Statistical Arbitrage & Walk-Forward Validation
The original result did not survive a broader development test. Fresh confirmation later turned positive, but uncertainty remained too wide for a strong claim.
Central findingFresh confirmation was positive but statistically inconclusive.
Evidence
The result in context
- Original total return
- +20.72%
- Robust-development total return
- −9.41%
- Frozen-confirmation return
- +3.83%
- Bootstrap Sharpe interval
- [−0.88, 2.00]
Question
Does a promising pairs-trading result persist across more pairs, groups, market periods and genuinely out-of-sample observations?
A pairs strategy taken from an encouraging small baseline through broad walk-forward development and a frozen confirmation period.
Original strategy
A small result that needed a larger test
The baseline returned 20.72% with a 0.68 Sharpe ratio across 29 trades, five unique pairs and three groups. That breadth was too narrow to treat the result as stable evidence.
Robust development
Walk-forward testing reversed the headline
Across 2015–2024, broader out-of-sample development covered 199 trades, 62 pairs and 17 groups. Total return was −9.41% with a −0.30 Sharpe ratio.
The reversal is informative: a strategy that works in a small selected setting may not survive wider opportunity sets and repeated re-estimation.
Research evolution
From small baseline to fresh evidence
Each stage increases breadth or separation from development decisions.
- Total return
- +20.72%
- Sharpe ratio
- 0.68
- Maximum drawdown
- −9.06%
- Trades
- 29
- Breadth
- 5 pairs · 3 groups
Encouraging, but too narrow to establish robustness.
Interactive evidence
The full development study reversed the archived headline
Cumulative growth of £1 from 1,886 committed daily strategy returns.
Read: Development finishes at 0.906×, a −9.41% total return, after a maximum drawdown of roughly 11.12%.
Data table · 1,886 verified rows
| Date | Strategy Return | Equity | Drawdown Pct |
|---|---|---|---|
| 2017-07-05 | 0 | 1 | 0 |
| 2017-07-27 | -0.007619 | 0.980827 | -2.071819 |
| 2018-04-30 | 0.000953 | 0.954656 | -4.684865 |
| 2019-02-25 | 0.001144 | 0.95475 | -4.675439 |
| 2020-01-10 | -0.001625 | 0.951232 | -5.026683 |
| 2020-11-03 | -0.000443 | 0.966195 | -3.532781 |
| 2021-08-27 | 0.000402 | 0.941605 | -5.987891 |
| 2022-06-23 | 0.001389 | 0.927207 | -7.425437 |
| 2023-05-11 | 0.000232 | 0.930491 | -7.097552 |
| 2024-03-07 | 0.005975 | 0.909941 | -9.149299 |
| 2024-12-06 | 0.000662 | 0.909709 | -9.17248 |
| 2024-12-31 | -0.000485 | 0.90586 | -9.556731 |
Frozen confirmation
The sign improved; the confidence did not
From 2025 to July 2026, return was +3.83% with a 0.59 Sharpe ratio across 43 trades, 19 pairs and 12 groups. One pair produced 28.34% of absolute confirmation P&L.
The bootstrap Sharpe interval spans −0.88 to 2.00 and the Newey–West p-value is 0.421. Fresh confirmation was positive but statistically inconclusive.
Interactive evidence
Confirmation turned positive without resolving uncertainty
Cumulative growth of £1 from 378 committed daily returns, 2 Jan 2025–8 Jul 2026.
Read: The frozen confirmation window ends at 1.038× (+3.83%); the evidence remains too short for a strong performance claim.
Data table · 378 verified rows
| Date | Strategy Return | Equity | Drawdown Pct |
|---|---|---|---|
| 2025-01-02 | 0 | 1 | 0 |
| 2025-01-08 | 0 | 1 | 0 |
| 2025-03-10 | 0.000882 | 0.994571 | -1.108011 |
| 2025-05-05 | -0.000451 | 0.988089 | -1.752524 |
| 2025-07-09 | 0 | 0.98433 | -2.126352 |
| 2025-09-04 | 0 | 0.98686 | -1.8748 |
| 2025-11-04 | -0.003051 | 0.997027 | -0.863814 |
| 2026-01-02 | 0.0002 | 1.000446 | -0.523892 |
| 2026-03-09 | 0 | 1.041589 | -0.353095 |
| 2026-05-04 | -0.000684 | 1.052239 | -0.413169 |
| 2026-07-01 | -0.000664 | 1.036317 | -1.920112 |
| 2026-07-08 | 0.000413 | 1.038338 | -1.728852 |
Interactive evidence
Confirmation P&L remained concentrated in a small number of pairs
Absolute share of pair-level weighted P&L; all 19 selected pairs are retained in the data table.
Read: MS/NTRS accounts for 28.34% of absolute pair P&L, making diversification risk visible alongside the positive aggregate result.
Data table · 19 verified rows
| Pair | Weighted Pnl | Absolute Pnl Share Pct |
|---|---|---|
| MS/NTRS | 0.03983 | 28.343109 |
| NXPI/QCOM | -0.022851 | 16.261303 |
| COF/MA | 0.018507 | 13.169421 |
| MU/QCOM | 0.012236 | 8.707019 |
| META/MSFT | 0.008639 | 6.147878 |
| COP/OXY | -0.008119 | 5.777591 |
| ADSK/NOW | 0.006205 | 4.41556 |
| INTU/NOW | -0.005625 | 4.002895 |
| IEFA/VEA | -0.00447 | 3.180934 |
| COF/V | -0.002614 | 1.860104 |
| IYW/QQQ | -0.002303 | 1.63869 |
| C/WFC | 0.002214 | 1.575463 |
| AMZN/MSFT | -0.001849 | 1.315811 |
| INTU/MSFT | -0.001782 | 1.268292 |
| GS/NTRS | 0.001167 | 0.830569 |
| IYR/VNQ | -0.001027 | 0.730724 |
| QQQ/XLK | 0.000965 | 0.686493 |
| VFH/XLF | -0.000124 | 0.088143 |
| VDE/XLE | 0 | 0 |
Limitations
What this evidence does not establish
- The confirmation sample is short and contains only 43 trades.
- Pair-level contribution remains concentrated, and the statistical intervals include weak or negative outcomes.
- The confirmation protocol and result were committed together, so the public Git history alone cannot verify the intended pre-result freeze.
Source and reproducibility
Trace the evidence
Source code, evaluation outputs and supporting material are available in the repository.
View repository- Development equity and drawdownreports/development/final/portfolio_daily_returns.csvCommit / evidence ID: 7f7ac62376630cd5eb715e38fbc87ab316f1747e
- Confirmation pair contributionsreports/confirmation/pair_contributions.csvCommit / evidence ID: 7f7ac62376630cd5eb715e38fbc87ab316f1747e