Designing Mean-Reverting Portfolios with Majorization-Minimization

Summary

This paper addresses portfolio construction for statistical arbitrage by seeking portfolios whose returns or spreads exhibit strong mean reversion. The optimization balances a criterion for mean-reversion strength with portfolio variance and an investment budget constraint. This formulation makes the design problem more practical than optimizing reversion alone, since risk and capital use also affect the resulting portfolio.

The proposed solution uses a majorization-minimization algorithm, an iterative optimization approach intended to solve the portfolio design problem efficiently. The paper reports numerical results in which the designed portfolio outperforms each underlying single spread and a literature benchmark. The provided description does not give the objective's precise mathematical form, data or asset universe, evaluation horizon, or the benchmark details. Nor does it state whether the results include trading costs or out-of-sample testing, so the reported comparison should not be treated by itself as evidence of deployable statistical-arbitrage profitability.

Key ideas

• The method constructs portfolios of spreads to seek stronger mean-reverting behavior.
• The objective accounts for mean-reversion strength, portfolio variance, and a budget constraint.
• A majorization-minimization algorithm is proposed to solve the design problem.
• Numerical comparisons report improvement over individual spreads and a published benchmark.
• The available description does not establish performance after costs or out of sample.

Tags

# Mean-Reverting Portfolio Design via Majorization-Minimization Method


# Mean-Reverting Portfolio Design via Majorization-Minimization Method









This paper considers the mean-reverting portfolio design problem arising from statistical arbitrage in the financial markets. The problem is formulated by optimizing a criterion characterizing the mean-reversion strength of the portfolio and taking into consideration the variance of the portfolio and an investment budget constraint at the same time. An efficient algorithm based on the majorization-minimization (MM) method is proposed to solve the problem. Numerical results show that our proposed mean-reverting portfolio design method can significantly outperform every underlying single spread and the benchmark method in the literature.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.