A Bollinger Band® is a technical analysis tool defined by a set of trendlines. They are plotted as two standard deviations, both positively and negatively, away from a simple moving average (SMA) of a security’s price and can be adjusted to user preferences.

Bollinger Bands® was developed by technical trader John Bollinger and designed to give investors a higher probability of identifying when an asset is oversold or overbought.

How to Calculate Bollinger Bands®

The first step in calculating Bollinger Bands® is to compute the simple moving average (SMA) of the security, typically using a 20-day SMA. A 20-day SMA averages the closing prices for the first 20 days as the first data point.

The next data point drops the earliest price, adds the price on day 21 and takes the average, and so on. Next, the standard deviation of the security price will be obtained. Standard deviation is a mathematical measurement of average variance and features prominently in statistics, economics, accounting, and finance.

For a given data set, the standard deviation measures how far numbers are from an average value. Standard deviation can be calculated by taking the square root of the variance, which itself is the average of the squared differences of the mean.

Next, multiply that standard deviation value by two and both add and subtract that amount from each point along the SMA. Those produce the upper and lower bands.

Here is this Bollinger Band® formula:

$\begin{aligned} &\text{BOLU} = \text {MA} ( \text {TP}, n ) + m * \sigma [ \text {TP}, n ] \\ &\text{BOLD} = \text {MA} ( \text {TP}, n ) – m * \sigma [ \text {TP}, n ] \\ &\textbf{where:} \\ &\text {BOLU} = \text {Upper Bollinger Band} \\ &\text {BOLD} = \text {Lower Bollinger Band} \\ &\text {MA} = \text {Moving average} \\ &\text {TP (typical price)} = ( \text{High} + \text{Low} + \text{Close} ) \div 3 \\ &n = \text {Number of days in smoothing period (typically 20)} \\ &m = \text {Number of standard deviations (typically 2)} \\ &\sigma [ \text {TP}, n ] = \text {Standard Deviation over last } n \text{ periods of TP} \\ \end{aligned}$​BOLU=MA(TP,n)+m∗σ[TP,n]BOLD=MA(TP,n)−m∗σ[TP,n]where:BOLU=Upper Bollinger BandBOLD=Lower Bollinger BandMA=Moving averageTP (typical price)=(High+Low+Close)÷3n=Number of days in smoothing period (typically 20)m=Number of standard deviations (typically 2)σ[TP,n]=Standard Deviation over last n periods of TP​

What Do Bollinger Bands® Tell You?

Bollinger Bands® is a popular technique. Many traders believe the closer the prices move to the upper band, the more overbought the market, and the closer the prices move to the lower band, the more oversold the market. John Bollinger has a set of 22 rules to follow when using the bands as a trading system.

The Squeeze

The “squeeze” is the central concept of Bollinger Bands®. When the bands come close together, constricting the moving average, it is called a squeeze. A squeeze signals a period of low volatility and is considered by traders to be a potential sign of future increased volatility and possible trading opportunities.

Conversely, the wider apart the bands move, the more likely the chance of a decrease in volatility and the greater the possibility of exiting a trade. These conditions are not trading signals. The bands do not indicate when the change may take place or in which direction the price could move.

Breakouts

Approximately 90% of price action occurs between the two bands. Any breakout above or below the bands is significant. The breakout is not a trading signal and many investors mistake that when the price hits or exceeds one of the bands as a signal to buy or sell. Breakouts provide no clue as to the direction and extent of future price movement.

Example of Bollinger Bands®

In the chart below, Bollinger Bands® bracket the 20-day SMA of the stock with an upper and lower band along with the daily movements of the stock’s price. Because standard deviation is a measure of volatility, when the markets become more volatile the bands widen; during less volatile periods, the bands’ contract.

Limitations of Bollinger Bands®

Bollinger Bands® is not a standalone trading system but just one indicator designed to provide traders with information regarding price volatility. John Bollinger suggests using them with two or three other non-correlated indicators that provide more direct market signals and indicators based on different types of data. Some of his favored technical techniques are moving average divergence/convergence (MACD), on-balance volume, and relative strength index (RSI).

Because Bollinger Bands® are computed from a simple moving average, they weigh older price data the same as the most recent, meaning that new information may be diluted by outdated data. Also, the use of 20-day SMA and 2 standard deviations is a bit arbitrary and may not work for everyone in every situation. Traders should adjust their SMA and standard deviation assumptions accordingly and monitor them.

The Bottom Line

Bollinger Bands® can be a useful tool for traders for assessing the relative level of over- or under-sold position of a stock and provides them with insight on when to enter and exit a position. Certain aspects of Bollinger Bands®, such as the squeeze, work well for currency trading. Buying when stock prices cross below the lower Bollinger Band® often helps traders take advantage of oversold conditions and profit when the stock price moves back up toward the center moving-average line.

The 50-day moving average marks a line in the sand for traders holding positions through inevitable drawdowns. The strategy we employ when price nears this inflection point often decides whether we walk away with a well-earned profit or a frustrating loss. Considering the consequences, it makes sense to improve our understanding about this price level, as well as finding new ways to manage risk when it comes into play.

