Interactive Financial Analytics with Python & IPython¶
Eurex Tutorial with Examples based on the VSTOXX Volatility Index
Dr. Yves J. Hilpisch
The Python Quants GmbH
PyData London – 21. February 2014
You find the presentation and the IPython Notebook here:
About Me¶
A brief bio:
- Managing Partner of The Python Quants
- Founder of Visixion GmbH – The Python Quants
- Lecturer Mathematical Finance at Saarland University
- Focus on Financial Industry and Financial Analytics
- Book (2013) "Derivatives Analytics with Python"
- Book (July 2014) "Python for Finance", O'Reilly
- Dr.rer.pol in Mathematical Finance
- Graduate in Business Administration
- Martial Arts Practitioner and Fan
See www.hilpisch.com.
Python for Analytics¶
Corporations, decision makers and analysts nowadays generally face a number of problems with data:
- sources: data typically comes from different sources, like from the Web, from in-house databases or it is generated in-memory, e.g. for simulation purposes
- formats: data is generally available in different formats, like SQL databases/tables, Excel files, CSV files, arrays, proprietary formats
- structure: data typically comes differently structured, be it unstructured, simply indexed, hierarchically indexed, in table form, in matrix form, in multidimensional arrays
- completeness: real-world data is generally incomplete, i.e. there is missing data (e.g. along an index) or multiple series of data cannot be aligned correctly (e.g. two time series with different time indexes)
- conventions: for some types of data there a many “competing” conventions with regard to formatting, like for dates and time
- interpretation: some data sets contain information that can be easily and intelligently interpreted, like a time index, others not, like texts
- performance: reading, streamlining, aligning, analyzing – i.e. processing – (big) data sets might be slow
In addition to these data-oriented problems, there typically are organizational issues that have to be considered:
- departments: the majority of companies is organized in departments with different technologies, databases, etc., leading to “data silos”
- analytics skills: analytical and business skills in general are possessed by people working in line functions (e.g. production) or administrative functions (e.g. finance)
- technical skills: technical skills, like retrieving data from databases and visualizing them, are generally possessed by people in technology functions (e.g. development, systems operations)
This tutorial focuses on
- Python as a general purpose financial analytics environment
- interactive analytics examples
- prototyping-like Python usage
It does not address such important issues like
- architectural issues regarding hardware and software
- development processes, testing, documentation and production
- real world problem modeling
Some Python Fundamentals¶
Fundamental Python Libraries¶
A fundamental Python stack for interactive data analytics and visualization should at least contain the following libraries tools:
- Python – the Python interpreter itself
- NumPy – high performance, flexible array structures and operations
- SciPy – collection of scientific modules and functions (e.g. for regression, optimization, integration)
- pandas – time series and panel data analysis and I/O
- PyTables – hierarchical, high performance database (e.g. for out-of-memory analytics)
- matplotlib – 2d and 3d visualization
- IPython – interactive data analytics, visualization, publishing
It is best to use either the Python distribution Anaconda or the Web-based analytics environment Wakari. Both provide almost "complete" Python environments.
For example, pandas can, among others, help with the following data-related problems:
- sources: pandas reads data directly from different data sources such as SQL databases, Excel files or JSON based APIs
- formats: pandas can process input data in different formats like CSV files or Excel files; it can also generate output in different formats like CSV, XLS, HTML or JSON
- structure: pandas' strength lies in structured data formats, like time series and panel data
- completeness: pandas automatically deals with missing data in most circumstances, e.g. computing sums even if there are a few or many “not a number”, i.e. missing, values
- conventions/interpretation: for example, pandas can interpret and convert different date-time formats to Python datetime objects and/or timestamps
- performance: the majority of pandas classes, methods and functions is implemented in a performance-oriented fashion making heavy use of the Python/C compiler Cython
First Interactive Steps with Python¶
As a simple example let's generate a NumPy array with five sets of 1000 (pseudo-)random numbers each.
import numpy as np # this imports the NumPy library
data = np.random.standard_normal((5, 1000)) # generate 5 sets with 1000 rn each
data[:, :5].round(3) # print first five values of each set rounded to 3 digits
Let's plot a histogram of the 1st, 2nd and 3rd data set.
