Risk Minimization and Portfolio 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.

Portfolio Optimization under Correlation Constraint

“…Although portfolio allocation within expected utility paradigm is very well explored problem in finance, few studies have considered portfolio allocation with correlation constraint. Recent works that stand out and are also the motivation of this study are Bernard and Vanduffel (2014), Pourbabaee et al (2016) and Bernard et al (2018). In Bernard and Vanduffel (2014), the authors addressed the problem of mean variance optimization along with correlations constraint.…”

“…The work Pourbabaee et al (2016) looks at the problem of capital allocation with correlation constraint, and the objective is minimizing capital at risk. The paper Bernard et al (2018) extended Bernard and Vanduffel (2014), and Pourbabaee et al (2016) to law invariant preferences. All these works consider a static framework; the optimization is performed at time zero and the optimal strategies are implemented.…”