Models / Equities / pairs_spread

Pairs spread

Does this spread pull back to its mean, and what is left of a hypothetical walk through the later window after costs?

Fits a log hedge ratio on the first part of two price series, tests the spread for pull-back to its mean, and walks the later part with those fit numbers and entry and exit z-scores, after costs. Prices come from the caller. It is a hypothetical walk through one sample, not a test of cointegration in any strict sense, a trade idea or a signal to follow.

The paste-ready prompt model.md

Loading the models. They run in your browser, and nothing is sent.

Template: made-up numbers

Entry z

Exit z

00.9

Cost per legbps

0flips at 19.4950

Share of points used to fit%

3070

{
  "series_a": [
    108.12, 108.57, 103.13, 103.28, 102.31, 104.84, 107.3, 104.71, 102.25, 99.76,
    100.82, 100.29, 100.27, 100.31, 102.79, 101.69, 102.56, 102.15, 104.54, 108.17,
    101.79, 102.04, 101.32, 100.85, 99.1, 96.83, 96.75, 97.23, 97.84, 95.01,
    94.87, 94.28, 96.59, 97.83, 96.15, 98.17, 97.7, 95.29, 95.82, 97.05,
    94.79, 96.32, 99.1, 98.71, 98.34, 97.28, 99.53, 98.69, 99.56, 99.39,
    101.5, 100.89, 97.23, 99.35, 101.55, 99.1, 99.4, 99.33, 100.55, 101.12,
    104.48, 106.08, 104.26, 106.52, 108.34, 106.24, 105.95, 103.44, 104.96, 104.46,
    107.19, 106.83, 104.73, 103.89, 103.81, 101.68, 98.76, 100.12, 99.72, 99.31,
    100.34, 101.1, 99.65, 98.28, 98.92, 101.36, 103.15, 101.98, 101.38, 104.99,
    103.88, 104.66, 105.52, 105.99, 106.45, 107.69, 108.35, 108.47, 110.48, 110.34,
    108.45, 107.75, 106.32, 106.49, 104.92, 105.62, 102.94, 102.82, 105.32, 104.97,
    105.1, 107.19, 105.74, 106.02, 103.25, 100.81, 102.17, 100.61, 100.92, 100.48,
    101.25, 98.02, 96.89, 96.4, 95.25, 94.18, 91.6, 88.51, 86.67, 86.33,
    86.05, 86.66, 88.49, 86.96, 85.07, 83.48, 83.86, 81.13, 81.38, 82.81,
    82.68, 82.27, 82.72, 83.14, 84.93, 81.84, 81.47, 82.31, 80.94, 82.77,
    81.43, 84.07, 84.72, 84.85, 85.56, 85.16, 85.77, 85.72, 83.98, 83.23,
    84.4, 83.87, 81.29, 79.32, 79.95, 81.29, 81.97, 81.18, 81.22, 82.95,
    80.72, 82.22, 83.5, 82.05, 83.4, 79.65, 79.95, 78.02, 75.87, 76.43,
    75.68, 75.07, 74.33, 71.12, 72.01, 71.81, 72.53, 72.69, 72.44, 73.33,
    73.83, 74.64, 76.35, 76.9, 77.04, 75.98, 74.18, 73.75, 73.68, 73.89,
    74.15, 71.69, 71.78, 71.49, 69.96, 69.68, 68.7, 69.15, 67.31, 70.81,
    70.64, 70.09, 70.53, 70.31, 70.64, 70.55, 71.25, 72.45, 73.08, 73.54,
    74.42, 74.52, 73.21, 72.9, 72.16, 71.05, 72.46, 72.75, 71.08, 69.57,
    70.58, 68.45, 71.43, 71.92, 71.79, 71.11, 71.26, 70.03, 68.98, 68.85,
    68.32, 67.81, 68.03, 67.15, 66.12, 65.89, 67.07, 66.25, 65.5, 67.16,
    68.57, 68.93, 68.13, 68.69, 67.88, 69.03, 70.61, 71.4, 70.77, 69.29,
