ID: S036
Slug: pairs-johansen-basket-v1
Run date: 2026-07-04
Failed at: Stage 1 (Quick-screen)
Outcome: FAILED — both cells NULL.
Headline metric: per-fold cointegration persistence 19% / 48% (gate ≥ 50%); Sharpe −0.37 / −0.32 (gate ≥ 0.8)
Fail reason: Both baskets are strongly cointegrated on the full sample (Johansen trace 58.6 / 40.3 vs 29.8 crit) — but under the honest per-fold walk-forward test the cointegration is intermittent (present in only 19% and 48% of folds, both below the 50% admission gate), and even in the folds where it does hold, the reverted spread loses money net of the triple-leg cost stack (negative Sharpe and negative expectancy). Full-sample cointegration is a long-horizon property that does not survive as a tradeable, per-fold signal.
What we found
| Cell | Basket | Full-sample Johansen | Per-fold persistence | Sharpe | β-SPY | Max-DD | Exp/trade | Verdict |
|---|---|---|---|---|---|---|---|---|
| c01 | [SHY,IEF,TLT] butterfly | 58.6 ✅ | 19% | −0.37 | 0.00 | 8.3% | −0.30% | NULL |
| c02 | [HYG,LQD,IEF] credit | 40.3 ✅ | 48% | −0.32 | 0.03 | 21.3% | −0.48% | NULL |
Two honest observations
The 504-day window under-powers a 3-asset Johansen. A persistence-by-window diagnostic shows the fold-level cointegration rate rises with the estimation window: butterfly 18% → 46%, credit 48% → 56% as the window grows 504 → 1260 days (see chart). So the frozen 504-day choice was on the short side for a three-variable test — a genuine calibration lesson. A longer window (≈ 1000–1260 days) would push the credit basket over the 50% persistence bar.
But persistence was not the binding failure — profitability was. In the folds where the basket is cointegrated, the traded spread still earns a negative Sharpe and negative expectancy. A longer estimation window fixes the admission gate, not the fact that the reverted spread is too thin to pay for six transactions plus borrow. Fixing the window would let more folds trade a losing signal.
Verdict & the pillar read
Both cells NULL — cut at Stage 1. With S034 (7 two-asset pairs, all NULL) this makes the pairs pillar 9 trials, all NULL: liquid-ETF relative value, whether as fixed-ratio pairs or per-fold Johansen baskets, does not clear an honest, walk-forward, cost-aware, tail-aware gate over 2007–2026. The recurring lesson: cointegration that is real on the full sample is either not persistent in tradeable windows or not profitable net of the multi-leg cost stack. A longer-window variant (≈ 1008–1260 days) is a possible next S-NNN, but the bar is the negative net edge, not the persistence gate — so the expectation is low, and it must be pre-registered as a new identifier (the 504-day gate here is frozen). The pillar's transparent fail record across the stat-arb design space is the point.
Baseline zero (market-neutral). Friction: 6 transactions/round-trip at 5 bps + 0.5%/yr borrow on shorts. Johansen vector estimated per fold (504-day window, monthly), never full-sample. Data: Tiingo EOD 2007–2026 (panel bounded by HYG/LQD inception). English per repo convention. Ledger: pairs-pillar-ledger.md. Predecessor: S034 (pairs-cointegration-etf-v1, all NULL).