Abstract

Portfolio optimization is one of the problems most frequently encountered by financial practitioners. The main goal of this paper is to fill a gap in the literature by providing a well-documented, step-by-step open-source implementation of Critical Line Algorithm (CLA) in scientific language. The code is implemented as a Python class object, which allows it to be imported like any other Python module, and integrated seamlessly with pre-existing code. We discuss the logic behind CLA following the algorithm’s decision flow. In addition, we developed several utilities that support finding answers to recurrent practical problems. We believe this publication will offer a better alternative to financial practitioners, many of whom are currently relying on generic-purpose optimizers which often deliver suboptimal solutions. The source code discussed in this paper can be downloaded at the authors’ websites (see Appendix).

Highlights

  • Since the work of Markowitz [1], portfolio optimization has become one of the most critical operations performed in investment management

  • Critical Line Algorithm (CLA) is the only algorithm designed for inequality-constrained portfolio optimization problems, which guarantees that the exact solution is found after a given number of iterations

  • Portfolio optimization is one of the problems most frequently encountered by financial practitioners

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Summary

Introduction

Since the work of Markowitz [1], portfolio optimization has become one of the most critical operations performed in investment management. The lack of publicly available CLA software, commercially or open-source, means that most researchers, practitioners and financial firms are resorting to generic linear or quadratic programming algorithms that have not been designed to solve the constrained portfolio optimization problem, and will often return suboptimal solutions. This is quite astounding, because as we said most financial practitioners face this problem with relatively high frequency. Results can be validated using the Python code in the Appendix

The Problem
The Solution
A Few Utilities
Search for the Minimum Variance Portfolio
Search for the Maximum Sharpe Ratio Portfolio
Computing the Efficient Frontier
A Numerical Example
Conclusions
Python Implementation of the Critical Line Algorithm
Full Text
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