Search icon CANCEL
Subscription
0
Cart icon
Your Cart (0 item)
Close icon
You have no products in your basket yet
Arrow left icon
Explore Products
Best Sellers
New Releases
Books
Videos
Audiobooks
Learning Hub
Newsletter Hub
Free Learning
Arrow right icon
timer SALE ENDS IN
0 Days
:
00 Hours
:
00 Minutes
:
00 Seconds
Mastering Python for Finance
Mastering Python for Finance

Mastering Python for Finance: Understand, design, and implement state-of-the-art mathematical and statistical applications used in finance with Python

eBook
zł59.99 zł177.99
Paperback
zł221.99
Subscription
Free Trial

What do you get with a Packt Subscription?

Free for first 7 days. $19.99 p/m after that. Cancel any time!
Product feature icon Unlimited ad-free access to the largest independent learning library in tech. Access this title and thousands more!
Product feature icon 50+ new titles added per month, including many first-to-market concepts and exclusive early access to books as they are being written.
Product feature icon Innovative learning tools, including AI book assistants, code context explainers, and text-to-speech.
Product feature icon Thousands of reference materials covering every tech concept you need to stay up to date.
Subscribe now
View plans & pricing
Table of content icon View table of contents Preview book icon Preview Book

Mastering Python for Finance

Chapter 2. The Importance of Linearity in Finance

Nonlinear dynamics plays a vital role in our world. Linear models are often employed in economics due to their simplicity for studies and easier modeling capabilities. In finance, linear models are widely used to help price securities and perform optimal portfolio allocation, among other useful things. One of the significance of linearity in financial modeling is its assurance that a problem terminates at a global optimal solution.

In order to perform prediction and forecasting, regression analysis is widely used in the field of statistics to estimate relationships among variables. With an extensive mathematics library being one of Python's greatest strength, Python is frequently used as a scientific scripting language to aid in these problems. Modules such as the SciPy and NumPy packages contain a variety of linear regression functions for data scientists to work with.

In traditional portfolio management, the allocation of...

The capital asset pricing model and the security market line

Many financial literatures devote exclusive discussions to the capital asset pricing model (CAPM). In this section, we will explore the key concepts that highlight the importance of linearity in finance.

In the famous CAPM, the relationship between risk and rates of returns in a security is described as follows:

The capital asset pricing model and the security market line

For a security The capital asset pricing model and the security market line, its returns is defined as The capital asset pricing model and the security market line and its beta as The capital asset pricing model and the security market line. The CAPM defines the return of the security as the sum of the risk-free rate The capital asset pricing model and the security market line and the multiplication of its beta with the risk premium. The risk premium can be thought of as the market portfolio's excess returns exclusive of the risk-free rate. The following figure is a visual representation of the CAPM:

The capital asset pricing model and the security market line

Beta is a measure of the systematic risk of a stock; a risk that cannot be diversified away. In essence, it describes the sensitivity of stock returns with respect to movements in the market. For example, a stock with a beta of zero produces no excess returns...

The Arbitrage Pricing Theory model

The CAPM suffers from several limitations, such as the use of a mean-variance framework and the fact that returns are captured by one risk factor—the market risk factor. In a well-diversified portfolio, the unsystematic risk of various stocks cancels out and is essentially eliminated.

The Arbitrage Pricing Theory (APT) model was put forward to address these shortcomings and offers a general approach of determining the asset prices other than the mean and variances.

The APT model assumes that the security returns are generated according to multiple factor models, which consist of a linear combination of several systematic risk factors. Such factors could be the inflation rate, GDP growth rate, real interest rates, or dividends.

The equilibrium asset pricing equation according to the APT model is as follows:

The Arbitrage Pricing Theory model

Here, The Arbitrage Pricing Theory model is the expected rate of return on security The Arbitrage Pricing Theory model, The Arbitrage Pricing Theory model is the expected return on stock The Arbitrage Pricing Theory model if all factors are negligible, The Arbitrage Pricing Theory model is the sensitivity of the The Arbitrage Pricing Theory modelth...

