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...