Minimal Investment Risk of Portfolio Optimization Problem with Budget and Investment Concentration Constraints

TL;DR

This paper analyzes the minimal investment risk in portfolio optimization with budget and investment concentration constraints using replica analysis, showing the impact of constraints and validating results with numerical experiments.

Contribution

It introduces a replica analysis approach to evaluate minimal investment risk considering both budget and investment concentration constraints.

Findings

Minimal investment risk increases with investment concentration constraints.

Replica analysis effectively predicts risk levels under constraints.

Numerical experiments confirm the analytical results.

Abstract

In the present paper, the minimal investment risk for a portfolio optimization problem with imposed budget and investment concentration constraints is considered using replica analysis. Since the minimal investment risk is influenced by the investment concentration constraint (as well as the budget constraint), it is intuitive that the minimal investment risk for the problem with an investment concentration constraint be larger than that without the constraint (that is, with only the budget constraint). Moreover, a numerical experiment shows the effectiveness of our proposed analysis.