Dynamic portfolio optimization is inherently challenging due to the complexity of asset price dynamics and forecasts. Robust optimization is proposed as an alternative that
incorporates return and risk uncertainty in portfolio optimization. Directional change (DC) methods complement the standard, fixed time interval, and asset price data in terms of measuring the relationships and scaling laws between different types of events. DC methods can be extended for portfolio optimization using DC representations of assets and empirical scaling laws which indicate expected price changes and their duration. In this paper, we study a robust DC-based portfolio optimization (RDC) method,
for returns maximization. The proposed method uses price signals from the DC representations of multiple assets for portfolio rebalancing and optimization, together with a robust portfolio optimization rule that maximizes portfolio returns under return uncertainty. We empirically study the effect of the robust DCbased portfolio optimization method with an application to 29 exchange-traded funds where each fund is a well-diversified asset with typically low-risk values. We compare the obtained portfolio results with benchmarks. The results indicate that the proposed method performs comparably to several benchmarks, and particularly improves a specific risk measure, maximum drawdown, in comparison to the benchmarks.

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