# Distance-method pairs trading on crypto perps lost 17 bp a trade

> Pairs of crypto perpetuals traded back to their usual spread for up to 24 hours lost about 7 bp before costs and 17.0 bp after, on 2,200 trades in the second half of the data; all 4 entry thresholds were negative.

E620 · Verdict: KILL · Cause: No signal · Market: Crypto & DeFi · Mechanism: Microstructure · Horizon: 1h-24h · Tested: October 2026

Source: https://alphanotfound.eu/experiments/E620-distance-pairs-trading-crypto-perps

Statistical arbitrage says two coins that have moved together will not drift apart for long: when one runs ahead, short it, buy the other and wait for the gap to close. We tested the classic distance method on 24 large crypto perpetual futures, picking the 10 closest-tracking pairs each week and trading gaps of three standard deviations or more, for at most 24 hours. The 2,200 trades in the second half of the data lost about 7 bp before costs and 17.0 bp after (bp, hundredths of a percent, measured on the average of the two legs). So the gaps did not close even before costs.

## Key numbers

- **Net per trade:** -17.0 bp (second half of the data, 2,200 trades at the chosen threshold; 95% interval -20.2 to +0.8 bp)
- **Before costs:** about -7 bp (approximate, before trading fees and slippage; funding not separated out)
- **Random-pair control:** -26 bp (same rules on randomly chosen pairs, holdout)
- **Selection period:** -11.0 to -12.9 bp (net per trade at every entry threshold tried)

## The idea being tested

**Belief:** Two coins that have moved together for weeks are close substitutes, so when their spread stretches it snaps back and a hedged trade earns the difference.

**Why people believe it:** Pairs trading is a long-standing statistical arbitrage idea. A sale of one coin by a forced seller, a liquidation or news on one token can push it away from a close substitute for a few hours. A trader who is long one and short the other is protected from the market direction and only needs the gap to close.

**Why it would persist:** People argue that the capital which trades such spreads is limited outside the very largest coins. This was not tested here.

## How it was tested

Each Monday we looked at the previous 30 days of hourly prices for 24 large crypto perpetual futures and picked the 10 pairs whose price paths had stayed closest together, with no coin in more than 3 pairs. During the next 7 days, when a pair's price gap was more than a set number of its usual widths away from its 30-day average, we shorted the coin that was ahead and bought the one that was behind, in equal dollar amounts. We closed when the gap crossed back to its average, after 24 hours, or at the end of the week, and charged trading fees and slippage of 20 bp (0.20%) on one leg's amount, which is 10 bp on the average of the two legs, plus the funding payments actually due. How far a gap had to stretch (the entry threshold, in units of its usual width) was chosen on the first half of the data and judged once on the second half, the "holdout". The same rules on randomly chosen pairs served as a control.

**Pre-registered:** yes

**Data:** Hourly closing prices and funding rates of 24 liquid USD-margined crypto perpetual futures (public hourly price and funding-rate data of the largest USD-margined crypto perpetual venue; 1 hour (funding every 8 hours); 2022-01..2026-10 (first trades about a month after the data start))

**Universe:** 24 liquid crypto perpetual futures. A coin enters a week's formation only if it has hourly prices for the whole 30 days and the following 7 days.

**Signal:** Formation every Monday 00:00 UTC on the previous 30 days: log prices rebased to 0 at the start of the window; pair distance is the sum of squared differences between the two rebased paths; the 10 pairs with the smallest distance are kept, each coin in at most 3 pairs. For each pair the spread is ln(A) - ln(B), z = (spread - formation mean) / formation standard deviation. Entry at an hourly close when |z| is above Z, with Z in {1.5, 2.0, 2.5, 3.0}.

**Execution:** Short the rich leg and long the cheap leg, equal dollar amounts. Exit at the first hourly close where z has crossed zero, or after 24 hours, or at the end of the 7-day trading week. At most one open position per pair. Each leg returns its simple price return on its own notional, a short leg floored at -100%.

**Costs:** 20 bp per round trip (4 market-order fills at 5 bp, fees and slippage), equal to 20 bp on one leg's notional and charged as 10 bp against the average of the two leg returns, plus the funding rate actually paid or received on each leg over the hold. Trade returns in this record are on that average-of-two-legs basis.

**Controls:** Negative control: 10 randomly drawn pairs per week from the same coins, same entry, exit and cost rules, same threshold, holdout period only.

**Sample split:** Selection 2022-01..2024-06: the threshold Z with the best mean net per trade was chosen. Holdout 2024-07..2026-10: judged once. Confidence intervals resample whole weeks.

**Pass criterion:** On the holdout: mean net per trade above zero, median above zero, week-clustered 95% interval of the mean above zero, both holdout halves above zero, and an annualised return on 10 pair slots of at least 10%. The control had to earn less than half of the strategy.

