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E002　 KILL　 Below costsTested · October 2026

Following or fading Bitcoin's last move does not pay

Across 50 trend-following and reversal rules on hourly Bitcoin perpetual data, none earns a positive Sharpe ratio after 7 bp per-side costs in all three windows; the median net Sharpe is -0.74.

bitcoin momentum reversal time-series trend-following perpetuals multiple-testing

Readable summary Full research record JSON recordFeedback on E002

A common belief says that Bitcoin keeps moving in the direction it has just moved, or that it snaps back. We tested both on hourly Bitcoin perpetual futures: 50 rules that go long or short according to the sign of the last 1 to 72 hours of return, re-checked every 1 to 48 hours. None was positive after costs in all three time windows. The median rule had a Sharpe ratio of 0.00 before costs and -0.74 after costs of 7 bp per side. The best rule in the first window, 0.72, was negative in the next two.

Rules positive in all 3 windows0 of 50net of 7 bp per side

Median net Sharpe-0.74median gross Sharpe 0.00

Best rule in first window0.72-0.15 in validation, -0.83 in holdout

Rules positive net, first window10 of 503 stayed positive in validation, 0 in holdout

01 · The idea being tested

Bitcoin trends: the direction of the last few hours or days tells you the direction of the next few.

Why people believe it

People commonly say that traders chase moves and that news is absorbed gradually, so a rise tends to continue. The opposite view is also held: short-term moves overshoot and then reverse. Either way, the sign of the recent return would be a signal that needs no model.

Why it would persist The argument, as stated before testing

The belief is that a simple sign rule is too small a gap to interest large funds, so it would not be traded away.

02 · How it was tested

We built 50 simple rules. Each looks at Bitcoin's return over the last 1, 4, 12, 24 or 72 hours. A trend-following version goes long after a rise and short after a fall; a reversal version does the opposite. Each rule re-checks its position every 1, 4, 12, 24 or 48 hours and pays a trading cost on every change. We split history into three consecutive windows and required a positive result after costs in all of them.

Pass required

Reconstructed after the test; no criteria were fixed in advance. Net Sharpe above 0 in selection, validation and holdout.

Killed if

Reconstructed after the test; no criteria were fixed in advance. No variant with a positive net Sharpe in all three windows.

Costs

7 bp per side (5 bp fee + 2 bp slippage), charged on the absolute change of position, so a flip from long to short costs 14 bp.

Controls

No separate control; the grid itself is the control. Long-only buy-and-hold is not the benchmark because every rule is long or short in equal size. The mirror pairs are exact: for each (L, H) the gross Sharpe of the reversal rule is the negative of its trend-following twin.

03 · What happened

Why it was rejected

No rule is positive net of 7 bp per side in all three windows; the median net Sharpe is -0.74.

0 of 50 variants had a positive net Sharpe in selection, validation and holdout at the same time.
The median gross Sharpe was 0.00 and the median net Sharpe was -0.74. Gross Sharpes ranged from -0.91 to +0.91, and the reversal rule is always the exact mirror of its trend-following twin (25 of 50 gross values are positive).
10 of 50 variants were positive net in selection, 7 in validation and 10 in holdout; only 3 were positive in both selection and validation, and none of those 3 was positive in holdout.
The best rule in selection (trend-following, 12-hour lookback, 48-hour rebalance) scored 0.72 there, then -0.15 in validation and -0.83 in holdout.
The median net Sharpe rises with the rebalance interval but never turns positive: -2.96 at 1 hour, -1.46 at 4, -0.67 at 12, -0.42 at 24 and -0.21 at 48 hours.
The fastest rule (1-hour lookback, 1-hour rebalance) had a net Sharpe of -10.99 over the whole period.

No rule survives all three windows

Number of the 50 variants with a positive net Sharpe, requiring each further window in turn. 10 are positive in selection, 3 of those stay positive in validation, and 0 stay positive in holdout.

Chart data (variants)

Stage	Count
All variants	50
Positive net in selection	10
and positive in validation	3
and positive in holdout	0

Trading less often loses less, never wins

Net of 7 bp per sideGross

Median Sharpe over the whole period of the 10 variants at each rebalance interval. Before costs the median is 0.00 at every interval; after costs it climbs from -2.96 to -0.21 as turnover falls, and stays below zero.

Chart data (Sharpe (annualised))

	Net of 7 bp per side	Gross
Every 1 hour	-2.96	0
Every 4 hours	-1.46	0
Every 12 hours	-0.67	0
Every 24 hours	-0.42	0
Every 48 hours	-0.21	0

The best rules in selection fall apart

SelectionValidationHoldout

The four variants with the highest net Sharpe in selection (L = lookback, H = rebalance interval, in hours), shown in each window. All four are 0.56 or higher in the first window and none is positive in holdout.

