# Replica Analysis for Portfolio Optimization with Single-Factor Model

## TL;DR

This paper employs replica analysis to study how asset return correlations affect portfolio optimization under a single-factor model, revealing increased risk and comparing methods with independent returns and operations research approaches.

## Contribution

It introduces a replica analysis framework to analytically evaluate the impact of correlations on portfolio risk in a single-factor model setting.

## Key findings

- Correlation increases investment risk compared to independent returns.
- Replica analysis provides analytical insights into risk behavior.
- Comparison with operations research methods highlights differences in risk minimization.

## Abstract

In this paper, we use replica analysis to investigate the influence of correlation among the return rates of assets on the solution of the portfolio optimization problem. We consider the behavior of the optimal solution for the case where the return rate is described with a single-factor model and compare the findings obtained from our proposed methods with correlated return rates with those obtained with independent return rates. We then analytically assess the increase in the investment risk when correlation is included. Furthermore, we also compare our approach with analytical procedures for minimizing the investment risk from operations research.