Geometric Dispersion Theory for Portfolio Accurate Out-of-Sample Predictions of Stock Market

This paper addresses portfolio selection under Geometric Dispersion Theory (GDT). GDT is a recently developed model for analyzing risk. GDT evaluates the risk of each alternative based on two new geometric dispersion measures; one for the risk-prone case and one for the risk-averse case. GDT risk measures satisfy convexity, non-negativity, and asymmetry where other models ignore the last property. Also, GDT model satisfies first-order stochastic dominance and resolves drawbacks of other decision-making models. GDT outperforms Mean-Variance, Expected utility theory, and Cumulative Prospect theory. In this study, we apply GDT for portfolio selection problem and compare it to Mean-Variance, Mean-absolute Deviation, Two-Sided Coherent Risk Measure. We show that GDT risk measures satisfy all of the desirable properties of risk measure including diversification, monotonicity, insensitivity to mean preserving spread, and asymmetry while other risk measures do not satisfy all of these properties. Also, we compare performances of the models based on real-world data and show that GDT models outperform the models in term of the diversification ratio and in out-of-sample data, GDT models outperform the models in term of tracking error, information ratio, Sharpe Ratio and expected returns rate of portfolios