Robust portfolio optimization meets Arbitrage Pricing Theory

Mateus Waga, Davi Valladão and Alexandre Street

European Journal of Operational Research, 2025, vol. 326, issue 3, 558-568

Abstract: Robust portfolio optimization models are crucial for mitigating the impact of significant forecasting errors on expected asset returns. However, despite their significance, existing approaches often overlook a fundamental characteristic of financial markets: the absence of arbitrage opportunities. This paper presents a novel portfolio optimization model that integrates the classical mean–variance approach, the Fama and French Factor Model, and the Arbitrage Pricing Theory within a robust optimization framework. The proposed model utilizes return statistics to shape the uncertainty set boundaries but further enhances its representation by explicitly incorporating the no-arbitrage condition. The resulting formulation is non-convex and can be viewed as a trilevel optimization problem. To address these challenges, a cutting-plane algorithm is presented. Numerical experiments on multiple datasets and under various transaction cost levels confirm consistent outperformance over benchmark models in terms of cumulative returns and risk-adjusted metrics.

Keywords: Robust optimization; Portfolio optimization; Arbitrage Pricing Theory; Factor modeling (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:326:y:2025:i:3:p:558-568

DOI: 10.1016/j.ejor.2025.04.004

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