The impact of model risk on dynamic portfolio selection under multi-period mean-standard-deviation criterion

TL;DR

This paper assesses the impact of model risk on multi-period portfolio optimization using a mean-standard-deviation criterion, proposing a robust strategy that accounts for distributional uncertainty measured by Kullback-Leibler divergence.

Contribution

It introduces a semi-analytical method to derive robust portfolio strategies under distributional uncertainty in a multi-period setting.

Findings

Robust strategy outperforms non-robust in worst-case scenarios.

Quantifies model risk using empirical data.

Provides a semi-analytical solution for robust optimization.

Abstract

We quantify model risk of a financial portfolio whereby a multi-period mean-standard-deviation criterion is used as a selection criterion. In this work, model risk is defined as the loss due to uncertainty of the underlying distribution of the returns of the assets in the portfolio. The uncertainty is measured by the Kullback-Leibler divergence, i.e., the relative entropy. In the worst case scenario, the optimal robust strategy can be obtained in a semi-analytical form as a solution of a system of nonlinear equations. Several numerical results are presented which allow us to compare the performance of this robust strategy with the optimal non-robust strategy. For illustration, we also quantify the model risk associated with an empirical dataset.