How to Maximize Stock Returns and Minimize Risk with Python and Markowitz Theory

Introduction

Modern data science aims to solve complex optimization problems to maximize profit for businesses. This article builds on a previous piece about linear programming with PuLP and applies the Nobel‑winning Markowitz Modern Portfolio Theory to the stock market using Python.

How to Maximize Returns and Minimize Risk?

Markowitz’s theory balances expected return against risk (volatility). An optimal portfolio provides protection (low risk) and opportunity (high return). The core optimization problem is to achieve a target expected return while minimizing variance, subject to non‑negative investment constraints.

Here the basic idea is simple: it stems from humans' innate risk‑avoidance nature.

Example Problem

We illustrate a simplified portfolio optimization using three stocks (Microsoft, Visa, Walmart) over 24 months of monthly average prices. Returns are computed as the month‑over‑month price change divided by the previous month’s price.

The calculated return rates are shown in the following figures.

Optimizing the Model

Stock returns are modeled as a random vector, and the portfolio as another vector. The portfolio’s return is the inner product of these vectors, a random variable. The optimization seeks to minimize risk (variance) while meeting a minimum expected return.

Solving with Python: CVXPY

CVXPY is a Python modeling language for convex optimization. The full notebook (link) contains the complete code; key steps include constructing the return matrix, computing expected returns and the covariance matrix, and defining the problem with Problem and quad_form functions.

Extensions

The same framework can be extended to more realistic scenarios, such as:

Hundreds of stocks over longer time spans

Multiple risk/return thresholds

Minimizing risk, maximizing return, or both

Joint investment in a set of companies

Integer constraints (e.g., invest in Coca‑Cola or Pepsi, but not both)

These extensions lead to larger matrices and additional constraints, which CVXPY can handle.

Conclusion

The article shows how a Nobel‑level economic theory can be translated into a linear programming model solved with Python, providing data scientists with valuable skills for tackling optimization problems across finance, technology, and beyond.