# Unleash Investment Potential: Portfolio Optimization with MILP

Published 16/04/2024 By NAG

The dynamic financial landscape demands optimal strategies to manage risks effectively while maintaining a desirable return level. Portfolio optimization utilizes mathematical models to allocate assets across portfolios efficiently. Here we look at Mixed Integer Linear Programming (MILP) and its application in portfolio optimization, as demonstrated through the new example using NAG’s high-performance MILP solver available in the NAG Library Optimization Modelling Suite.

##### Understanding Portfolio Optimization

Portfolio optimization involves constructing an investment portfolio that balances risk and return according to predefined objectives and constraints. Traditional approaches, such as Modern Portfolio Theory (MPT), rely on statistical methods to optimize portfolios based on historical data. While effective, these methods may overlook real-world complexities and fail to capture the intricacies of financial markets.

##### Enter MILP

MILP offers a powerful alternative for portfolio optimization by formulating the problem as a mathematical optimization task. Unlike traditional methods, MILP considers discrete decisions, such as asset selection and allocation, alongside continuous variables. This flexibility allows for more flexible modelling, enabling investors to incorporate diverse constraints and preferences into their portfolio strategies. A new high-performance MILP solver was introduced to the NAG Library Optimization Modelling Suite earlier this year.

##### Application Example

The new example featured in NAG’s optimization code repository demonstrates portfolio optimization using MILP in Python. In the step-by-step example, you can see how to:

1. Define the problem: Specify the objective function, decision variables, and constraints.
2. Implement the model: Utilize the NAG Optimization Modelling Suite to construct the MILP problem.
3. Optimize: Employ an efficient solver to find the optimal portfolio allocation.
4. Analyze results: Interpret the optimized portfolio composition and evaluate its performance.
##### Value to Users
1. Robustness: MILP-based portfolio optimization accounts for discrete decisions and complex constraints, leading to more robust investment strategies.
2. Customization: Users can tailor optimization models to accommodate various investment goals, risk tolerances, and regulatory requirements.
3. Efficiency: Leveraging advanced optimization algorithms, MILP enables efficient computation of optimal portfolios, even for large-scale problems.

Image shows first MILP model constraint from portfolio optimization notebook

Portfolio optimization is a vital tool for investors seeking to navigate financial markets effectively. Through MILP-based approaches, such as the one demonstrated in the new NAG MILP Solver example, users can unlock the full potential of mathematical optimization in portfolio management. By combining mathematical rigor with practical implementation, MILP helps investors to construct resilient portfolios tailored to their objectives and constraints. Utilizing MILP methodology can lead to more informed investment decisions and ultimately, enhanced returns.

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