Book Image

Mastering Python for Finance

Book Image

Mastering Python for Finance

Overview of this book

Table of Contents (17 chapters)
Mastering Python for Finance
Credits
About the Author
About the Reviewers
www.PacktPub.com
Preface
Index

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, , and . 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:

With all of the coefficients...