# Location and portfolio selection problems: A unified framework

**Authors:** Justo Puerto, Moises Rodríguez-Madrena, Andrea Scozzari  
**arXiv:** [1907.07101](https://arxiv.org/abs/1907.07101)  
**Date:** 2019-07-15  
**Summary page:** https://www.summarizepaper.com/en/paper/1907.07101v1/

## Key points

- The paper addresses the classical portfolio selection problem
- Goal is to maximize mean rate of return while minimizing risk measure
- Various mathematical programming models and techniques proposed in literature
- Introduces a promising approach leveraging clustering information from assets network
- Correlation coefficients used to establish metric for assets network
- Classical location problems on networks utilized for clustering assets based on metric
- New criterion proposed to measure effect of clustering on selected assets
- Unified phase approach using Mixed-Integer Linear Programming formulation presented
- Preliminary computational experiments demonstrate effectiveness of unified framework
- Integration of location problems on networks with portfolio optimization offers a unified framework
- Enhances decision-making in asset allocation strategies with potential applications in various financial domains.

## Summary

The paper titled "Location and portfolio selection problems: A unified framework" addresses the classical portfolio selection problem which involves determining the optimal allocation of investment capital among a set of assets to build the most profitable portfolio. The goal is to maximize the mean rate of return while minimizing a given risk measure. Various mathematical programming models and techniques have been proposed in the literature to solve this problem efficiently. This paper introduces a promising approach that leverages clustering information from an assets network to develop new paradigms for portfolio optimization. Specifically, correlation coefficients between assets' returns are used to establish a metric for the assets network and classical location problems on networks are utilized for clustering assets based on this metric. To measure the effect of clustering on selected assets compared to non-selected ones, a new criterion is proposed that is based on an objective function derived from a classical location problem. Most existing papers dealing with clustering and portfolio selection models solve these problems in two separate steps; however, this paper presents an innovative contribution by proposing a unified phase approach using Mixed-Integer Linear Programming formulation. Preliminary computational experiments using real financial datasets demonstrate the effectiveness of their unified framework for solving both clustering and portfolio selection problems simultaneously. This paper provides valuable insights into integrating location problems on networks with portfolio optimization, offering a unified framework that enhances decision-making in asset allocation strategies with potential applications in various financial domains where efficient and effective portfolio management is crucial.