    70.9, 72.13, 74.27, 73.7, 74.35, 73.28, 75.06, 75.77, 73.85, 72.74,
    72.29, 72.79, 72.3, 73.63, 75.22, 75.3, 75.55, 74.1, 73.82, 74.8,
    74.92, 75.89, 75.9, 76.07, 77.1, 76.49, 73.32, 72.95, 73.4, 76.44,
    75.78, 75.48, 73.77, 74.6, 74.87, 73.37, 71.53, 70.76, 70.91, 72.12,
    71.81, 72.47, 70.81, 69.78, 69.7, 69.03, 68.65, 68.14, 70.17, 69.15,
    66.99, 68.4, 68, 68.91, 71.28, 70.05, 70.53, 73.98, 73.15, 73.56,
    73.25, 71.05, 72.55, 74.1, 73.66, 72.63, 72.48, 71.59, 70.58, 70.61,
    71.85, 72.14, 71.41, 73.37, 75.11, 72.43, 72.28, 71.8, 70.66, 69.93,
    70.07, 69.56, 70.48, 69.65, 69.98, 70.38, 71.84, 72.18, 73.81, 74.64,
    74.69, 73.64, 73.3, 72.48, 72.83, 73.7, 74.26, 75.16, 76.51, 76.56,
    78.76, 79.02, 76.71, 76.34, 75.73, 74.2, 73.22, 74.02, 71.63, 71.26,
    70.51, 70.74, 71.14, 72.48, 73.16, 71.83, 73.75, 74.17, 72.31, 71.53,
    70.86, 69.51, 69.51, 70.29, 70.48, 72.24, 71.45, 70.35, 70.79, 71.27,
    71.14, 72.51, 73.33, 73.48, 72.58, 73.31, 74.91, 77.81, 79.32, 77.92,
    79.36, 80.13, 80.86, 78.81, 80.84, 79.97, 80.07, 77.41, 77.89, 77.68,
    78.59, 77.79, 78.2, 76.06, 75.64, 74.62, 75.52, 76.54, 76.14, 76.9,
    77.87, 74.2, 75.83, 75.53, 76.46, 75.92, 75.37, 79.44, 80.92, 78.71,
    82.66, 81.17, 83.28, 80.79, 81.99, 84.3, 84.99, 86.34, 87.32, 87.88,
    86.42, 84.29, 84.95, 86.3, 86.79, 87.05, 86.43, 87.47, 89.55, 91.81,
    91.3, 92.07, 93.51, 95.49, 96.59, 95.44, 96.95, 98.63, 98.6, 101.11,
    100.11, 98.41, 99.38, 101.46, 101.24, 98.48, 97.44, 97.48, 96.36, 95.08,
    98.74, 99.78, 98.94, 101.19, 98.97, 98.83, 98.96, 96.84, 97.82, 98.12,
    96.49, 97.01, 93.21, 92.38, 94.76, 94.14, 95.32, 96.07, 96.83, 97.44,
    99.83, 98.6, 98.62, 99.63, 99.79, 96.51, 94.69, 95.14, 97.03, 97.8
  ],
  "series_b": [
    49.48, 49.95, 48.68, 48.5, 47.89, 48.74, 48.72, 48.11, 47.72, 47.66,
    47.54, 47.91, 47.56, 47.96, 48.9, 47.8, 48, 47.66, 48.13, 48.9,
    47.31, 47.11, 46.71, 47.1, 46.57, 46.21, 46.27, 46.92, 46.84, 46.3,
    46.18, 46.12, 46.42, 46.52, 45.5, 46.03, 45.57, 44.92, 45.16, 45.88,
    45.45, 45.76, 45.87, 45.87, 45.23, 45.04, 45.18, 44.15, 44.88, 44.96,
    45.34, 45.15, 44.38, 45.51, 46.42, 46.47, 46.63, 46.35, 46.56, 46.7,
    47.62, 48.34, 47.23, 48.19, 49.03, 49.04, 48.64, 47.73, 48.02, 48.34,
    48.73, 48.19, 48.18, 47.76, 47.49, 46.96, 46.32, 47.01, 47.34, 47.55,
    47.2, 47.21, 47.24, 46.6, 46.43, 47.22, 47.99, 48.39, 48.06, 48.97,
    48.89, 49.08, 49.08, 49.83, 48.86, 48.68, 49.11, 48.84, 48.47, 48.82,
    47.94, 47.29, 46.95, 47.17, 46.85, 46.77, 46.49, 46.22, 46.96, 47.67,
    47.21, 47.67, 47.09, 46.86, 46.32, 45.58, 46.06, 45.82, 45.34, 45.44,
    45.27, 45.23, 45.01, 45.2, 44.96, 44.63, 43.41, 42.05, 41.35, 40.59,
