## What is the Bollinger Bands?

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

https://www.investopedia.com/terms/b/bollingerbands.asp

The Bollinger Bands are used to discover if a stock is oversold or overbought. It is called a mean reversion indicator, which measures how far a price swing will stretch before a counter impulse triggers a retracement.

It is a lagging indicator, which is looking at historical background of the current price. Opposed to a leading indicator, which tries to where the price is heading.

## Step 1: Get some time series data on a stock

In this tutorial we will use the Apple stock as example, which has ticker AAPL. You can change to any other stock of your interest by changing the ticker below. To find the ticker of your favorite company/stock you can use Yahoo! Finance ticker lookup.

To get some time series of stock data we will use the Pandas-datareader library to collect it from Yahoo! Finance.

```import pandas_datareader as pdr
import datetime as dt

ticker = pdr.get_data_yahoo("AAPL", dt.datetime(2020, 1, 1), dt.datetime.now())[['Close', 'High', 'Low']]
print(ticker)
```

We will use the Close, High and Low columns to do the further calculations.

```                 Close        High         Low
Date
2020-01-02  300.350006  300.600006  295.190002
2020-01-03  297.429993  300.579987  296.500000
2020-01-06  299.799988  299.959991  292.750000
2020-01-07  298.390015  300.899994  297.480011
2020-01-08  303.190002  304.440002  297.160004
...                ...         ...         ...
2020-08-06  455.609985  457.649994  439.190002
2020-08-07  444.450012  454.700012  441.170013
2020-08-10  450.910004  455.100006  440.000000
2020-08-11  437.500000  449.929993  436.429993
2020-08-12  452.040009  453.100006  441.190002
```

## Step 2: How are the Bollinger Bands calculated

Luckily, we can refer to Investopedia.org to get the answer, which states that the Bollinger Bands are calculated as follows.

BOLU=MA(TP,n)+mσ[TP,n]

BOLD=MA(TP,n)−mσ[TP,n]

Where BOLU is the Upper Bollinger Band and BOLD is Lower Bollinger Band. The MA is the Moving Average. The TP and σ are calculated as follows.

TP (typical price)=(High+Low+Close)÷3

σ[TP,n] = Standard Deviation over last n periods of TP​

Where n is the number of days in smoothing period (typically 20), and m is the number of standard deviations (typically 2).

## Step 3: Calculate the Bollinger Bands

This is straight forward. We start by calculating the typical price TP and then the standard deviation over the last 20 days (the typical value). Then we calculate the simple moving average of rolling over the last 20 days (the typical value). Then we have the values to calculate the upper and lower values of the Bolling Bands (BOLU and BOLD).

```ticker['TP'] = (ticker['Close'] + ticker['Low'] + ticker['High'])/3
ticker['std'] = ticker['TP'].rolling(20).std(ddof=0)
ticker['MA-TP'] = ticker['TP'].rolling(20).mean()
ticker['BOLU'] = ticker['MA-TP'] + 2*ticker['std']
ticker['BOLD'] = ticker['MA-TP'] - 2*ticker['std']
print(ticker)
```

Resulting in the following output.

```Date
Close        High  ...        BOLU        BOLD
Date                                ...
2020-01-02  300.350006  300.600006  ...         NaN         NaN
2020-01-03  297.429993  300.579987  ...         NaN         NaN
2020-01-06  299.799988  299.959991  ...         NaN         NaN
2020-01-07  298.390015  300.899994  ...         NaN         NaN
2020-01-08  303.190002  304.440002  ...         NaN         NaN
...                ...         ...  ...         ...         ...
2020-08-06  455.609985  457.649994  ...  445.784036  346.919631
2020-08-07  444.450012  454.700012  ...  453.154374  346.012626
2020-08-10  450.910004  455.100006  ...  459.958160  345.317173
2020-08-11  437.500000  449.929993  ...  464.516981  346.461685
2020-08-12  452.040009  453.100006  ...  469.891271  346.836730
```

Note, that if you compare you results with Yahoo! Finance for Apple, there will be some small difference. The reason is, that they by default use TP to be closing price and not the average of the Close, Low and High. If you change TP to equal Close only, you will get the same figures as they do.

## Step 4: Plotting it on a graph

Plotting the three lines is straight forward by using plot() on the DataFrame. Making an filled area with color between BOLU and BOLD can be achieved by using fill_between().

This results in the full program to be.

```import pandas_datareader as pdr
import datetime as dt
import matplotlib.pyplot as plt

ticker = pdr.get_data_yahoo("AAPL", dt.datetime(2020, 1, 1), dt.datetime.now())[['Close', 'High', 'Low']]
# Boillinger band calculations
ticker['TP'] = (ticker['Close'] + ticker['Low'] + ticker['High'])/3
ticker['std'] = ticker['TP'].rolling(20).std(ddof=0)
ticker['MA-TP'] = ticker['TP'].rolling(20).mean()
ticker['BOLU'] = ticker['MA-TP'] + 2*ticker['std']
ticker['BOLD'] = ticker['MA-TP'] - 2*ticker['std']
ticker = ticker.dropna()
print(ticker)
# Plotting it all together
ax = ticker[['Close', 'BOLU', 'BOLD']].plot(color=['blue', 'orange', 'yellow'])
ax.fill_between(ticker.index, ticker['BOLD'], ticker['BOLU'], facecolor='orange', alpha=0.1)
plt.show()
```

Giving the following graph.

## Step 5: How to use the Bollinger Band Indicator?

If the stock price are continuously touching the upper Bollinger Band (BOLU) the market is thought to be overbought. While if the price continuously touches the lower Bollinger Band (BOLD) the market is thought to be oversold.

The more volatile the market is, the wider the upper and lower band will be. Hence, it also indicates how volatile the market is at a given period.

The volatility measured by the Bollinger Band is referred to as a squeeze when the upper and lower band are close. This is considered to be a sign that there will be more volatility in the coming future, which opens up for possible trading opportunities.

A common misconception of the bands are that when the price outbreaks the the bounds of the upper and lower band, it is a trading signal. This is not the case.

As with all trading indicators, it should not be used alone to make trading decisions.

## 12% Investment Solution

Would you like to get 12% in return of your investments?

D. A. Carter promises and shows how his simple investment strategy will deliver that in the book The 12% Solution. The book shows how to test this statement by using backtesting.

Did Carter find a strategy that will consistently beat the market?

Actually, it is not that hard to use Python to validate his calculations. But we can do better than that. If you want to work smarter than traditional investors then continue to read here.