Risk minimization and portfolio diversification

TL;DR

This paper analyzes risk minimization in portfolio selection within the Black-Scholes model, showing how correlation constraints influence diversification and deriving the optimal portfolio in closed form.

Contribution

It introduces a closed-form solution for risk-minimizing portfolios under correlation constraints, highlighting their impact on diversification.

Findings

Correlation constraints lead to more diversified portfolios

Optimal portfolio derived explicitly in closed form

Imposing correlation constraints affects risk and diversification

Abstract

We consider the problem of minimizing capital at risk in the Black-Scholes setting. The portfolio problem is studied given the possibility that a correlation constraint between the portfolio and a financial index is imposed. The optimal portfolio is obtained in closed form. The effects of the correlation constraint are explored; it turns out that this portfolio constraint leads to a more diversified portfolio.