## What will we cover in this tutorial?

We will calculate the volatility of historic stock prices with Python library Pandas.

## Step 1: Read Historic Stock Prices with Pandas Datareader

We will use **Pandas Datareader** to read some historic stock prices. See this tutorial for details.

```
import pandas_datareader as pdr
import datetime as dt
ticker = "AAPL"
start = dt.datetime(2019, 1, 1)
end = dt.datetime(2020, 12, 31)
data = pdr.get_data_yahoo(ticker, start, end)
print(data.head())
```

Resulting in this.

```
High Low Open Close Volume Adj Close
Date
2019-01-02 39.712502 38.557499 38.722500 39.480000 148158800.0 38.505024
2019-01-03 36.430000 35.500000 35.994999 35.547501 365248800.0 34.669640
2019-01-04 37.137501 35.950001 36.132500 37.064999 234428400.0 36.149662
2019-01-07 37.207500 36.474998 37.174999 36.982498 219111200.0 36.069202
2019-01-08 37.955002 37.130001 37.389999 37.687500 164101200.0 36.756794
```

## Step 2: Calculate the Volatility of an Asset

Let’s explore the difference between daily simple returns and daily log returns. Shortly explained, the log returns have the advantage that you can add them together, while this is not the case for simple returns. Therefore the log returns are used in most financial analysis.

To calculate the daily log returns we need the **NumPy** library. For the purpose here, we will not explore the depths of **NumPy**, all we need is to apply the **log**-function on a full column in our **DataFrame** (see my other FREE course for more details on **NumPy**).

```
import numpy as np
data['Log returns'] = np.log(data['Close']/data['Close'].shift())
```

This creates a column called **Log returns** with the daily log return of the **Close** price.

We need the standard deviation for the volatility of the stock.

This can be calculated from our **Log returns **as follows.

```
data['Log returns'].std()
```

The above gives the daily standard deviation. The volatility is defined as the annualized standard deviation. Using the above formula we can calculate it as follows.

```
volatility = data['Log returns'].std()*252**.5
```

Notice that square root is the same as ****.5**, which is the power of 1/2.

## Step 3: Visualize the Volatility of Historic Stock Prices

This can be visualized with Matplotlib.

str_vol = str(round(volatility, 4)*100)

fig, ax = plt.subplots()

data[‘Log returns’].hist(ax=ax, bins=50, alpha=0.6, color=’b’)

ax.set_xlabel(“Log return”)

ax.set_ylabel(“Freq of log return”)

ax.set_title(“AAPL volatility: ” + str_vol + “%”)

Resulting in the following output.

## Next steps?

Want to learn more?

This is part of the **FREE** online course on my page. No signup required and 2 hours of free video content with code and **Jupyter** **Notebooks** available on **GitHub**.

Follow the link and read more.