Pairs spread

The code

Be clear about the data before reading the result. The script that made these two series pulls their gap back towards zero for the first 300 days, on purpose. Then it switches the pull off and pushes the gap steadily apart. The first part of the output therefore shows a rule working on data that was built for it. That proves only that the code does what it says.

The second part is the lesson. Nothing in the prices announces the day the link ends.

Data the script reads: invented-pair.csv. Invented values, never a real market. Save it in one folder and run the script from that folder.

The file that was run: pairs_spread.py

# A pairs spread: watch the gap between two instruments that have moved together.
# Prices come from invented-pair.csv. Both series were made by a script, never a real market.
# The script that made them pulls the gap back towards zero for the first 300 days and then
# switches that off. So the first part works because it was built to, and the second part
# shows what happens when a relationship ends. Neither says anything about any real market.
import csv

a, b = [], []
with open("invented-pair.csv", newline="") as f:
    for row in csv.DictReader(f):
        a.append(float(row["a"]))
        b.append(float(row["b"]))

spread = [x - y for x, y in zip(a, b)]


def average(values):
    return sum(values) / len(values)


def standard_deviation(values):
    mean = average(values)
    return (sum((v - mean) ** 2 for v in values) / len(values)) ** 0.5


def z_score(end, days):
    """How unusual the spread at position `end` is, measured against the `days` days before it."""
    window = spread[end - days:end]
    return (spread[end] - average(window)) / standard_deviation(window)


# Example values, picked only because they are easy to follow. They are not a suggestion.
DAYS = 30            # history the spread is measured against
ENTER = 2.0          # how unusual the spread must be before acting
COST = 0.20          # points per completed trade: two instruments, so two spreads to pay


def run(first, last):
    """Run the rule over days first..last-1 and return the result of each trade."""
    side = 0             # +1 means long the spread (bought a, sold b). -1 is the reverse. 0 is flat.
    entry = 0.0
    results = []
    for day in range(first, last):
        z = z_score(day - 1, DAYS)           # yesterday's reading, from yesterday's history
        price = spread[day]
        if side == 0 and z > ENTER:
            side, entry = -1, price          # spread unusually wide: act as if it will narrow
        elif side == 0 and z < -ENTER:
            side, entry = 1, price           # spread unusually narrow: act as if it will widen
        elif (side == 1 and z >= 0) or (side == -1 and z <= 0):
            results.append(side * (price - entry) - COST)
            side = 0
    if side != 0:
        results.append(side * (spread[last - 1] - entry) - COST)
    return results


def report(label, first, last):
    results = run(first, last)
    print(label)
    print("  Trades:", len(results), "of which above zero:", len([r for r in results if r > 0]))
    if results:
        print("  Worst single trade:", round(min(results), 2))
    print("  Total points after costs:", round(sum(results), 2))
    print("  Simply holding a over the same days:", round(a[last - 1] - a[first] - COST / 2, 2))
    print("  Simply holding b over the same days:", round(b[last - 1] - b[first] - COST / 2, 2))


BREAK = 300          # the day the generator stops pulling the gap back
report("Days when the link was built in:", DAYS + 1, BREAK)
report("Days after the link was switched off:", BREAK, len(spread))

What the run printed

Days when the link was built in:
  Trades: 8 of which above zero: 8
  Worst single trade: 0.09
  Total points after costs: 10.26
  Simply holding a over the same days: 20.11
  Simply holding b over the same days: 19.29
Days after the link was switched off:
  Trades: 4 of which above zero: 0
  Worst single trade: -8.25
  Total points after costs: -13.19
  Simply holding a over the same days: -0.82
  Simply holding b over the same days: -13.8

Output of the run on 9 Oct 2026, copied as printed. Every input to this run was invented, so the result says nothing about any real market.

How to read it

In the first block every trade ended above zero. Do not read that as a result. The generator forces the gap to close, so a rule that waits for the gap to close cannot fail there. It is a check that the code is right, nothing more. Even so, simply holding either series ended higher over those days.

In the second block the same code, with the same settings, lost on every trade, and lost more in four trades than it had gained in eight. The gaps it judged unusually wide did not come back.

This is the shape of the technique's risk: a long run of small gains, then losses that are larger and arrive together. Real pairs carry no label saying which block you are in. Neither block says anything about any real market.