This paper proposes a new optimization-based method for finding statistical arbitrage (stat-arb) portfolios that can include multiple assets. The problem is formulated as maximizing the portfolio's price volatility subject to the price staying within a fixed band and a leverage constraint. This nonconvex problem is approximately solved using the convex-concave procedure, a sequential convex programming method that linearizes the objective and solves a linear program at each iteration. The method scales to large asset universes and can find stat-arbs with ten or more assets.

The paper also introduces moving-band stat-arbs, where the band midpoint varies over time based on the recent average portfolio price, similar to Bollinger bands but applied to a constructed portfolio. The same convex-concave procedure is extended to handle this case. Numerical experiments on real data show that moving-band stat-arbs outperform fixed-band stat-arbs in terms of out-of-sample profitability and remain profitable for longer periods. The approach directly optimizes for high variance and mean reversion without relying on co-integration or statistical testing, offering a practical and scalable tool for quantitative finance.