import matplotlib as mpl # this imports matplotlib
import matplotlib.pyplot as plt # this imports matplotlib.pyplot
%matplotlib inline
# inline plotting
plt.hist([data[0], data[1], data[2]], label=['Set 0', 'Set 1', 'Set 2'])
plt.grid(True) # grid for better readability
plt.legend()
We then want to plot the 'running' cumulative sum of each set.
plt.figure() # initialize figure object
plt.grid(True)
for data_set in enumerate(data): # iterate over all rows
plt.plot(data_set[1].cumsum(), label='Set %s' % data_set[0])
# plot the running cumulative sums for each row
plt.legend(loc=0) # write legend with labels
Some fundamental statistics from our data sets.
data.mean(axis=1) # average value of the 5 sets
data.std(axis=1) # standard deviation of the 5 sets
np.corrcoef(data).round(3) # correltion matrix of the 5 data sets
First Financial Analytics Example¶
We need to make a couple of imports for what is to come.
import pandas as pd
import pandas.io.data as pdd
from urllib import urlretrieve
The convenience function DataReader makes it easy to read historical stock price data from Yahoo! Finance (http://finance.yahoo.com).
index = pdd.DataReader('^GDAXI', data_source='yahoo', start='2007/3/30')
# e.g. the EURO STOXX 50 ticker symbol -- ^SX5E
index.info()
pandas strength is the handling of indexed/labeled/structured data, like times series data.
index.tail()
pandas makes it easy to implement vectorized operations, like calculating log-returns over whole time series.
index['Returns'] = np.log(index['Close'] / index['Close'].shift(1))
In addition, pandas makes plotting quite simple and compact.
index[['Close', 'Returns']].plot(subplots=True, style='b', figsize=(8, 5))
We now want to check how annual volatility changes over time.
index['Mov_Vol'] = pd.rolling_std(index['Returns'], window=252) * np.sqrt(252)
Obviously, the annual volatility changes significantly over time.
index[['Close', 'Returns', 'Mov_Vol']].plot(subplots=True, style='b', figsize=(8, 5))
Exercise¶
Trend-based investment strategy with the EURO STOXX 50 index:
- 2 trends 42d & 252d
- long, short, cash positions
- no transaction costs
Signal generation:
- invest (go long) when the 42d trend is more than 100 points above the 252d trend
- sell (go short) when the 42d trend is more than 20 points below the 252d trend
- invest in cash (no interest) when neither of both is true
Historical Correlation between EURO STOXX 50 and VSTOXX¶
It is a stylized fact that stock indexes and related volatility indexes are highly negatively correlated. The following example analyzes this stylized fact based on the EURO STOXX 50 stock index and the VSTOXX volatility index using Ordinary Least-Squares regession (OLS).
First, we collect historical data for both the EURO STOXX 50 stock and the VSTOXX volatility index.
import pandas as pd
import datetime as dt
from urllib import urlretrieve
es_url = 'http://www.stoxx.com/download/historical_values/hbrbcpe.txt'
vs_url = 'http://www.stoxx.com/download/historical_values/h_vstoxx.txt'
urlretrieve(es_url, 'es.txt')
urlretrieve(vs_url, 'vs.txt')
The EURO STOXX 50 data is not yet in the right format. Some house cleaning is necessary (I).
lines = open('es.txt').readlines() # reads the whole file line-by-line
lines[:5] # header not well formatted
The EURO STOXX 50 data is not yet in the right format. Some house cleaning is necessary (II).
lines[3883:3890] # from 27.12.2001 additional semi-colon
The EURO STOXX 50 data is not yet in the right format. Some house cleaning is necessary (III).
lines = open('es.txt').readlines() # reads the whole file line-by-line
new_file = open('es50.txt', 'w') # opens a new file
new_file.writelines('date' + lines[3][:-1].replace(' ', '') + ';DEL' + lines[3][-1])
# writes the corrected third line (additional column name)
# of the orginal file as first line of new file
new_file.writelines(lines[4:-1]) # writes the remaining lines of the orginal file
The EURO STOXX 50 data is not yet in the right format. Some house cleaning is necessary (IV).