**Kill criterion:** Any of the pass conditions failing.

**Power:** 2,200 holdout trades at the chosen threshold. The week-clustered 95% interval for the mean is 21.0 bp wide. Trades in the same week and in pairs sharing a coin are not independent, so the effective sample is smaller than the count.

## Result

**Why it was rejected:** The mean and the median net return per trade were negative, the 95% interval for the mean did not lie above zero, neither holdout half was positive, and the return per pair slot was -16% a year; all four entry thresholds were negative.

**Observations:** 2,200

**Net mean:** -17 bp

**95% interval:** -20.2 bp to +0.8 bp

**Median:** -1.6 bp

**Worst:** -2,135 bp

- On the selection period (2022-01 to 2024-06) the mean net return per trade was negative at every entry threshold, between -11.0 bp and -12.9 bp. The best of the four, Z of 3.0, was chosen.
- On the holdout (2024-07 to 2026-10) the chosen threshold had 2,200 trades with a mean net return of -17.0 bp, a median of -1.6 bp and a week-clustered 95% interval of -20.2 to +0.8 bp. The worst single trade lost 2,135 bp.
- The two halves of the holdout had the same mean, about -17 bp each, so the loss was not confined to one stretch. Per pair slot, meaning per $1 held in each of the 10 pair positions, the holdout return was -16% a year.
- The other 3 thresholds were also negative on the holdout, so no threshold of the 4 tried was positive on either period.
- Before trading fees and slippage the average trade lost about 7 bp (approximate; funding is not separated out). On the average of the two legs the 10 bp charge brings that to -17.0 bp. The median trade ran to the 24-hour time limit rather than closing at the average, so the spreads kept moving away for hours rather than reverting.
- The random-pair control lost 26 bp per trade on the holdout, 9 bp more than the pairs chosen by the distance method. Choosing close-tracking pairs did not turn the result positive.

### Every net result is negative, in every part of the sample (bp net per trade)

Mean net return per trade for the chosen threshold: the whole holdout, each of its two halves (both about -17 bp), and the random-pair control (-26 bp).

|   | Net per trade |
| --- | --- |
| Holdout, all trades | -17.0 |
| Holdout, first half | -17 |
| Holdout, second half | -17 |
| Random pairs, holdout | -26 |

### The holdout interval touches zero only at its top (bp net per trade)

Mean net return per trade on 2,200 holdout trades with its 95% interval (-20.2 to +0.8 bp). The interval resamples weekly averages, so it is not centred on the trade-weighted mean. The median trade was -1.6 bp, but the average is pulled down by large losses, the worst at -2,135 bp.

|   | Mean | 95% low | 95% high |
| --- | --- | --- | --- |
| Chosen threshold, holdout | -17.0 | -20.2 | 0.8 |

## Interpretation

**Why it failed (interpretation, not established):** Close substitutes do not seem to pull back to a common level within hours. The pairs lost about 7 bp per trade before costs, and at least half of the trades ran to the 24-hour limit rather than to the zero crossing. The costs then added to the loss. Why the gaps kept widening is not established by this test.

**Lesson:** Hedging removes market direction, not relative movement, and relative movement can persist as well as revert. The distance-selected pairs lost 9 bp less than random pairs (one random draw, no interval for the difference), and both were negative. A control built from random pairs shows whether the selection step carries any information.

**Scope:** Covers 24 large crypto perpetual futures, hourly prices, weekly pair selection on 30 days of prices, the 10 closest pairs with at most 3 per coin, entry thresholds of 1.5 to 3.0 standard deviations, holds up to 24 hours, and a 20 bp round-trip cost with actual funding.

## Reproducibility

**Steps:** 1) Download hourly closes and funding rates for 24 liquid USD-margined crypto perpetual futures from 2022-01. 2) Each Monday 00:00 UTC, rebase the previous 30 days of log prices to 0, compute the sum of squared differences for every pair and keep the 10 smallest, at most 3 per coin. 3) Spread = ln(A) - ln(B); z = (spread - formation mean) / formation standard deviation. 4) During the next 7 days enter at an hourly close when |z| is above Z (short the rich leg, long the cheap leg, equal dollars), exit at the first zero crossing, after 24 hours or at week end, one position per pair. 5) Trade return = average of the two leg returns, minus 10 bp, plus the average of the two funding amounts. 6) Pick Z from {1.5, 2.0, 2.5, 3.0} on 2022-01..2024-06 by mean net per trade and judge once on 2024-07..2026-10 with week-clustered intervals. 7) Repeat with 10 random pairs per week as the control.

**Grade:** COMPLETE

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