Portfolio Optimization under Correlation Constraint

TL;DR

This paper develops analytical solutions for portfolio optimization with correlation constraints in a multiperiod stochastic market, showing strategies that reduce risk with minimal utility loss.

Contribution

It introduces and derives analytical expressions for constrained subgame perfect and precommitment portfolio strategies under correlation constraints.

Findings

Both strategies significantly lower risk compared to unconstrained portfolios.

The constrained strategies have similar performance.

They incur only a small utility loss.

Abstract

We consider the problem of portfolio optimization with a correlation constraint. The framework is the multiperiod stochastic financial market setting with one tradable stock, stochastic income and a non-tradable index. The correlation constraint is imposed on the portfolio and the non-tradable index at some benchmark time horizon. The goal is to maximize portofolio's expected exponential utility subject to the correlation constraint. Two types of optimal portfolio strategies are considered: the subgame perfect and the precommitment ones. We find analytical expressions for the constrained subgame perfect (CSGP) and the constrained precommitment (CPC) portfolio strategies. Both these portfolio strategies yield significantly lower risk when compared to the unconstrained setting, at the cost of a small utility loss. The performance of the CSGP and CPC portfolio strategies is similar.