list(open('es50.txt'))[:5] # opens the new file for inspection
Now, the data can be safely read into a DataFrame object.
es = pd.read_csv('es50.txt', index_col=0, parse_dates=True, sep=';', dayfirst=True)
del es['DEL'] # delete the helper column
es.info()
The VSTOXX data can be read without touching the raw data.
vs = pd.read_csv('vs.txt', index_col=0, header=2, parse_dates=True, sep=',', dayfirst=True)
# you can alternatively read from the Web source directly
# without saving the csv file to disk:
# vs = pd.read_csv(vs_url, index_col=0, header=2,
# parse_dates=True, sep=',', dayfirst=True)
We now merge the data for further analysis.
import datetime as dt
data = pd.DataFrame({'EUROSTOXX' :
es['SX5E'][es.index > dt.datetime(1999, 12, 31)]})
data = data.join(pd.DataFrame({'VSTOXX' :
vs['V2TX'][vs.index > dt.datetime(1999, 12, 31)]}))
data.info()
Let's inspect the two time series.
data.head()
A picture can tell almost the complete story.
data.plot(subplots=True, grid=True, style='b', figsize=(10, 5))
We now generate log returns for both time series.
rets = np.log(data / data.shift(1))
rets.head()
To this new data set, also stored in a DataFrame object, we apply OLS.
xdat = rets['EUROSTOXX']
ydat = rets['VSTOXX']
model = pd.ols(y=ydat, x=xdat)
model
Again, we want to see how our results look graphically.
plt.plot(xdat, ydat, 'r.')
ax = plt.axis() # grab axis values
x = np.linspace(ax[0], ax[1] + 0.01)
plt.plot(x, model.beta[1] + model.beta[0] * x, 'b', lw=2)
plt.grid(True)
plt.axis('tight')
Let us see if we can identify systematics over time. And indeed, during the crisis 2007/2008 (yellow dots) volatility has been more pronounced than more recently (red dots).
mpl_dates = mpl.dates.date2num(rets.index)
plt.figure(figsize=(8, 4))
plt.scatter(rets['EUROSTOXX'], rets['VSTOXX'], c=mpl_dates, marker='o')
plt.grid(True)
plt.xlabel('EUROSTOXX')
plt.ylabel('VSTOXX')
plt.colorbar(ticks=mpl.dates.DayLocator(interval=250),
format=mpl.dates.DateFormatter('%d %b %y'))
Exercise¶
We want to test whether the EURO STOXX 50 and/or the VSTOXX returns are normally distributed or not (e.g. if they might have fat tails). We want to do a
- graphical illustration (using qqplot of statsmodels.api) and a
- statistical test (using normaltest of scipy.stats)
Add on: plot a histogram of the log return frequencies and compare that to a normal distribution with same mean and variance (using e.g. norm.pdf from scipy.stats)
Constant Proportion VSTOXX Investment¶
There has been a number of studies which have illustrated that constant proportion investments in volatility derivatives – given a diversified equity portfolio – might improve investment performance considerably. See, for instance, the study
The Benefits of Volatility Derivatives in Equity Portfolio Management
We now want to replicate (in a simplified fashion) what you can flexibly test here on the basis of two backtesting applications for VSTOXX-based investment strategies:
The strategy we are going to implement and test is characterized as follows:
- An investor has total wealth of say 100,000 EUR
- He invests, say, 70% of that into a diversified equity portfolio
- The remainder, i.e. 30%, is invested in the VSTOXX index directly
- Through (daily) trading the investor keeps the proportions constant
- No transaction costs apply, all assets are infinitely divisible
We already have the necessary data available. However, we want to drop 'NaN' values and want to normalize the index values.
data = data.dropna()
data = data / data.ix[0] * 100
data.head()
First, the initial invest.
invest = 100
cratio = 0.3
data['Equity'] = (1 - cratio) * invest / data['EUROSTOXX'][0]
data['Volatility'] = cratio * invest / data['VSTOXX'][0]
This can already be considered an static investment strategy.
