The Lab

How we tested

• Six pairs: Ether/Bitcoin, Solana/Ether, Solana/Bitcoin, BNB/Bitcoin, XRP/Bitcoin and Dogecoin/Bitcoin, hourly, October 2022 to September 2026.
• Both sides as perpetual futures, at the exchange's market-order fee (0.055% each side, each way), with the lower resting-order fee shown as a best case, and funding paid or received on each side.
• The rule:
  • measure how far the gap sits from its own recent average, in units of its usual spread (the z-score), over the last 3, 7, 14 or 30 days;
  • open when it is 1.5, 2 or 2.5 units out;
  • close when it is back at 0 (or 0.5), when it reaches 4 units (a stop for a gap that breaks), or after 14 days.
  • 96 settings for each pair.
• Fairness:
  • every setting is shown;
  • the first two years pick a setting, and the last two judge it;
  • each setting's trades are also opened at random times, 200 times;
  • each month is also run 20 times with its hours shuffled, the same way for both coins. That keeps each hour's moves and loses their order.
• The bar, set before we looked: a pair counts only if its gap returns halfway within 30 days in both halves, and the setting picked on the first half makes money on the second half while beating 90% of random entries and 18 of 20 shuffles.

The maths, step by step

1. The gap. Take the logarithm of each price. The gap is ln(Ether) − ln(Bitcoin): the size of their ratio, so a 1% move in either counts the same.

2. The z-score. Over a window, take the gap's average and its usual spread, called σ (sigma).

• Example: five readings of the gap, 0, 0, 0, 0 and 0.1. The average is 0.02 and σ is 0.04. The latest reading is (0.1 − 0.02) ÷ 0.04 = 2.0 units out. At 2.0 the rule would sell the dear coin and buy the cheap one.

3. The half-life. Fit how much of the gap closes each day (the Ornstein–Uhlenbeck model's pull, from 1930).

• Example: if 0.83% of the gap closes each day, half of it has closed after ln 0.5 ÷ ln(1 − 0.0083) = 83 days.
• A gap that comes back fast enough to trade should halve in days or weeks, not months.

4. The fees. Each trade buys one coin and sells the other, then reverses both: 4 market orders at 0.055% = 0.22% a trade, before funding.

5. Luck. If a setting were no better than its shuffles, it would beat 19 or 20 of 20 by chance 2 times in 21. Of 576 settings, about 55 would do that by luck.

What we found

1. No pair's gap reliably came back.

• Gaps took from 20 days to over 1,000 days to halve, and no pair passed the test in both halves.
• The best mix of the two coins changed between halves. For Ether/Bitcoin it went from 0.69 Bitcoin per Ether to 1.11.

2. Every pair lost money.

• These add up each trade's result as a share of the starting money. Below −100% means the money had run out; at 1x that happened in 520 of 576 settings.
• Even at the lower fee, only 25 of 576 settings ended up.
• More than half of trades won (56–63%), but the losers were larger.

3. It did worse than chance, not only because of fees.

• The middle setting did better than only 9% of its random-time entries.
• Half the settings (291 of 576) did worse than all 20 of their shuffled markets. Only 1 beat 19 or 20, where luck alone gives about 55.
• The gaps kept going. Betting on them closing lost money before fees. On Ether/Bitcoin with a 7-day window: −70% from the trades, −46% in fees, and +2% from funding.

4. Why most trades "came back" and still lost. The average the z-score measures from moves too. When the gap jumps and stays there, the window's average catches up, the z-score drifts back to 0, and the trade closes, at its loss. Of 208 Ether/Bitcoin trades on the 7-day window, 204 closed "back at 0".

5. Picking on the first two years didn't carry. For four of the six pairs, the setting that did best in the first half lost in the second (Ether/Bitcoin: +53%, then −52%). None met the bar.

Credits

• Evan Gatev, William N. Goetzmann and K. Geert Rouwenhorst, "Pairs Trading: Performance of a Relative-Value Arbitrage Rule", Review of Financial Studies, 2006.
• G. E. Uhlenbeck and L. S. Ornstein, "On the Theory of the Brownian Motion", Physical Review, 1930: the half-life's model.
• Robert F. Engle and C. W. J. Granger, "Co-integration and Error Correction", Econometrica, 1987: the formal test of whether two prices are tied (named here as background; not run).
• R. A. Fisher, The Design of Experiments, Oliver and Boyd, 1935: the permutation test behind the shuffled months.
• The entry and exit rules and the pass bar are our own design.
• Data: Binance's public hourly futures prices; Bybit's public funding history and fees.
• PerpGremlin and Claude, Pairs trading: does the gap between two coins come back?, TerminalGremlin, 2026: the tests, the code and the words.