.e. the closing price is below the lower Bollinger Band®. Therefore, an oversold condition exists on April 3rd (as defined by Rule 3), and we can set a limit order for the next trading day, which is April 4th. As per Rule 4, the limit price is 2% below the Setup day’s closing price of $22.80, which is $22.34. However, the lowest price on April 4th is $22.66, so our limit order does not get filled that day.
On April 4th, the oversold condition still exists, because %b was less than zero for April 2nd and 3rd, and almost exactly 0 on April 4th. Again we use Rule 4 to set a limit order for the next day, this time 2% below the April 4th closing price of $22.85, which is $22.39. On April 5th, the price of HAO opens below our limit price, so our order gets filled at the open price of $22.23.
Rule 5 requires %b to be greater than 1.0, which is the same as saying that the price closes above the upper Bollinger Band®. We can see that on April 9th, the price of HAO closes above the upper green line, which means that %b is greater than our target of 1.0. Thus, an exit is triggered and we sell our shares at the close on April 9th for a price near the closing price $22.92. This gives us a tidy 3.1% profit before commissions and brokerage fees.
Test Results
We can never know for sure how a trading strategy will perform in the future. However, for a fully quantified strategy such as the Bollinger Bands® strategy described in this Article, we can at least evaluate how the strategy has performed in the past. This process is known as “back testing”.
To execute a back test, we first select a group of securities (sometimes called a watchlist) that we want to test our strategy on. In this case, the watchlist is comprised of equity-based ETFs. No leveraged, inverse, commodity or bond-based ETFs are included. Next we choose a timeframe over which to test. The longer the timeframe, the more significant and informative the back testing results will be. The back tests for the Bollinger Bands® strategy start in January 2006, because prior to 2006 there were very few ETFs available to trade. Since then, the number of ETFs has grown steadily every year. The back tests end on April 30th, 2013, the latest date for which we have data as of this writing. Finally, we apply our entry and exit rules to each ETF for the entire test period, recording data for each trade that would have been entered, and aggregating all trade data across a specific strategy variation.
After we’ve generated all that data, there are a few key statistics that we can look at. First is the Average % Profit/Loss, also known as the Average Gain per Trade. Some traders refer to this as the “edge”. The Average % P/L is the sum of all the gains (expressed as a percentage) and all the losses (also as a percentage) divided by the total number of trades. Consider the following ten trades:
The Average % P/L would be calculated as:
Average % P/L = (1.7% + 2.1% – 4.0% + 0.6% – 1.2% + 3.8% + 1.9% -0.4% + 3.7% + 2.6%) / 10
Average % P/L = 1.08%
For short-term trades lasting three to ten trading days, most traders look for an Average % P/L of 0.5% to 2.5% across all trades. All other things being equal, the larger the Average % P/L, the more your account will grow over time.
Another important statistic is the Winning Percentage. This is simply the number of profitable trades divided by the total number of trades. In the table above, 7 of the 10 trades were profitable, i.e. had positive returns. For this example, the Winning Percentage is 7 / 10 = 70%.
Why do we care about Winning Percentage, as long as we have a sufficiently high Average % P/L? Because higher Winning Percentages generally lead to less volatile portfolio growth. Losing trades have a way of “clumping up”, and when they do that, the value of your portfolio decreases. Those decreases, in turn, can make you lose sleep or even consider abandoning your trading altogether. If there are fewer losers, i.e. a higher Winning Percentage, then losses are less likely to clump, and your portfolio value is more likely to grow smoothly upward rather than experiencing violent up and down swings.
Let’s turn our attention to the test results for the different variations of the Bollinger Bands® strategy. In all cases, we have filtered out any variations that generated less than 100 trades, as such infrequent signals make it difficult to draw any conclusions from the results. First, we’ll look at the 20 variations that produced the highest Average Gain.
Top 20 Variations Based on Avg % Profit/Loss
Below is an explanation of each column.
# Trades is the number of times this variation triggered from January 1, 2006 – April 30, 2013.
Average % Profit/Loss is the average gain for all trades (including the losing trades). The top 20 variations have shown average gains from 1.47% per trade to 4.28% (a very respectable number for ETFs, which are not known for big price moves).
Average Days Held is the number of days on average the trade was held. In all cases it’s less than six trading days.
Win Rate is the percentage of signals which closed out at a profit. We see lots of values in the 70’s, as well as a few in the 80’s and 90’s.
%b Cut-Off is the %b Level required for entering the trade. The test results predominantly show that the lower the %b level, the more oversold the ETF is and the higher the historical returns have been.
Days Under is the number of days under the %b cut-off level. We tested two days under, three days under and 4 days under the %b cut-off level. As you can see, the more days the ETF is under its cut-off level, the more oversold the ETF is and the higher the average gains per trade have been.
Entry % Limit is the intraday pullback used to trigger an entry. For example, a value of 3% means that we enter the trade on a 3% limit order the day after the oversold condition occurs.
Exit Method shows the rule that was used to exit the trade.
We can see that the strategy variations with the strictest setup and entry criteria (those that require a %b value below 0 for multiple days and use larger limit percentages) have historically produced the highest Average % P/L. However, such strict entry criteria mean that we enter relatively few trades. If we relax the criteria slightly by allowing higher %b values or requiring fewer days, then we get more trades but typically at a lower average gain per trade.
Next let’s sort the test results to show the variations with the highest Win Rate.
Top 20 Variations Based on Win Rate
Note the high Win Rate values, ranging from 74% to over 92%. Few quantified trading strategies can boast this kind of success rate. Also notice that there is a great deal of overlap between this table and the previous one, which tells us that the strategy variations that have historically produced the biggest gains are also the ones that are profitable the most often.
Conclusion
As you have seen throughout this Article, Bollinger Bands® and especially the %b component of the Bollinger Bands® have had large quantified edges when you apply them in a systematic manner. Perhaps even more importantly, trading ETFs with Bollinger Bands® has historically been extremely accurate, with success rates typically over 70% and in many cases over 80%.
There are dozens of potential variations for you to use, each with its own unique combination of the depth of the %b level (X), the number of days below that level (Y), and the size of the limit (Z). Look at the entire scope and then identify the variation or variations that fit best for your trading style.
Slippage and commission were not used in the testing. Factor them into your trading (the entries are at limit prices so slippage is not an issue) and make sure you are trading at the lowest possible costs. Most firms are now allowing traders to trade for under 1 cent a share, so shop your business, especially if you are an active trader. The online brokerage firms want your business.
As you have seen here with the ETF Trading with Bollinger Bands® Strategy, there are large edges in ETFs which sell-off and then sell-off further intraday. These trades are often accompanied by fear and uncertainty and this is when large edges appear. Seek out these trades because as you have seen, they’ve been lucrative for many years.
Editor’s note: We hope you enjoyed this article. If you have any questions about this strategy please feel free to email us at
info@connorsresearch.com.
If you are interested in how to apply %b to stock trading, please go to www.tradingmarkets.com and click on the Books tab or call 888-484-8220 extension 3.
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