data['Static'] = (data['Equity'] * data['EUROSTOXX']
+ data['Volatility'] * data['VSTOXX'])
data[['EUROSTOXX', 'Static']].plot(figsize=(10, 5))
Second, the dynamic strategy with daily adjustments to keep the value ratio constant.
for i in range(1, len(data)):
evalue = data['Equity'][i - 1] * data['EUROSTOXX'][i]
# value of equity position
vvalue = data['Volatility'][i - 1] * data['VSTOXX'][i]
# value of volatility position
tvalue = evalue + vvalue
# total wealth
data['Equity'][i] = (1 - cratio) * tvalue / data['EUROSTOXX'][i]
# re-allocation of total wealth to equity ...
data['Volatility'][i] = cratio * tvalue / data['VSTOXX'][i]
# ... and volatility position
Third, the total wealth position.
data['Dynamic'] = (data['Equity'] * data['EUROSTOXX']
+ data['Volatility'] * data['VSTOXX'])
data.head()
A brief check if the ratios are indeed constant.
(data['Volatility'] * data['VSTOXX'] / data['Dynamic'])[:5]
(data['Equity'] * data['EUROSTOXX'] / data['Dynamic'])[:5]
Let us inspect the performance of the strategy.
data[['EUROSTOXX', 'Dynamic']].plot(figsize=(10, 5))
Exercise¶
Write a Python function which allows for an arbitrary but constant ratio to be invested in the VSTOXX index and which returns net performance values (in percent) for the constant proportion VSTOXX strategy.
Add on: find the ratio to be invested in the VSTOXX that gives the maximum performance.
Analyzing High Frequency Data¶
Using standard Python functionality and pandas, the code that follows reads intraday, high-frequency data from a Web source, plots it and resamples it.
url = 'http://hopey.netfonds.no/posdump.php?'
url += 'date=%s%s%s&paper=AAPL.O&csv_format=csv' % ('2014', '02', '19')
# you may have to adjust the date since only recent dates are available
urlretrieve(url, 'aapl.csv')
AAPL = pd.read_csv('aapl.csv', index_col=0, header=0, parse_dates=True)
AAPL.info()
The intraday evolution of the Apple stock price.
AAPL['bid'].plot()
AAPL = AAPL[AAPL.index > dt.datetime(2014, 2, 19, 10, 0, 0)]
# only data later than 10am at that day
A resampling of the data is easily accomplished with pandas.
# this resamples the record frequency to 5 minutes, using mean as aggregation rule
AAPL_5min = AAPL.resample(rule='5min', how='mean').fillna(method='ffill')
AAPL_5min.head()
Let's have a graphical look at the new data set.
AAPL_5min['bid'].plot()
With pandas you can easily apply custom functions to time series data.
AAPL_5min['bid'].apply(lambda x: 2 * 540 - x).plot()
# this mirrors the stock price development at
Why Python for Financial Analytics & Visualization?¶
10 years ago, Python was considered exotic in the analytics space – at best. Languages/packages like R and Matlab dominated the scene. Today, Python has become a major force in financial analytics & visualization due to a number of characteristics:
- multi-purpose: prototyping, development, production, sytems administration – Python is one for all
- libraries: there is a library for almost any task or problem you face
- efficiency: Python speeds up all IT development tasks for analytics applications and reduces maintenance costs
- performance: Python has evolved from a scripting language to a 'meta' language with bridges to all high performance environments (e.g. LLVM, multi-core CPUs, GPUs, clusters)
- interoperalbility: Python seamlessly integrates with almost any other language and technology
- interactivity: Python allows domain experts to get closer to their business and financial data pools and to do real-time analytics
- collaboration: solutions like Wakari with IPython Notebook allow the easy sharing of code, data, results, graphics, etc.
One of the easiest ways to deploy Python today across a whole organization with a heterogenous IT infrastructure is via Wakari, Continuum's Web-/Browser- and Python-based Data Analytics environment. It is availble both as a cloud as well as an enterprise solution for in-house deployment.
The Python Quants GmbH – Python Data Exploration & Visualization¶
The Python Quants – the company Web site
Dr. Yves J. Hilpisch – my personal Web site
Derivatives Analytics with Python – my new book
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