Robust profit opportunities in risky financial portfolios

For a set of risky financial securities whose expected return vector and covariance matrix are given, we propose the concept of a robust profit opportunity as an alternative to arbitrage opportunities. We formulate the problem of finding the “most robust” profit opportunity in a single investment period, and show that it can be solved as a convex quadratic programming problem. Furthermore, we demonstrate that this problem contains the problem of finding the portfolio with the highest Sharpe ratio as a special case. We also develop a multi-period extension of robust profit opportunities.