Variance and Semi-Variance with a Multi-Objective Approach Using the Spiral Optimization Method

Abstract

In minimizing the risk faced by investors while maximizing returns, it is necessary to study different risk measures for portfolio optimization, namely mean-variance, and semi-variance, so that it can provide a deeper understanding of how each approach works in various market conditions. The mean-variance approach measures risk based on the total variance of portfolio returns. While the semi-variance approach only focuses on downside risk, which is the risk of loss that is more relevant to investors who tend to be conservative. By comparing these two risk measures, investors can understand the trade-offs in choosing a portfolio management strategy. To conduct a study on portfolio optimization, the author uses a multi-objective optimization approach on the mean-variance and semi-variance models, which will be solved with a spiral model. The results of this study are that the spiral model with a simple case that does not involve high dimensions can be solved quickly. However, for high dimensions with significant maximum spread points and iterations, the algorithm in this Matlab programming runs slowly, so it is ineffective in computation. This spiral method is suspected of having several solutions trapped in local minima, or the results obtained have not converged, so the resulting Pareto front is not optimal.