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
€22.99 €32.99
Paperback
€41.99
Subscription
Free Trial
Renews at €18.99p/m

What do you get with Print?

Product feature icon Instant access to your digital copy whilst your Print order is Shipped
Product feature icon Paperback book shipped to your preferred address
Product feature icon Redeem a companion digital copy on all Print orders
Product feature icon Access this title in our online reader with advanced features
Product feature icon DRM FREE - Read whenever, wherever and however you want
OR
Modal Close icon
Payment Processing...
tick Completed

Shipping Address

Billing Address

Shipping Methods
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
Estimated delivery fee Deliver to Ireland

Premium delivery 7 - 10 business days

€23.95
(Includes tracking information)

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 Print?

Product feature icon Instant access to your digital copy whilst your Print order is Shipped
Product feature icon Paperback book shipped to your preferred address
Product feature icon Redeem a companion digital copy on all Print orders
Product feature icon Access this title in our online reader with advanced features
Product feature icon DRM FREE - Read whenever, wherever and however you want
OR
Modal Close icon
Payment Processing...
tick Completed

Shipping Address

Billing Address

Shipping Methods
Estimated delivery fee Deliver to Ireland

Premium delivery 7 - 10 business days

€23.95
(Includes tracking information)

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
€18.99 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
€189.99 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 €5 each
Feature tick icon Exclusive print discounts
€264.99 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 €5 each
Feature tick icon Exclusive print discounts

Frequently bought together


Stars icon
Total 120.97
Python for Finance
€36.99
Mastering R for Quantitative Finance
€41.99
Mastering Python for Finance
€41.99
Total 120.97 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 the digital copy I get with my Print order? Chevron down icon Chevron up icon

When you buy any Print edition of our Books, you can redeem (for free) the eBook edition of the Print Book you’ve purchased. This gives you instant access to your book when you make an order via PDF, EPUB or our online Reader experience.

What is the delivery time and cost of print book? Chevron down icon Chevron up icon

Shipping Details

USA:

'

Economy: Delivery to most addresses in the US within 10-15 business days

Premium: Trackable Delivery to most addresses in the US within 3-8 business days

UK:

Economy: Delivery to most addresses in the U.K. within 7-9 business days.
Shipments are not trackable

Premium: Trackable delivery to most addresses in the U.K. within 3-4 business days!
Add one extra business day for deliveries to Northern Ireland and Scottish Highlands and islands

EU:

Premium: Trackable delivery to most EU destinations within 4-9 business days.

Australia:

Economy: Can deliver to P. O. Boxes and private residences.
Trackable service with delivery to addresses in Australia only.
Delivery time ranges from 7-9 business days for VIC and 8-10 business days for Interstate metro
Delivery time is up to 15 business days for remote areas of WA, NT & QLD.

Premium: Delivery to addresses in Australia only
Trackable delivery to most P. O. Boxes and private residences in Australia within 4-5 days based on the distance to a destination following dispatch.

India:

Premium: Delivery to most Indian addresses within 5-6 business days

Rest of the World:

Premium: Countries in the American continent: Trackable delivery to most countries within 4-7 business days

Asia:

Premium: Delivery to most Asian addresses within 5-9 business days

Disclaimer:
All orders received before 5 PM U.K time would start printing from the next business day. So the estimated delivery times start from the next day as well. Orders received after 5 PM U.K time (in our internal systems) on a business day or anytime on the weekend will begin printing the second to next business day. For example, an order placed at 11 AM today will begin printing tomorrow, whereas an order placed at 9 PM tonight will begin printing the day after tomorrow.


Unfortunately, due to several restrictions, we are unable to ship to the following countries:

  1. Afghanistan
  2. American Samoa
  3. Belarus
  4. Brunei Darussalam
  5. Central African Republic
  6. The Democratic Republic of Congo
  7. Eritrea
  8. Guinea-bissau
  9. Iran
  10. Lebanon
  11. Libiya Arab Jamahriya
  12. Somalia
  13. Sudan
  14. Russian Federation
  15. Syrian Arab Republic
  16. Ukraine
  17. Venezuela
What is custom duty/charge? Chevron down icon Chevron up icon

Customs duty are charges levied on goods when they cross international borders. It is a tax that is imposed on imported goods. These duties are charged by special authorities and bodies created by local governments and are meant to protect local industries, economies, and businesses.

Do I have to pay customs charges for the print book order? Chevron down icon Chevron up icon

The orders shipped to the countries that are listed under EU27 will not bear custom charges. They are paid by Packt as part of the order.

List of EU27 countries: www.gov.uk/eu-eea:

A custom duty or localized taxes may be applicable on the shipment and would be charged by the recipient country outside of the EU27 which should be paid by the customer and these duties are not included in the shipping charges been charged on the order.

How do I know my custom duty charges? Chevron down icon Chevron up icon

The amount of duty payable varies greatly depending on the imported goods, the country of origin and several other factors like the total invoice amount or dimensions like weight, and other such criteria applicable in your country.