Multivariate linear regression of factor models

Many Python packages such as SciPy come with several variants of regression functions. In particular, the statsmodels package is a complement to SciPy with descriptive statistics and estimation of statistical models. The official page for statsmodels is http://statsmodels.sourceforge.net/.

In this example, we will use the ols function of the statsmodels module to perform an ordinary least squares regression and view its summary.

Let's assume that you have implemented an APT model with seven factors that return the values of Y. Consider the following set of data collected over 9 time periods, Multivariate linear regression of factor models to Multivariate linear regression of factor models. X1 to X7 are independent variables observed at each period. The regression problem is therefore structured as:Multivariate linear regression of factor models.

A simple ordinary least squares regression on values of X and Y can be performed with the following code:

""" Least squares regression with statsmodels """
import numpy as np
import statsmodels.api as sm
...

Linear optimization

In the CAPM and APT pricing theories, we assumed linearity in the models and solved for expected security prices using regressions in Python.

As the number of securities in our portfolio increases, certain limitations are introduced as well. A portfolio manager would find himself constrained by these rules in pursing certain objectives mandated by investors.

Linear optimization helps you overcome the problem of portfolio allocation. Optimization focuses on minimizing or maximizing the value of the objective functions. The examples are maximizing returns and minimizing volatility. These objectives are usually governed by certain regulations, such as no short-selling rule, limits on the number of securities to be invested, and so on.

Unfortunately, in Python there is no single official package that supports this solution. However, there are third-party packages available with the implementation of the simplex algorithm for linear programming. For the purpose of this demonstration...

Solving linear equations using matrices

In the previous section, we looked at solving a system of linear equations with inequality constraints. If a set of systematic linear equations has constraints that are deterministic, we can represent the problem as matrices and apply matrix algebra. Matrix methods represent multiple linear equations in a compact manner while using the existing matrix library functions.

Suppose we would like to build a portfolio consisting of 3 securities, Solving linear equations using matrices, Solving linear equations using matrices and Solving linear equations using matrices. The allocation of the portfolio must meet certain constraints: it must consist of 6 units of a long position in security a. With every 2 units of security a, 1 unit of security b, and 1 unit of security c invested, the net position must be 4 units long. With every 1 unit of security a, 3 units of security b, and 2 units of security c invested, the net position must be long 5 units.

To find out the number of securities to invest in, we can frame the problem mathematically as follows:

Solving linear equations using matrices
Solving linear equations using matrices
Solving linear equations using matrices

With all of the coefficients...

The capital asset pricing model and the security market line


Many financial literatures devote exclusive discussions to the capital asset pricing model (CAPM). In this section, we will explore the key concepts that highlight the importance of linearity in finance.

In the famous CAPM, the relationship between risk and rates of returns in a security is described as follows:

For a security , its returns is defined as and its beta as . The CAPM defines the return of the security as the sum of the risk-free rate and the multiplication of its beta with the risk premium. The risk premium can be thought of as the market portfolio's excess returns exclusive of the risk-free rate. The following figure is a visual representation of the CAPM:

Beta is a measure of the systematic risk of a stock; a risk that cannot be diversified away. In essence, it describes the sensitivity of stock returns with respect to movements in the market. For example, a stock with a beta of zero produces no excess returns regardless...

The Arbitrage Pricing Theory model


The CAPM suffers from several limitations, such as the use of a mean-variance framework and the fact that returns are captured by one risk factor—the market risk factor. In a well-diversified portfolio, the unsystematic risk of various stocks cancels out and is essentially eliminated.

The Arbitrage Pricing Theory (APT) model was put forward to address these shortcomings and offers a general approach of determining the asset prices other than the mean and variances.

The APT model assumes that the security returns are generated according to multiple factor models, which consist of a linear combination of several systematic risk factors. Such factors could be the inflation rate, GDP growth rate, real interest rates, or dividends.

The equilibrium asset pricing equation according to the APT model is as follows:

Here, is the expected rate of return on security , is the expected return on stock if all factors are negligible, is the sensitivity of the th asset...