    40.4, 40.69, 41.18, 40.71, 40.23, 39.89, 40.17, 39.21, 38.92, 39.2,
    39, 38.82, 38.86, 39.24, 40.06, 39.56, 38.76, 39.24, 39.03, 39.51,
    38.99, 40.23, 40.52, 40.55, 40.48, 40.14, 40.44, 40.33, 39.89, 39.63,
    39.86, 39.64, 39.15, 37.96, 38.23, 38.6, 38.81, 38.65, 38.49, 39,
    37.95, 38.07, 38.41, 37.93, 37.76, 36.58, 36.79, 36.05, 36.07, 35.88,
    35.83, 35.46, 35.3, 34.57, 34.57, 34.11, 34.43, 34.53, 34.36, 34.98,
    35.13, 35.29, 35.61, 35.75, 35.59, 35.18, 34.42, 33.74, 33.49, 33.38,
    33.36, 32.68, 32.49, 32.41, 32.21, 31.79, 31.78, 32.25, 31.67, 32.53,
    32.43, 32.12, 31.81, 31.89, 31.81, 31.62, 31.9, 32.42, 32.79, 33.37,
    33.79, 34.24, 33.58, 33.83, 33.53, 33.66, 34, 34, 33.26, 33.06,
    32.92, 32.61, 33.52, 33.19, 33.12, 33.23, 33.21, 33.3, 32.89, 33.09,
    32.8, 32.45, 32.95, 32.54, 32.11, 32.1, 32.12, 32.14, 32.07, 32.33,
    32.48, 32.59, 32.46, 32.11, 31.71, 32.03, 32.58, 32.78, 32.85, 32.5,
    32.47, 32.71, 32.91, 33.45, 33.17, 33.18, 33.69, 34.18, 33.91, 33.42,
    33.73, 33.55, 33.63, 33.6, 34.17, 34.11, 34.45, 34.04, 33.77, 33.88,
    33.57, 33.57, 33.53, 34.16, 34.08, 33.88, 33.18, 33.3, 33.79, 34.15,
    34.07, 34.44, 34.24, 34.55, 34.68, 34.18, 33.87, 33.67, 33.35, 33.74,
    33.43, 33.47, 33.13, 33.25, 33.08, 32.74, 32.78, 32.75, 33.18, 32.65,
    32.03, 32.44, 32.28, 32.07, 32.5, 32.37, 32.62, 33.58, 33.96, 34.12,
    33.98, 33.53, 33.84, 33.64, 34.03, 34.11, 33.86, 33.73, 33.1, 33.11,
    33.19, 33.34, 33.53, 34.03, 34.71, 33.93, 33.98, 33.9, 33.5, 33.02,
    33.26, 33.15, 33.67, 33.63, 33.63, 34.1, 34.28, 34.21, 34.65, 35.18,
    35.61, 35.56, 35.3, 35.01, 34.56, 34.77, 34.79, 34.9, 35.42, 35.68,
    35.94, 36.42, 35.96, 35.43, 35.36, 34.93, 34.75, 35.11, 34.32, 34.46,
    34.34, 34.45, 34.56, 34.55, 34.6, 34.19, 34.65, 35.17, 34.01, 33.58,
    33.75, 33.91, 33.29, 33.49, 33.4, 33.8, 33.94, 33.55, 33.97, 34.34,
    33.83, 34.5, 34.93, 34.81, 34.93, 35.42, 35.78, 36.17, 36.66, 36.21,
    36.43, 36.84, 36.97, 36.4, 37.1, 36.89, 36.92, 36.4, 37.07, 36.82,
    36.76, 36.67, 36.63, 36.16, 36.33, 36.37, 36.49, 36.59, 36.94, 37.26,
    37.16, 36.37, 36.52, 36.15, 36.23, 36.17, 36.13, 37.07, 37.41, 36.81,
    37.82, 37.8, 38.52, 38.25, 38.63, 38.96, 39.22, 39.59, 39.98, 39.77,
    39.11, 38.35, 38.23, 38.39, 38.03, 38.21, 38.17, 39.02, 39.34, 40.07,
    40.28, 40.99, 41.21, 41.85, 42.31, 42.1, 42.33, 42.5, 42.46, 43.09,
    42.35, 42.04, 42.65, 42.89, 43, 41.63, 42.25, 42.16, 42.08, 41.97,
    42.66, 43.17, 43.17, 43.85, 43.03, 43, 43.06, 42.22, 42.78, 42.61,
    42.24, 42.2, 41.31, 40.9, 41.45, 41.62, 41.6, 41.2, 41.8, 42.07,
    42.36, 42.26, 42.77, 42.74, 42.15, 41.47, 40.92, 40.57, 40.35, 40.19
  ],
  "entry_z": 2,
  "exit_z": 0.5,
  "cost_bps_per_leg": 5,
  "fit_share_pct": 50
}