For example:

  • If you live in Mexico, and the declared value of your ordered items is over $ 50, for you to receive a package, you will have to pay additional import tax of 19% which will be $ 9.50 to the courier service.
  • Whereas if you live in Turkey, and the declared value of your ordered items is over € 22, for you to receive a package, you will have to pay additional import tax of 18% which will be € 3.96 to the courier service.
How can I cancel my order? Chevron down icon Chevron up icon

Cancellation Policy for Published Printed Books:

You can cancel any order within 1 hour of placing the order. Simply contact customercare@packt.com with your order details or payment transaction id. If your order has already started the shipment process, we will do our best to stop it. However, if it is already on the way to you then when you receive it, you can contact us at customercare@packt.com using the returns and refund process.

Please understand that Packt Publishing cannot provide refunds or cancel any order except for the cases described in our Return Policy (i.e. Packt Publishing agrees to replace your printed book because it arrives damaged or material defect in book), Packt Publishing will not accept returns.

What is your returns and refunds policy? Chevron down icon Chevron up icon

Return Policy:

We want you to be happy with your purchase from Packtpub.com. We will not hassle you with returning print books to us. If the print book you receive from us is incorrect, damaged, doesn't work or is unacceptably late, please contact Customer Relations Team on customercare@packt.com with the order number and issue details as explained below:

  1. If you ordered (eBook, Video or Print Book) incorrectly or accidentally, please contact Customer Relations Team on customercare@packt.com within one hour of placing the order and we will replace/refund you the item cost.
  2. Sadly, if your eBook or Video file is faulty or a fault occurs during the eBook or Video being made available to you, i.e. during download then you should contact Customer Relations Team within 14 days of purchase on customercare@packt.com who will be able to resolve this issue for you.
  3. You will have a choice of replacement or refund of the problem items.(damaged, defective or incorrect)
  4. Once Customer Care Team confirms that you will be refunded, you should receive the refund within 10 to 12 working days.
  5. If you are only requesting a refund of one book from a multiple order, then we will refund you the appropriate single item.
  6. Where the items were shipped under a free shipping offer, there will be no shipping costs to refund.

On the off chance your printed book arrives damaged, with book material defect, contact our Customer Relation Team on customercare@packt.com within 14 days of receipt of the book with appropriate evidence of damage and we will work with you to secure a replacement copy, if necessary. Please note that each printed book you order from us is individually made by Packt's professional book-printing partner which is on a print-on-demand basis.

What tax is charged? Chevron down icon Chevron up icon

Currently, no tax is charged on the purchase of any print book (subject to change based on the laws and regulations). A localized VAT fee is charged only to our European and UK customers on eBooks, Video and subscriptions that they buy. GST is charged to Indian customers for eBooks and video purchases.

What payment methods can I use? Chevron down icon Chevron up icon

You can pay with the following card types:

  1. Visa Debit
  2. Visa Credit
  3. MasterCard
  4. PayPal
What is the delivery time and cost of print books? Chevron down icon Chevron up icon

Shipping Details

USA:

'

Economy: Delivery to most addresses in the US within 10-15 business days

Premium: Trackable Delivery to most addresses in the US within 3-8 business days

UK:

Economy: Delivery to most addresses in the U.K. within 7-9 business days.
Shipments are not trackable

Premium: Trackable delivery to most addresses in the U.K. within 3-4 business days!
Add one extra business day for deliveries to Northern Ireland and Scottish Highlands and islands

EU:

Premium: Trackable delivery to most EU destinations within 4-9 business days.

Australia:

Economy: Can deliver to P. O. Boxes and private residences.
Trackable service with delivery to addresses in Australia only.
Delivery time ranges from 7-9 business days for VIC and 8-10 business days for Interstate metro
Delivery time is up to 15 business days for remote areas of WA, NT & QLD.

Premium: Delivery to addresses in Australia only
Trackable delivery to most P. O. Boxes and private residences in Australia within 4-5 days based on the distance to a destination following dispatch.

India:

Premium: Delivery to most Indian addresses within 5-6 business days

Rest of the World:

Premium: Countries in the American continent: Trackable delivery to most countries within 4-7 business days

Asia:

Premium: Delivery to most Asian addresses within 5-9 business days

Disclaimer:
All orders received before 5 PM U.K time would start printing from the next business day. So the estimated delivery times start from the next day as well. Orders received after 5 PM U.K time (in our internal systems) on a business day or anytime on the weekend will begin printing the second to next business day. For example, an order placed at 11 AM today will begin printing tomorrow, whereas an order placed at 9 PM tonight will begin printing the day after tomorrow.


Unfortunately, due to several restrictions, we are unable to ship to the following countries:

  1. Afghanistan
  2. American Samoa
  3. Belarus
  4. Brunei Darussalam
  5. Central African Republic
  6. The Democratic Republic of Congo
  7. Eritrea
  8. Guinea-bissau
  9. Iran
  10. Lebanon
  11. Libiya Arab Jamahriya
  12. Somalia
  13. Sudan
  14. Russian Federation
  15. Syrian Arab Republic
  16. Ukraine
  17. Venezuela