No arbitrage and a linear portfolio selection model

We propose a linear bi-objective optimization approach to the problem of finding a portfolio that maximizes average excess return with respect to a benchmark index while minimizing underperformance over a learning period. We establish some theoretical results linking classical No Arbitrage conditions to the existence of a feasible portfolio for our model that strictly outperforms the index. Empirical analyses on publicly available real-world financial datasets show the effectiveness of the model and confirm the described theoretical results.