Realized Volatility

Introduction

Realized volatility refers to the measure of daily changes in the price of a security over a particular period of time. It assumes the daily mean price to be zero in order to provide movement regardless of direction.  It is different from Implied volatility in the sense that realized volatility is the actual change in historical prices, while implied volatility predicts future price volatility. Realized volatility can be calculated by firstly calculating continuously compounded daily returns using the following formula:

 

 

where, Ln = natural logarithm
 

Pt = Underlying Reference Price (“closing price”) at day t

Pt–1 = Underlying Reference Price at day immediately preceding day t

Then, by plugging the value of Rt in the formula below:

 

 

where, Vol = Realized volatility

252 = approximate number of trading days in a year

t = a counter representing each trading day

n = number of trading days in the specific time frame

Rt = continuously compounded daily returns
 

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Advantages

• The realized volatility is the measure of the historical performance of an asset which implies that one comes to know if the asset’s price has been fluctuating a lot or not. Hence, the asset’s volatility is predicted by the historical performance.

• The realized volatility also concentrates on the time period and hence you can analyse a particular time period in this manner.
• For measuring the implied volatility (future volatility), an analysis of historical performance is always helpful. Hence, realized volatility is the base of implied volatility.

 

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Disadvantages

The only disadvantage of the realized volatility is that it does not take into account the current price and also does not look into the future volatility, unlike implied volatility. Hence, realized volatility is actually directionless and simply chases the upward and downward trends of the historical data.

 

Let us find out realized volatility with the help of Python. We begin with extracting the data from yahoo finance. We will take Amazon’s data here.
 

# For data manipulation

import pandas as pd

import numpy as np

# To fetch financial data

import yfinance as yf

# Download the price data of Apple from Jan 2019 to Dec 2019

# Set the ticker as 'AAPL' and specify the start and end dates

price_data_AMZN= yf.download('AMZN', start='2020-11-06', end='2023-1-3', auto_adjust = True)

price_data_AMZN


Output:

[*********************100%***********************]  1 of 1 completed

 

Output:

	Open	High	Low	Close	Volume
Date
2020-11-05	165.998505	168.339996	164.444000	166.100006	115786000
2020-11-06	165.231995	166.100006	161.600006	165.568497	92946000
2020-11-09	161.551498	164.449997	155.605499	157.186996	143808000
2020-11-10	154.751007	155.699997	150.973999	151.751007	131820000
2020-11-11	153.089005	156.957504	152.500000	156.869507	87338000
...	...	...	...	...	...
2022-12-23	83.250000	85.779999	82.930000	85.250000	57433700
2022-12-27	84.970001	85.349998	83.000000	83.040001	57284000
2022-12-28	82.800003	83.480003	81.690002	81.820000	58228600
2022-12-29	82.870003	84.550003	82.550003	84.180000	54995900
2022-12-30	83.120003	84.050003	82.470001	84.000000	62401200

 

542 rows × 5 columns

 

Now, let us plot the data.
 

import matplotlib.pyplot as plt

%matplotlib inline

# Compute the logarithmic returns using the Closing price

price_data_AMZN['Log_Ret'] = np.log(price_data_AMZN['Close'] / price_data_AMZN['Close'].shift(1))

 
# Compute Volatility using the pandas rolling standard deviation function

price_data_AMZN['Realized Volatility'] = price_data_AMZN['Log_Ret'].rolling(window=252).std() * 
np.sqrt(252)

 
# Plot the AMZN Price series and the Volatility

price_data_AMZN[['Close']].plot(subplots=True, color='blue',figsize=(8, 6))

plt.title('Close price', color='purple', size=15)

 
# Setting axes labels for close prices plot

plt.xlabel('Dates', {'color': 'orange', 'fontsize':15})

plt.ylabel('Prices', {'color': 'orange', 'fontsize':15})

 
price_data_AMZN[['Realized Volatility']].plot(subplots=True, color='blue',figsize=(8, 6))

 
plt.title('Realized Volatility', color='purple', size=15)

 
# Setting axes labels for realized volatility plot

plt.xlabel('Dates', {'color': 'orange', 'fontsize':15})

plt.ylabel('Realized volatility', {'color': 'orange', 'fontsize':15})


# Rotating the values along x-axis to 45 degrees

plt.xticks(rotation=45)

Output:

The output above shows a steep rise in the realized volatility between November 2021 and January 2023.