Matrix Statistical Arbitrage with SVD and Stability Filters

Summary

The article proposes an automated workflow for finding relative-value baskets from a universe of instruments. It arranges log prices in a time-by-instrument matrix, uses singular value decomposition to estimate common movement and residual directions, and applies a random-matrix heuristic to choose how many common factors to remove. Residual portfolios are intended to reduce shared market exposure while exposing relative deviations across several instruments at once.

The method screens candidates for spectral separation and checks whether residual subspaces remain consistent across halves of the training sample. It then monitors misalignment with a covariance-scaled distance and describes additional validation, stationarity, and adverse-movement checks. The article emphasizes that these filters do not establish profitability: financial returns violate simplifying random-matrix assumptions, orthogonal directions need not be independent, and extensive screening creates multiple-testing and overfitting risks. It presents no adequate forward sample for a performance conclusion and identifies implementation issues that should be addressed before live use.

Key ideas

• Log prices allow relative price ratios to be analyzed as differences in a matrix framework.
• SVD separates dominant common movement from candidate relative-value directions.
• Random-matrix factor counts and singular-value ratios are heuristics that require stability checks.
• Principal angles between separately estimated subspaces can reveal unstable basket structure.
• Large-scale searches create multiple-testing risk, so untouched forward validation and uncertainty estimates are necessary.
• The article identifies unresolved code and exposure checks that should be addressed before live deployment.

Tags

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