On these numbers, the fit window gives a hedge ratio of 1.0325 and a half-life of 6.29 points, and a hypothetical walk through the later window makes 3 trades for a total of 1.74% after costs.

Hypothetical, and on made-up numbers until you replace them. Nobody traded this, and nothing here is on offer.

Readings

The numbers, with their units.

Hedge ratio h

1.0325

Value of B per 1 of value in A, because the fit is in logs. From the first 250 points.

Half-life

6.2938points

t-stat of b

-3.6525

Read against about -3.34, a rule of thumb for two series. Ordinary t tables don't apply.

z-score at the last point

5.294

On fit-window mean and stdev. A diagnostic of the spread, not a signal.

Hypothetical trades in the later window

Includes one marked at the last point.

Hypothetical hit rate

66.67%

Share of trades above zero after costs.

Hypothetical total after costs

1.7387%log, per unit of A

Before costs: 2.34%.

Longest hold

56points

What flips it

The value of one input where the outcome changes, with the others held.

cost_bps_per_leg
19.49bpsnow 5
At this cost per leg the later-window total is zero. Above it, the total is negative. The trades themselves don't depend on cost.

Flags

What went past a line, and what to read before you trust the rest.

watch
The walk's last hypothetical trade hasn't closed at the end of the series. It is marked at the last point at -7.98% and counted in the total. That isn't a position to take. open_at_end

What this leaves out

What the formula leaves out, by name.

Borrow and financing on the short leg, and dividends on either leg.
The delay between seeing a close and trading it, and slippage beyond cost_bps_per_leg.
Share counts: the log spread treats the hedge as reset every point, while a real position with fixed shares drifts.
Stop-losses, position sizing and limits on a trade's length.
Exact small-sample critical values for the reversion test.
Taxes and fees.

What it took as given (9)

What it took as given to get here.

The fit window is the first fit_share_pct of the points. The hedge ratio, spread mean, spread stdev and reversion test come from it alone, so the walk never sees its own later numbers.
Stdev divides by n - 1. Half-life is in points of the series. A b under 1e-12 in size is rounding, so it reads as zero.
The t-stat of b is read against about -3.34, a rule of thumb for two series at the 5% level. Ordinary t tables don't apply, because h was fitted to the same numbers.
Above +entry_z the walk is short the spread, below -entry_z long. A short spread leaves once z is at or below exit_z and a long spread once z is at or above -exit_z, so a jump straight across the band also leaves. That is how this walk runs, not a side to take.
A leave and a new entry can happen on the same point if z jumps past the other side. Trades fill at the close that triggers them.
A trade still open at the end is marked at the last point, pays its four legs and counts in the totals, so a pair that stops converging still shows up.
Return is in log terms, per unit of A, and the B leg is charged one full leg of cost whatever h is.
The hedge ratio comes from log prices, so it is a ratio of values: 1 of value in A against h of value in B, not h shares per share.
The sleeve counts 100 of A against h times 100 of B.

