ID: S034
Slug: pairs-cointegration-etf-v1
Run date: 2026-07-03
Failed at: Stage 1 (Quick-screen)
Outcome: FAILED — all 7 cells FAILED.
Headline metric: cointegration p-values 0.06–0.99 (gate needs < 0.05); best cell Sharpe 0.15 (gate ≥ 0.8)
Fail reason: None of the seven economically-tethered ETF pairs is cointegrated over 2010–2026 — not with the fixed β=1 log-ratio, and not with a fitted hedge ratio either. The spreads trend rather than mean-revert, so the cointegration gate correctly refuses to trade almost every window; what little does trade earns no risk-adjusted edge. The discipline works exactly as designed — it just finds nothing here.
What we tested
Seven ETF pairs chosen a priori on economic tether — GLD/SLV, IEF/TLT, SPY/QQQ, IWM/QQQ, IWM/SPY, XLE/XOP, HYG/LQD — traded as dollar-neutral log-ratio spreads, each traded only in the folds where its spread is stationary (ADF p<0.05, re-confirmed monthly). The gate requires per-fold cointegration and a Sharpe ≥ 0.8 net of friction. Market-neutral by construction, over 2010–2026, with an Engle-Granger fitted-β cross-check alongside the frozen β=1 log-ratio.
What we found
| Cell | Pair | ADF β=1 | EG fitted-β | Cointegrated folds | Trades | Sharpe | β-SPY | Max-drawdown (DD) | Verdict |
|---|---|---|---|---|---|---|---|---|---|
| c01 | GLD/SLV | 0.33 | 0.74 | 4% | 3 | −0.23 | 0.00 | 4.9% | FAILED |
| c02 | IEF/TLT | 0.50 | 0.99 | 5% | 4 | −0.03 | 0.00 | 4.3% | FAILED |
| c03 | SPY/QQQ | 0.91 | 0.24 | 3% | 2 | −0.41 | 0.00 | 5.6% | FAILED |
| c04 | IWM/QQQ | 0.96 | 0.07 | 5% | 5 | +0.09 | 0.00 | 4.1% | FAILED |
| c05 | IWM/SPY | 0.86 | 0.06 | 5% | 5 | −0.31 | 0.00 | 4.8% | FAILED |
| c06 | XLE/XOP | 0.83 | 0.98 | 9% | 6 | −0.17 | 0.00 | 11.5% | FAILED |
| c07 | HYG/LQD | 0.80 | 0.73 | 13% | 12 | +0.15 | 0.00 | 4.0% | FAILED |
The spread-drift charts above show the mechanism directly: each "plausible" pair's price ratio wanders away from its long-run mean and stays there rather than oscillating around it — a trend, not a reversion.
Why the plausible pairs still trended (2010–2026)
- XLE/XOP — the 2014–2020 oil collapse hit the E&P subset (XOP) far harder than the sector (XLE); XOP never recovered on a relative basis, so the ratio structurally decoupled. Sub-period analysis confirms it: XLE/XOP was genuinely cointegrated in 2010–2013 (ADF 0.00) and then broke — the exact cointegration-break tail the pillar warns about, in the open.
- IEF/TLT and HYG/LQD — the 2022 rate shock hammered long duration (TLT, LQD) far more than short (IEF, HYG), so a duration mismatch trended each ratio. HYG/LQD only became cointegrated in 2022–2026 (EG p 0.02), not before.
- GLD/SLV — gold structurally outperformed silver; the classic ratio trended rather than ranged.
Cointegration, where it appears at all, is regime-fleeting — present in one four-year window and absent in the next — which validates the per-fold re-confirmation design but is too intermittent to build a strategy on.
What we learned
We validated the test machinery on two ETFs that must be cointegrated — SPY vs IVV and SPY vs VOO, all S&P-500 trackers. Result: they fail the fixed-β=1 ADF (p ≈ 0.94 / 0.82) yet are overwhelmingly cointegrated with a fitted β (Engle-Granger p = 0.0000). So the frozen β=1 log-ratio construction is genuinely too restrictive — it can reject even textbook cointegration. But the fitted-β test that correctly passes SPY/IVV still rejects all seven economic pairs — so the NULL is not a β=1 artifact; these pairs are genuinely not cointegrated over this sample.
The deeper lesson is the fundamental tension of liquid-ETF stat-arb: the pairs that are truly cointegrated (SPY/IVV) have essentially no spread to trade (they are the same thing), while economically-tethered-but-distinct pairs have a tradeable spread but are, at best, fleetingly cointegrated. The tradeable-and-stationary sweet spot is absent from this preset set.
What this doesn't tell us yet
The frozen β=1 log-ratio is genuinely too restrictive — the SPY/IVV control passes cointegration with a fitted β (Engle-Granger p = 0.0000) yet fails β=1 — so this run does not rule out a fitted-β / Johansen construction (the successor S036 went there). Nor does it condemn pairs trading broadly: it condemns this preset set over this sample. The tradeable-and-stationary sweet spot may exist in a tighter, differently-selected pair universe — untested here.
What happens next
All seven cells are FAILED — cut at Stage 1 on the cointegration gate. The pillar's discipline is vindicated (it refused to trade non-reverting spreads and lost nothing), and the market-neutrality machinery is confirmed. Two things the run establishes for the next experiment: (1) the fixed β=1 construction must be replaced with a fitted-β / Johansen ratio (the SPY/IVV control proves β=1 alone can miss real cointegration); (2) pair selection matters more than the ratio — the next set should target tighter mechanical tethers where a tradeable, persistent cointegration can actually exist. Both are pre-registered as a proposed follow-up (lab/candidates/pairs-fitted-beta-johansen-v1.md).
What we tested — the recipe
Slice & dice
For the specialist — methodology details (click to expand)
- Cointegration gate: per-fold ADF on the dollar-neutral log-ratio (p<0.05), re-confirmed monthly, plus an Engle-Granger fitted-β cross-check. Full-sample ADF β=1 p 0.33–0.96; EG fitted-β p 0.06–0.99.
- Control: SPY/IVV and SPY/VOO (all S&P trackers) — β=1 ADF p ≈ 0.94 / 0.82 but EG fitted-β p = 0.0000, proving β=1 alone can reject textbook cointegration; the fitted-β test still rejects all seven economic pairs, so the null is not a β=1 artifact.
- Friction & baseline: four transactions per round-trip + modelled 0.5%/yr borrow; baseline zero (market-neutral, β-SPY ≈ 0.00 on every cell).
- Data: Tiingo EOD 2010–2026; successor S036 (fitted-β / Johansen baskets).
Baseline was zero (market-neutral has no beta to lift it). Friction: 4 transactions/round-trip + modeled 0.5%/yr borrow. Data: Tiingo EOD 2010–2026. English per repo convention. Ledger: pairs-pillar-ledger.md.