# How to Calculate Volatility as Average True Range (ATR) with Python DataFrames and NumPy

## What will we cover?

In this tutorial we will learn about the volatility of a stock price measured with Average True Range. The Volatility of a stock is one measure of investment risk.

The Average True Range was originally designed to calculate the volatility of commodities, but the technical indicator can also be used for stock prices, as we will do in this tutorial.

We will get some stock price time series data and make the calculation using pandas DataFrames and NumPy.

## Step 1: Get historic stock price data

To get started, we need some historic stock prices. This can be done as follows and is covered in Lesson 1.

```import numpy as np
import datetime as dt
import pandas as pd

start = dt.datetime(2020, 1, 1)
data = pdr.get_data_yahoo("NFLX", start)
```

This reads the time series data of the historic stock prices of Netflix (ticker NFLX).

## Step 2: The formula of Average True Range (ATR)

To calculate the Average True Range (ATR) we need a formula, which is given on investoperia.org.

The Average True Range (ATR) is a moving average of the True Range (TR). And the TR is given by the maximum of the current high (H) minus current low (L), the absolute value of current high (H) minus previous close (Cp), and the absolute value of current low (L) and previous close (Cp).

## Sted 3: The calculations of Average True Range with DataFrames and NumPy

The above formula can look intimidating at first, but don’t worry, this is where the power of Pandas DataFrames and Series come into the picture.

It is always a good idea to make your calculations simple.

```high_low = data['High'] - data['Low']
high_cp = np.abs(data['High'] - data['Close'].shift())
low_cp = np.abs(data['Low'] - data['Close'].shift())
```

Here we make a Series for each of the values needed. Notice, that we get the previous close by using shift() (data[‘Close’].shift()).

Then a great way to get the maximum value of these is to create a DataFrame with all the values.

```df = pd.concat([high_low, high_cp, low_cp], axis=1)
true_range = np.max(df, axis=1)
```

Now that is nice.

Then we get the ATR as the moving average of 14 days (14 days is the default).

```average_true_range = true_range.rolling(14).mean()
```

## Step 4: Visualize the result with Matplotlib

Finally, let’s try to visualize it. Often visualization helps us understand it better.

```import matplotlib.pyplot as plt
%matplotlib notebook

fig, ax = plt.subplots()
average_true_range.plot(ax=ax)
ax2 = data['Close'].plot(ax=ax, secondary_y=True, alpha=.3)
ax.set_ylabel("ATR")
ax2.set_ylabel("Price")
```

Resulting in the following chart.