Multivariate linear regression of factor models


Many Python packages such as SciPy come with several variants of regression functions. In particular, the statsmodels package is a complement to SciPy with descriptive statistics and estimation of statistical models. The official page for statsmodels is http://statsmodels.sourceforge.net/.

In this example, we will use the ols function of the statsmodels module to perform an ordinary least squares regression and view its summary.

Let's assume that you have implemented an APT model with seven factors that return the values of Y. Consider the following set of data collected over 9 time periods, to . X1 to X7 are independent variables observed at each period. The regression problem is therefore structured as:.

A simple ordinary least squares regression on values of X and Y can be performed with the following code:

""" Least squares regression with statsmodels """
import numpy as np
import statsmodels.api as sm

# Generate some sample data
num_periods...

Linear optimization


In the CAPM and APT pricing theories, we assumed linearity in the models and solved for expected security prices using regressions in Python.

As the number of securities in our portfolio increases, certain limitations are introduced as well. A portfolio manager would find himself constrained by these rules in pursing certain objectives mandated by investors.

Linear optimization helps you overcome the problem of portfolio allocation. Optimization focuses on minimizing or maximizing the value of the objective functions. The examples are maximizing returns and minimizing volatility. These objectives are usually governed by certain regulations, such as no short-selling rule, limits on the number of securities to be invested, and so on.

Unfortunately, in Python there is no single official package that supports this solution. However, there are third-party packages available with the implementation of the simplex algorithm for linear programming. For the purpose of this demonstration...

Left arrow icon Right arrow icon

Description

If you are an undergraduate or graduate student, a beginner to algorithmic development and research, or a software developer in the financial industry who is interested in using Python for quantitative methods in finance, this is the book for you. It would be helpful to have a bit of familiarity with basic Python usage, but no prior experience is required.

Who is this book for?

If you are an undergraduate or graduate student, a beginner to algorithmic development and research, or a software developer in the financial industry who is interested in using Python for quantitative methods in finance, this is the book for you. It would be helpful to have a bit of familiarity with basic Python usage, but no prior experience is required.

What you will learn

  • Perform interactive computing with IPython Notebook
  • Solve linear equations of financial models and perform ordinary least squares regression
  • Explore nonlinear modeling and solutions for optimum points using rootfinding algorithms and solvers
  • Discover different types of numerical procedures used in pricing options
  • Model fixedincome instruments with bonds and interest rates
  • Manage big data with NoSQL and perform analytics with Hadoop
  • Build a highfrequency algorithmic trading platform with Python
  • Create an eventdriven backtesting tool and measure your strategies

Product Details

Country selected
Publication date, Length, Edition, Language, ISBN-13
Publication date : Apr 29, 2015
Length: 340 pages
Edition : 1st
Language : English
ISBN-13 : 9781784394516
Category :
Languages :
Concepts :

What do you get with a Packt Subscription?

Free for first 7 days. $19.99 p/m after that. Cancel any time!
Product feature icon Unlimited ad-free access to the largest independent learning library in tech. Access this title and thousands more!
Product feature icon 50+ new titles added per month, including many first-to-market concepts and exclusive early access to books as they are being written.
Product feature icon Innovative learning tools, including AI book assistants, code context explainers, and text-to-speech.
Product feature icon Thousands of reference materials covering every tech concept you need to stay up to date.
Subscribe now
View plans & pricing

Product Details

Publication date : Apr 29, 2015
Length: 340 pages
Edition : 1st
Language : English
ISBN-13 : 9781784394516
Category :
Languages :
Concepts :

