Robust portfolio optimization meets Arbitrage Pricing Theory

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.