Matrix Statistical Arbitrage with Stable Null Spaces and Out-of-Sample Tests
Summary
This research and paper-trading framework searches baskets of TradFi perpetual contracts for mean-reverting combinations. It arranges log prices in a time-by-asset matrix, uses singular value decomposition to estimate shared trends, and treats the remaining near-null space as candidate spread directions. Ward clustering proposes baskets; stability checks include a singular-value gap, rolling subspace angles, stationarity tests, and estimated mean-reversion half-life.
Live monitoring distinguishes structural deviations from broad factor shocks. A Mahalanobis distance in the null space measures the former, while changes in common-factor scores measure the latter; entries are considered only when the first is elevated and the second is not. Leave-one-out regressions attribute deviations to individual assets, and the central validation is whether alerts revert out of sample. The document provides a detailed design and defaults to simulated trading, but reports no validation outcomes. It cautions that these perpetuals lack a forced convergence mechanism, funding can create spread drift, and contract histories may be too short to cover a full reporting cycle.
Key ideas
- The framework uses low-rank structure in log prices to separate common trends from candidate mean-reverting basket directions.
- Basket admission depends on subspace stability, stationarity, and estimated reversion speed.
- A null-space distance detects structural dislocations, while a factor-shock measure screens for broad market moves.
- Leave-one-out regressions help identify which assets contribute most to a basket deviation.
- Out-of-sample alert reversion is the key test, and the framework defaults to paper trading.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.