Z-score of the spread, on fit-window numbers. The walk starts at point 250.z

z-score
+entry_z
-entry_z

The data

Fit numbers

item	value
Hedge ratio h, fit window	1.0325
Intercept c, fit window	0.643334
Spread mean, fit window	0
Spread stdev, fit window	0.0237691
Reversion a	-0.000136985
Reversion b	-0.104284
t-stat of b	-3.6525
Hedge ratio, first half of all points	1.0325
Hedge ratio, second half of all points	1.3061
Fit window points	250
Later window points	250
Cost per round trip, %	0.2

Hypothetical trades

direction	entry_point	exit_point	z_in	z_out	gross_pct	net_pct	points_held	status
short spread	262	270	2.3963	0.1904	5.2433	5.0433	8	closed
short spread	281	292	2.4416	0.3911	4.8737	4.6737	11	closed
not shown, still open	443	499	2.0216	5.294	-7.7783	-7.9783	56	marked at the end

Paste it into your agent

No connection needed. This prompt carries the method, the conventions and what this site's engine gives on the made-up numbers, so your agent can check its own work before it touches real ones. Every prompt, with its hash, is listed at /prompts.json. A copy that stays fixed for this version, for a stack to point at: /v/1.0/models/pairs_spread.md.

prompt.md

# Pairs spread: a prompt from hedgefund.mdPaste this into your AI agent. It needs no connection to hedgefund.md. An agent that can run code should write and run it, and shouldn't work a long series by hand.**Question.** Does this spread pull back to its mean, and what is left of a hypothetical walk through the later window after costs?## MethodOn the fit window: ln A = c + h ln B + e. S_t = ln A_t - h ln B_t - c. z_t = (S_t - mean_fit) / stdev_fit. delta S_t = a + b S_t-1, half-life = -ln 2 / ln(1 + b) when -1 < b < 0. Trade return = direction * (S_exit - S_entry) - 4 * cost_bps_per_leg / 10000. Flip cost per leg = sum of gross trade returns * 10000 / (4 * trades).## Conventions- The fit window is the first fit_share_pct of the points. The hedge ratio, spread mean, spread stdev and reversion test come from it alone, so the walk never sees its own later numbers.- Stdev divides by n - 1. Half-life is in points of the series. A b under 1e-12 in size is rounding, so it reads as zero.- The t-stat of b is read against about -3.34, a rule of thumb for two series at the 5% level. Ordinary t tables don't apply, because h was fitted to the same numbers.- Above +entry_z the walk is short the spread, below -entry_z long. A short spread leaves once z is at or below exit_z and a long spread once z is at or above -exit_z, so a jump straight across the band also leaves. That is how this walk runs, not a side to take.- A leave and a new entry can happen on the same point if z jumps past the other side. Trades fill at the close that triggers them.- A trade still open at the end is marked at the last point, pays its four legs and counts in the totals, so a pair that stops converging still shows up.