Chart data (net Sharpe)

	Selection	Validation	Holdout
Trend, L12 / H48	0.72	-0.15	-0.83
Trend, L72 / H4	0.58	-0.32	-1.87
Trend, L72 / H48	0.58	-0.22	-0.04
Reversal, L1 / H24	0.56	0.18	-0.01

04 · What it means

Why it failed Interpretation · not established

Interpretation: the sign of the recent return gave no net edge at these horizons. Gross Sharpes reach only +/-0.91, and trend-following and reversal twins mirror each other exactly. The few rules positive in one window may be what 50 tries produce by chance, and costs of 7 bp per side weigh most on rules that trade every hour (net -10.99 for the fastest).

Lesson

With 50 variants, the best in-sample result is expected to look good. Here 10 of 50 were positive in selection, the best scored 0.72, and none stayed positive in both later windows. Cost scales with turnover: median net Sharpe improves from -2.96 to -0.21 as the rebalance interval grows from 1 to 48 hours.

Scope of this result

Covers Bitcoin perpetual hourly closes from 2020-01 to 2026-10, sign-of-return rules with lookbacks of 1 to 72 hours and rebalance intervals of 1 to 48 hours, full-size positions, and costs of 7 bp per side.

A rejected experiment applies to the tested conditions and does not prove an idea can never work. bp = basis point, 0.01%.

1. Test design

Pre-registered

Data

Hourly closing prices of the Bitcoin perpetual future (USDT-margined) — the largest USD-margined crypto perpetual venue, public historical klines; 1 hour; 2020-01..2026-10; public download, no login

Universe

Bitcoin only. 5 lookbacks L in {1, 4, 12, 24, 72} hours x 5 rebalance intervals H in {1, 4, 12, 24, 48} hours x 2 directions (trend-following and reversal) = 50 variants.

Signal

Position = sign of the return over the previous L hourly bars, re-evaluated every H bars and held in between. Trend-following takes that sign, reversal takes its opposite. Full size long or short, almost always in the market.

Execution

The position set at an hourly close earns the return of the following hour. Almost always in the market.

Costs

7 bp per side (5 bp fee + 2 bp slippage), charged on the absolute change of position, so a flip from long to short costs 14 bp.

Controls

Sample split

Three consecutive windows by position in the hourly series: first 60% (selection, to 2024-01), next 20% (validation, to 2025-06), last 20% (holdout, after 2025-06).

Pass criterion

Reconstructed after the test; no criteria were fixed in advance. Net Sharpe above 0 in selection, validation and holdout.

Kill criterion

Reconstructed after the test; no criteria were fixed in advance. No variant with a positive net Sharpe in all three windows.

Power

Not computed.

2. Result

Observations

Instruments

Net mean

—

95% interval

Not reported

Median

-0.74

Worst

-10.99

Finding 1

0 of 50 variants had a positive net Sharpe in selection, validation and holdout at the same time.

Finding 2

The median gross Sharpe was 0.00 and the median net Sharpe was -0.74. Gross Sharpes ranged from -0.91 to +0.91, and the reversal rule is always the exact mirror of its trend-following twin (25 of 50 gross values are positive).

Finding 3

10 of 50 variants were positive net in selection, 7 in validation and 10 in holdout; only 3 were positive in both selection and validation, and none of those 3 was positive in holdout.

Finding 4

The best rule in selection (trend-following, 12-hour lookback, 48-hour rebalance) scored 0.72 there, then -0.15 in validation and -0.83 in holdout.

Finding 5

The median net Sharpe rises with the rebalance interval but never turns positive: -2.96 at 1 hour, -1.46 at 4, -0.67 at 12, -0.42 at 24 and -0.21 at 48 hours.

Finding 6

The fastest rule (1-hour lookback, 1-hour rebalance) had a net Sharpe of -10.99 over the whole period.

3. Interpretation

Why it failed

Lesson

Scope

4. Reproducibility

Steps

1) Download hourly closing prices of the Bitcoin perpetual future for 2020-01 to 2026-10. 2) For each lookback L in {1, 4, 12, 24, 72}, take the sign of the L-bar return at each close; hold it for H in {1, 4, 12, 24, 48} bars, with the position set at every H-th bar; reverse it for the reversal variants. 3) Earn the return of the next bar, subtract 7 bp times the absolute change of position, and compute the Sharpe ratio as mean over standard deviation times the square root of 8,760 hourly bars. 4) Split the series by position into 60%, 20% and 20%, and count the variants positive in all three.

Grade

COMPLETE