The most common formula takes the last 50 price bars and divides by the total. This yields the 50-day simple moving average (SMA) used by technicians for many decades. The calculation has been tweaked in many ways over the years as market players try to build a better mousetrap. The 50-day exponential moving average (EMA) offers the most popular variation, responding to price movement more quickly than its simple minded cousin. This extra speed in signal production defines a clear advantage over the slower version, making it a superior choice.

The 50-day EMA gives technicians a seat at the 50-yard line, the perfect location to watch the entire playing field for mid-term opportunities and natural counterswings after active trends, higher or lower. It’s also neutral ground when price action is often misinterpreted by the majority. And as our contrary market proves over and over again, the most reliable signals tend to erupt when the majority is sitting on the wrong side of the action.

There are dozens of ways to use the 50-day EMA in market strategies. It works as a reality check when a position hits the magic line after a rally or selloff. It has equal benefit in lower and higher time frames, applying the indicator to intraday charts or tracking long term trends with the 50-week or 50-month version. Or play a game of pinball, trading oscillations between the 50-day EMA and longer term 200-day EMA. It even works in the arcane world of market voodoo, with 50/200 day crossovers signaling bullish golden crosses or bearish death crosses.

Pullbacks

The 50-day EMA most often comes into play when you’re positioned in a trend that turns against you in a natural counterswing, or in reaction to an impulse that’s dragging thousands of financial instruments along for the ride. It makes sense to place a stop just across the moving average because it represents intermediate support (resistance in a downtrend) that should hold under normal tape conditions. The problem with this reasoning is it doesn’t work as intended in our volatile modern markets.

The 50 and 200-day EMAs have morphed from narrow lines into broad zones in the last two decades due to aggressive stop hunting. You need to consider how deep these violations will go before placing a stop or timing an entry at or near the moving average. Patience is key in these circumstances because testing at the 50-day EMA usually resolves within three to four price bars. The trick is to stay out of the way until a) the reversal kicks in or b) the level breaks, yielding a price thrust against your position.

The risk of getting it wrong will hurt your wallet, so how long should you stick around when price tests the 50-day EMA? While there’s no perfect way to avoid whipsaws, examining other technicals often pinpoints the exact extension of a reversal. For example, Intel (INTC) returned to the January high in April and sold off to the 50-day EMA. It broke support, dropped to the .386 Fibonacci rally retracement and bounced back to the moving average in the next session. The stock regained support on the third day and entered a recovery, completing a cup and handle breakout pattern.

50-Day Fractals

The moving average works just as well in lower and higher time frames. As a result, day traders will find benefit in placing 50-bar EMAs on 15 and 60 minute charts because they define natural end points for intraday oscillations. Just keep in mind that noise increases as time frame decreases, lowering its value on 5 and 1 minute charts. On the flip side, the indicator shows excellent reliability on weekly and monthly charts, often pinpointing exact turning points in corrections and long term trends.

This makes sense when considering that the 50-week EMA defines mean reversion over an entire year while the 50-month EMA tracks more than four years of market activity, approaching the average length of a typical business cycle. Market timers can use these long-term moving averages to establish profitable positions lasting for months or years while violations offer perfect levels to take profits and reallocate capital into other long term instruments.

Apple (AAPL) set up excellent buying opportunities at the 50-month EMA in 2009 and 2013. It broke moving average support in September 2008 and spent 5 months grinding sideways before remounting that level in April 2009, issuing a “failure of a failure” buy signal that yielded more than 80 points over three years. It tested the moving average a second time in 2013, spending four months building a double bottom that triggered a 100 percent rally into 2014. Note how the lows matched support perfectly, offering an incredible low risk entry for patient market players.

50-200 Day Pinball

Fast trends in both directions tend to increase the separation between the 50 and 200-day EMAs. Once a countertrend breaks one of these averages, it often carries into the other average, setting up a few rounds of the 50-200 “pinball” strategy. Swing traders are natural beneficiaries of this two-sided technique, going long and then short until one side of the box gives way to a more active trend impulse.

Biogen (BIIB) hit a new high in March after a long uptrend and entered a steep correction that broke the 50-day EMA a few days later. Price action then entered a two month game of 50-200 pinball, traversing more than 75 points between new resistance at the 50-day EMA and long term support at the 200-day EMA. Swing reversals took place close to target numbers, allowing easy entry and relatively tight stops for a triple digit stock.

Bullish and Bearish Crossovers

The downward crossover of the 50-day EMA through the 200-day EMA signals a death cross that many technicians believe marks the end of an uptrend. An upward crossover or golden cross is alleged to possess similar magic properties in establishing a new uptrend. In reality, numerous crisscrosses can print in the life cycle of an uptrend or downtrend and these classic signals show little reliability. 

It’s a different story with the 50 and 200-week EMAs. SPDR S&P Trust (SPY) shows four valid cross signals going back 15 years, two in each direction. More importantly, there were no false signals during this time, which included three bull markets and two bear markets. Looking at historic Dow Industrial data, the last invalid cross occurred more than 30 years ago, in 1982. This tells us that golden and death crosses deserve a respected place in market analysis.

The Bottom Line

The 50-day EMA identifies a natural mean reversion level for the intermediate time frame. It has numerous applications in price prediction, position choice and strategy building. Traders, market timers and investors all benefit from 50-day EMA study, making it an indispensable ingredient in your technical market analysis.