Packt Subscriptions

See our plans and pricing
Modal Close icon
$19.99 billed monthly
Feature tick icon Unlimited access to Packt's library of 7,000+ practical books and videos
Feature tick icon Constantly refreshed with 50+ new titles a month
Feature tick icon Exclusive Early access to books as they're written
Feature tick icon Solve problems while you work with advanced search and reference features
Feature tick icon Offline reading on the mobile app
Feature tick icon Simple pricing, no contract
$199.99 billed annually
Feature tick icon Unlimited access to Packt's library of 7,000+ practical books and videos
Feature tick icon Constantly refreshed with 50+ new titles a month
Feature tick icon Exclusive Early access to books as they're written
Feature tick icon Solve problems while you work with advanced search and reference features
Feature tick icon Offline reading on the mobile app
Feature tick icon Choose a DRM-free eBook or Video every month to keep
Feature tick icon PLUS own as many other DRM-free eBooks or Videos as you like for just zł20 each
Feature tick icon Exclusive print discounts
$279.99 billed in 18 months
Feature tick icon Unlimited access to Packt's library of 7,000+ practical books and videos
Feature tick icon Constantly refreshed with 50+ new titles a month
Feature tick icon Exclusive Early access to books as they're written
Feature tick icon Solve problems while you work with advanced search and reference features
Feature tick icon Offline reading on the mobile app
Feature tick icon Choose a DRM-free eBook or Video every month to keep
Feature tick icon PLUS own as many other DRM-free eBooks or Videos as you like for just zł20 each
Feature tick icon Exclusive print discounts

Frequently bought together


Stars icon
Total 641.97
Python for Finance
zł197.99
Mastering R for Quantitative Finance
zł221.99
Mastering Python for Finance
zł221.99
Total 641.97 Stars icon

Table of Contents

11 Chapters
1. Python for Financial Applications Chevron down icon Chevron up icon
2. The Importance of Linearity in Finance Chevron down icon Chevron up icon
3. Nonlinearity in Finance Chevron down icon Chevron up icon
4. Numerical Procedures Chevron down icon Chevron up icon
5. Interest Rates and Derivatives Chevron down icon Chevron up icon
6. Interactive Financial Analytics with Python and VSTOXX Chevron down icon Chevron up icon
7. Big Data with Python Chevron down icon Chevron up icon
8. Algorithmic Trading Chevron down icon Chevron up icon
9. Backtesting Chevron down icon Chevron up icon
10. Excel with Python Chevron down icon Chevron up icon
Index Chevron down icon Chevron up icon

Customer reviews

Top Reviews
Rating distribution
Full star icon Full star icon Full star icon Half star icon Empty star icon 3.3
(7 Ratings)
5 star 14.3%
4 star 28.6%
3 star 28.6%
2 star 28.6%
1 star 0%
Filter icon Filter
Top Reviews

Filter reviews by




Duncan W. Robinson Jun 14, 2015
Full star icon Full star icon Full star icon Full star icon Full star icon 5
Wow… good stuff. Mastering Python for Finance really delivers. It does a fine job blending academic theory with a practitioner’s penchant for useful applications, delivering Python code all the way to guide the reader along his / her journey. I have not worked all of the examples yet, but I am looking forward to doing so – especially the sections that use Hadoop & Python together.
Amazon Verified review Amazon
Federico Han Feb 28, 2018
Full star icon Full star icon Full star icon Full star icon Empty star icon 4
A pretty good survey on many object-oriented implementations common in Finance.Plenty of applications and examples -some indeed with errors , though on the positive it is a useful learning experience to do some minor debugging !-.As with many practical reference books try to buy the print version, this is not bedtime reading stuff.
Amazon Verified review Amazon
Kindleのお客様 Jul 06, 2016
Full star icon Full star icon Full star icon Full star icon Empty star icon 4
金融工学の基礎を一通り習得した人が、pythonでコードをかけるようになるための一冊。目次の内容に対して、特に数学的な証明等なしで天下り的にPythonのコードが羅列されているので、ファイナンスの入門者にはお勧めしない。費用対効果は高い。
Amazon Verified review Amazon
Martin Galli Jan 01, 2017
Full star icon Full star icon Full star icon Empty star icon Empty star icon 3
Bon livre en général mais dommage qu'il soit en Python 2.7 et non Python3.5. Sinon, les solutions sont très bien expliquées et l'organisation est claire.
Amazon Verified review Amazon
Ho Yan Chan May 02, 2018
Full star icon Full star icon Full star icon Empty star icon Empty star icon 3
ok
Amazon Verified review Amazon
Get free access to Packt library with over 7500+ books and video courses for 7 days!
Start Free Trial

FAQs

What is included in a Packt subscription? Chevron down icon Chevron up icon

A subscription provides you with full access to view all Packt and licnesed content online, this includes exclusive access to Early Access titles. Depending on the tier chosen you can also earn credits and discounts to use for owning content

How can I cancel my subscription? Chevron down icon Chevron up icon

To cancel your subscription with us simply go to the account page - found in the top right of the page or at https://subscription.packtpub.com/my-account/subscription - From here you will see the ‘cancel subscription’ button in the grey box with your subscription information in.