- Return is in log terms, per unit of A, and the B leg is charged one full leg of cost whatever h is.- The hedge ratio comes from log prices, so it is a ratio of values: 1 of value in A against h of value in B, not h shares per share.- The sleeve counts 100 of A against h times 100 of B.## Step 1: check your method on these made-up numbersThe numbers and names below are made up. They aren't market levels, typical values or anyone's real figures.```json{  "series_a": [    108.12, 108.57, 103.13, 103.28, 102.31, 104.84, 107.3, 104.71, 102.25, 99.76,    100.82, 100.29, 100.27, 100.31, 102.79, 101.69, 102.56, 102.15, 104.54, 108.17,    101.79, 102.04, 101.32, 100.85, 99.1, 96.83, 96.75, 97.23, 97.84, 95.01,    94.87, 94.28, 96.59, 97.83, 96.15, 98.17, 97.7, 95.29, 95.82, 97.05,    94.79, 96.32, 99.1, 98.71, 98.34, 97.28, 99.53, 98.69, 99.56, 99.39,    101.5, 100.89, 97.23, 99.35, 101.55, 99.1, 99.4, 99.33, 100.55, 101.12,    104.48, 106.08, 104.26, 106.52, 108.34, 106.24, 105.95, 103.44, 104.96, 104.46,    107.19, 106.83, 104.73, 103.89, 103.81, 101.68, 98.76, 100.12, 99.72, 99.31,    100.34, 101.1, 99.65, 98.28, 98.92, 101.36, 103.15, 101.98, 101.38, 104.99,    103.88, 104.66, 105.52, 105.99, 106.45, 107.69, 108.35, 108.47, 110.48, 110.34,    108.45, 107.75, 106.32, 106.49, 104.92, 105.62, 102.94, 102.82, 105.32, 104.97,    105.1, 107.19, 105.74, 106.02, 103.25, 100.81, 102.17, 100.61, 100.92, 100.48,    101.25, 98.02, 96.89, 96.4, 95.25, 94.18, 91.6, 88.51, 86.67, 86.33,    86.05, 86.66, 88.49, 86.96, 85.07, 83.48, 83.86, 81.13, 81.38, 82.81,    82.68, 82.27, 82.72, 83.14, 84.93, 81.84, 81.47, 82.31, 80.94, 82.77,    81.43, 84.07, 84.72, 84.85, 85.56, 85.16, 85.77, 85.72, 83.98, 83.23,    84.4, 83.87, 81.29, 79.32, 79.95, 81.29, 81.97, 81.18, 81.22, 82.95,    80.72, 82.22, 83.5, 82.05, 83.4, 79.65, 79.95, 78.02, 75.87, 76.43,    75.68, 75.07, 74.33, 71.12, 72.01, 71.81, 72.53, 72.69, 72.44, 73.33,    73.83, 74.64, 76.35, 76.9, 77.04, 75.98, 74.18, 73.75, 73.68, 73.89,    74.15, 71.69, 71.78, 71.49, 69.96, 69.68, 68.7, 69.15, 67.31, 70.81,    70.64, 70.09, 70.53, 70.31, 70.64, 70.55, 71.25, 72.45, 73.08, 73.54,    74.42, 74.52, 73.21, 72.9, 72.16, 71.05, 72.46, 72.75, 71.08, 69.57,    70.58, 68.45, 71.43, 71.92, 71.79, 71.11, 71.26, 70.03, 68.98, 68.85,    68.32, 67.81, 68.03, 67.15, 66.12, 65.89, 67.07, 66.25, 65.5, 67.16,    68.57, 68.93, 68.13, 68.69, 67.88, 69.03, 70.61, 71.4, 70.77, 69.29,    70.9, 72.13, 74.27, 73.7, 74.35, 73.28, 75.06, 75.77, 73.85, 72.74,    72.29, 72.79, 72.3, 73.63, 75.22, 75.3, 75.55, 74.1, 73.82, 74.8,    74.92, 75.89, 75.9, 76.07, 77.1, 76.49, 73.32, 72.95, 73.4, 76.44,    75.78, 75.48, 73.77, 74.6, 74.87, 73.37, 71.53, 70.76, 70.91, 72.12,    71.81, 72.47, 70.81, 69.78, 69.7, 69.03, 68.65, 68.14, 70.17, 69.15,    66.99, 68.4, 68, 68.91, 71.28, 70.05, 70.53, 73.98, 73.15, 73.56,    73.25, 71.05, 72.55, 