Matrix Statistical Arbitrage with Stability Tests and Out-of-Sample Validation
Summary
This article develops a systematic approach to finding multi-asset relative-value baskets rather than manually selecting pairs. It arranges log prices in a matrix, uses singular value decomposition to separate common factors from residual directions, and applies a random-matrix threshold to estimate factor count. It then checks whether the residual subspace is stable across time, monitors normalized residual distance for dislocations, and blocks entries when common factors are moving sharply. Leave-one-out regressions help attribute a basket deviation to a constituent and derive hedge weights.
The workflow also addresses practical failure modes: leveraged funds can have persistent volatility drag, earnings jumps can resemble mean-reverting dislocations, and intraday volatility varies by session. It calls for out-of-sample reversion tracking, hedge fidelity checks after contract rounding, and funding-cost accounting. The method is statistical rather than guaranteed arbitrage; the article stresses that its relationships may drift, samples are limited, and in-sample fit or formal tests alone do not establish profitability.
Key ideas
- Log-price matrices and singular value decomposition can identify shared factors and candidate residual trading directions.
- Factor selection and subspace stability checks aim to reject structures that may be noise or unstable through time.
- Normalized residual dislocations and factor-shock filters distinguish relative mispricing from broad repricing.
- Out-of-sample reversion rates, time to convergence, and adverse excursion are central strategy checks.
- Execution rounding, funding costs, leveraged products, and event jumps can undermine an apparently market-neutral basket.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.