What are credits? Chevron down icon Chevron up icon

Credits can be earned from reading 40 section of any title within the payment cycle - a month starting from the day of subscription payment. You also earn a Credit every month if you subscribe to our annual or 18 month plans. Credits can be used to buy books DRM free, the same way that you would pay for a book. Your credits can be found in the subscription homepage - subscription.packtpub.com - clicking on ‘the my’ library dropdown and selecting ‘credits’.

What happens if an Early Access Course is cancelled? Chevron down icon Chevron up icon

Projects are rarely cancelled, but sometimes it's unavoidable. If an Early Access course is cancelled or excessively delayed, you can exchange your purchase for another course. For further details, please contact us here.

Where can I send feedback about an Early Access title? Chevron down icon Chevron up icon

If you have any feedback about the product you're reading, or Early Access in general, then please fill out a contact form here and we'll make sure the feedback gets to the right team. 

Can I download the code files for Early Access titles? Chevron down icon Chevron up icon

We try to ensure that all books in Early Access have code available to use, download, and fork on GitHub. This helps us be more agile in the development of the book, and helps keep the often changing code base of new versions and new technologies as up to date as possible. Unfortunately, however, there will be rare cases when it is not possible for us to have downloadable code samples available until publication.

When we publish the book, the code files will also be available to download from the Packt website.

How accurate is the publication date? Chevron down icon Chevron up icon

The publication date is as accurate as we can be at any point in the project. Unfortunately, delays can happen. Often those delays are out of our control, such as changes to the technology code base or delays in the tech release. We do our best to give you an accurate estimate of the publication date at any given time, and as more chapters are delivered, the more accurate the delivery date will become.

How will I know when new chapters are ready? Chevron down icon Chevron up icon

We'll let you know every time there has been an update to a course that you've bought in Early Access. You'll get an email to let you know there has been a new chapter, or a change to a previous chapter. The new chapters are automatically added to your account, so you can also check back there any time you're ready and download or read them online.

I am a Packt subscriber, do I get Early Access? Chevron down icon Chevron up icon

Yes, all Early Access content is fully available through your subscription. You will need to have a paid for or active trial subscription in order to access all titles.

How is Early Access delivered? Chevron down icon Chevron up icon

Early Access is currently only available as a PDF or through our online reader. As we make changes or add new chapters, the files in your Packt account will be updated so you can download them again or view them online immediately.

How do I buy Early Access content? Chevron down icon Chevron up icon

Early Access is a way of us getting our content to you quicker, but the method of buying the Early Access course is still the same. Just find the course you want to buy, go through the check-out steps, and you’ll get a confirmation email from us with information and a link to the relevant Early Access courses.

What is Early Access? Chevron down icon Chevron up icon

Keeping up to date with the latest technology is difficult; new versions, new frameworks, new techniques. This feature gives you a head-start to our content, as it's being created. With Early Access you'll receive each chapter as it's written, and get regular updates throughout the product's development, as well as the final course as soon as it's ready.We created Early Access as a means of giving you the information you need, as soon as it's available. As we go through the process of developing a course, 99% of it can be ready but we can't publish until that last 1% falls in to place. Early Access helps to unlock the potential of our content early, to help you start your learning when you need it most. You not only get access to every chapter as it's delivered, edited, and updated, but you'll also get the finalized, DRM-free product to download in any format you want when it's published. As a member of Packt, you'll also be eligible for our exclusive offers, including a free course every day, and discounts on new and popular titles.