Bollinger Bands (20/2σ)
Price spends 95% of the time inside the bands, so touching them means being statistically cheap or dear. The band adjusts itself to volatility — widening in an agitated market and narrowing in a calm one — which avoids the false signal a fixed threshold gives when volatility changes.
Measured in forex — EUR/USD and GBP/USD · daily bars built from 15m · 1 pip spread (~0.009% per round trip) · no survivorship bias
- ✓invariance
- ✗costs
- ?placebo
- ✗benchmark
- ?out of sample
- ?multiple testing
At its worst the account was worth 0% less than its own best previous moment, and it spent 2,329 days below that peak.
What was measured
How many of those trades actually count
What it paid, before any deductions
Why it did not pass — it died here · the broker's fee
What would have happened to the money
What this result does NOT say
- One market, one universe
- Measured on 2 spot currency pairs. It says nothing about futures, equities or indices, nor about how the same technique behaves in another market.
- One window of time, not every window
- The measured period runs from 2020-01-01 to 2026-06-26. A market moves through regimes, and a technique can work in one and fail in another — the card measures the regimes that fit inside this window, not the ones still to come.
- One cost structure
- The cost charged is a 1.0 pip spread, crossed once. Anyone paying more than that gets a worse result, and anyone paying less gets a better one — the verdict holds for this fee.
- One exit rule
- The trade was closed by: the auditor's fixed horizon (10 bars). The same entry measured with a different exit is a different strategy, and can earn a different verdict — it happens in this archive.
- The number of trades is not the sample size
- There are 254 trades, but only 134 independent market episodes: trades that overlap in time are not independent observations, and counting them as if they were inflates any result. It is the smaller number that governs the arithmetic. With 134 episodes, what the data supports is a range from -0.19% to +0.17% per trade — the published average is the centre of it, not the exact measurement.
- Daily bars
- Measured at the daily close. Nothing here measures what happens inside the day, and an intraday technique is not auditable with this data.
Numbers and reproducibility
The six controls
| control | status | t | threshold | episodes |
|---|---|---|---|---|
| invariance | passed | — | — | — |
| costs | failed | -0.22 | 1.98 | 134 |
| placebo | inconclusive | -0.05 | 1.98 | 134 |
| benchmark | failed | — | — | — |
| out of sample | inconclusive | — | — | — |
| multiple testing | inconclusive | — | — | — |
- invariance254 signals across 4055 bars
- costsgross -0.011% · cost 0.008% · net -0.019% (t=-0.22)
- placeboactual -0.019% · placebo -0.015% · excess -0.004% ± 0.091% (t=-0.05 against a threshold of 1.98, 134 real groups, 12,700 sham dates, draw error ±0.014%) — the status flips inside the placebo's own Monte Carlo error
- benchmarktechnique -0.02% · buy and hold (same horizon) +0.01% · excess -0.03%
- out of sampleasset half A: +0.019% (t=0.16, 104 episodes) · asset half B: -0.064% (t=-0.46, 99 episodes) · liquid half (>= US$ 0/day): -0.019% (t=-0.22, 134 episodes) · period 1/4 (2020-01-24 a 2021-09-17): -0.127% (t=-0.70, 35 episodes) · period 2/4 (2021-09-20 a 2023-04-13): -0.019% (t=-0.08, 33 episodes) · period 3/4 (2023-04-28 a 2024-11-08): -0.193% (t=-1.48, 31 episodes) · period 4/4 (2024-11-11 a 2026-06-05): +0.258% (t=1.61, 36 episodes)
- multiple testing1 variation(s) tested · t=-0.22 across 134 episodes (equivalent to t=-0.22) · p≈0.8288 · false positives expected by chance ≈ 0.83
Equity — outside the six controls, and here is why
The t of the trade series is invariant to bet size: 0.5%, 1% and 3% agree to the sixth decimal. Nothing here moves the verdict — it moves what the account would have lived through.
- risking 1.0% per trade
- ×1.00
- worst drawdown from the peak
- −0%
- days below the previous peak
- 2,329
- signals refused for lack of capital
- 0%
- paths where the account halved (out of 12)
- 0
Reproducibility
- period
- 2020-01-01 to 2026-06-26
- assets that traded
- 2
- variations tested before this one
- 1
- gross per trade
- −0.01%
- net per trade
- −0.02%
- exit rule
- the auditor's fixed horizon (10 bars)
- horizon bars
- 10
- spread pips
- 1.0
- episode days
- 12
- seed
- 20260728
- band period
- 20
- deviations
- 2.0
Twelve Data forex (15m aggregated to 1d) · collected on 2026-07-25 · 2 assets · 4,055 bars · 2020-01-01 to 2026-06-26
Hypothesis, filed before the result
A specific prediction: the bands are the RSI with a moving threshold, and in crypto both died in the same place. In forex I expect the same fate as the RSI here — INCONCLUSIVE from a small effect. An additional and riskier prediction: gross return in forex will be POSITIVE where in crypto it was negative, because major currency pairs mean-revert more than crypto. If the gross comes out negative here too, my reading of the mechanism is wrong. Context that informs this prediction, declared so that it can be assessed: (a) the corpus has 101 claims in crypto, 4 of them passed — all from the moving average crossover family; (b) the available forex universe is only 2 pairs (EUR/USD, GBP/USD) over 6.5 years, against 540 pairs and 9 years in crypto, which gives ~88 trades against ~8,600; (c) the cost of turnover in forex is ~20× lower (1 pip ≈ 0.009% against 0.2% commission), so control 2 stops being the main killer; (d) I ran ONE smoke test on the 20/50 crossover and saw the result — see the disclosure in its own hypothesis.
filed on 2026-07-29, before the number existed
The original, as it was filed
Previsão específica: as bandas são o RSI com limiar móvel, e em cripto as duas morreram no mesmo lugar. Em forex espero o mesmo destino do RSI aqui — INCONCLUSIVO por efeito pequeno. Previsão adicional e mais arriscada: o retorno bruto em forex será POSITIVO onde em cripto era negativo, porque câmbio de majors reverte à média mais que cripto. Se o bruto vier negativo também aqui, minha leitura do mecanismo está errada. Contexto que informa esta previsão, declarado para que ela seja avaliável: (a) o corpus tem 101 alegações em cripto, das quais 4 aprovadas — todas da família do cruzamento de médias; (b) o universo de forex disponível é de apenas 2 pares (EUR/USD, GBP/USD) em 6,5 anos, contra 540 pares e 9 anos em cripto, o que dá ~88 operações contra ~8.600; (c) o custo do giro em forex é ~20× menor (1 pip ≈ 0,009% contra 0,2% de comissão), então o controle 2 deixa de ser o principal matador; (d) ⚠️ rodei UM ensaio de fumaça no cruzamento 20/50 e vi o resultado — ver a divulgação na hipótese dele.
Pre-registration exists to keep prediction apart from rationalisation: written after the number, every hypothesis is right.