An adaptive robust portfolio optimization model with loss constraints based on data-driven polyhedral uncertainty sets

Robust portfolio optimization models widely presented in the financial literature usually assume that asset returns lie in a parametric uncertainty set with a controlled level of conservatism expressed in terms of the variability of the uncertain parameters. In practice however, it is not clear how investors should choose the conservatism parameter to reflect their own preferences, while considering price dynamics. In this paper, we provide a new perspective on robust portfolio optimization where we impose an intuitive loss constraint for the optimal portfolio considering asset returns in a data-driven polyhedral uncertainty set. Adaptively updated in a rolling horizon scheme, the proposed model captures price dynamics, absorbing new patterns and forgetting old ones, by means of a data-driven polyhedral-based loss constraint and an optimal mixture of asset price signals. We perform a case study to illustrate that it is possible to obtain a loss-controlled portfolio with higher expected returns than chosen benchmark strategies. Considering realistic transaction costs, out-of-sample results, obtained by applying our model for each day of the historical data (2000–2015) and updating with realized returns, indicate that our robust portfolio exhibited an enhanced performance while successfully constraining possible losses.