74.1, 73.66, 72.63, 72.48, 71.59, 70.58, 70.61,    71.85, 72.14, 71.41, 73.37, 75.11, 72.43, 72.28, 71.8, 70.66, 69.93,    70.07, 69.56, 70.48, 69.65, 69.98, 70.38, 71.84, 72.18, 73.81, 74.64,    74.69, 73.64, 73.3, 72.48, 72.83, 73.7, 74.26, 75.16, 76.51, 76.56,    78.76, 79.02, 76.71, 76.34, 75.73, 74.2, 73.22, 74.02, 71.63, 71.26,    70.51, 70.74, 71.14, 72.48, 73.16, 71.83, 73.75, 74.17, 72.31, 71.53,    70.86, 69.51, 69.51, 70.29, 70.48, 72.24, 71.45, 70.35, 70.79, 71.27,    71.14, 72.51, 73.33, 73.48, 72.58, 73.31, 74.91, 77.81, 79.32, 77.92,    79.36, 80.13, 80.86, 78.81, 80.84, 79.97, 80.07, 77.41, 77.89, 77.68,    78.59, 77.79, 78.2, 76.06, 75.64, 74.62, 75.52, 76.54, 76.14, 76.9,    77.87, 74.2, 75.83, 75.53, 76.46, 75.92, 75.37, 79.44, 80.92, 78.71,    82.66, 81.17, 83.28, 80.79, 81.99, 84.3, 84.99, 86.34, 87.32, 87.88,    86.42, 84.29, 84.95, 86.3, 86.79, 87.05, 86.43, 87.47, 89.55, 91.81,    91.3, 92.07, 93.51, 95.49, 96.59, 95.44, 96.95, 98.63, 98.6, 101.11,    100.11, 98.41, 99.38, 101.46, 101.24, 98.48, 97.44, 97.48, 96.36, 95.08,    98.74, 99.78, 98.94, 101.19, 98.97, 98.83, 98.96, 96.84, 97.82, 98.12,    96.49, 97.01, 93.21, 92.38, 94.76, 94.14, 95.32, 96.07, 96.83, 97.44,    99.83, 98.6, 98.62, 99.63, 99.79, 96.51, 94.69, 95.14, 97.03, 97.8  ],  "series_b": [    49.48, 49.95, 48.68, 48.5, 47.89, 48.74, 48.72, 48.11, 47.72, 47.66,    47.54, 47.91, 47.56, 47.96, 48.9, 47.8, 48, 47.66, 48.13, 48.9,    47.31, 47.11, 46.71, 47.1, 46.57, 46.21, 46.27, 46.92, 46.84, 46.3,    46.18, 46.12, 46.42, 46.52, 45.5, 46.03, 45.57, 44.92, 45.16, 45.88,    45.45, 45.76, 45.87, 45.87, 45.23, 45.04, 45.18, 44.15, 44.88, 44.96,    45.34, 45.15, 44.38, 45.51, 46.42, 46.47, 46.63, 46.35, 46.56, 46.7,    47.62, 48.34, 47.23, 48.19, 49.03, 49.04, 48.64, 47.73, 48.02, 48.34,    48.73, 48.19, 48.18, 47.76, 47.49, 46.96, 46.32, 47.01, 47.34, 47.55,    47.2, 47.21, 47.24, 46.6, 46.43, 47.22, 47.99, 48.39, 48.06, 48.97,    48.89, 49.08, 49.08, 49.83, 48.86, 48.68, 49.11, 48.84, 48.47, 48.82,    47.94, 47.29, 46.95, 47.17, 46.85, 46.77, 46.49, 46.22, 46.96, 47.67,    47.21, 47.67, 47.09, 46.86, 46.32, 45.58, 46.06, 45.82, 45.34, 45.44,    45.27, 45.23, 45.01, 45.2, 44.96, 44.63, 43.41, 42.05, 41.35, 40.59,    40.4, 40.69, 41.18, 40.71, 40.23, 39.89, 40.17, 39.21, 38.92, 39.2,    39, 38.82, 38.86, 39.24, 40.06, 39.56, 38.76, 39.24, 39.03, 39.51,    38.99, 40.23, 40.52, 40.55, 40.48, 40.14, 40.44, 40.33, 39.89, 39.63,    39.86, 39.64, 39.15, 37.96, 38.23, 38.6, 38.81, 38.65, 38.49, 39,    37.95, 38.07, 38.41, 37.93, 37.76, 36.58, 36.79, 36.05, 36.07, 35.88,    35.83, 35.46, 35.3, 34.57, 34.57, 34.11, 34.43, 34.53, 34.36, 34.98,    35.13, 35.29, 35.61, 35.75, 35.59, 35.18, 34.42, 33.74, 33.49, 33.38,    33.36, 32.68, 32.49, 32.41, 32.21, 31.79, 31.78, 32.25, 31.67, 32.53,    32.43, 32.12, 31.81, 31.89, 31.81, 31.62, 31.9, 32.42, 32.79, 33.37,    33.79, 34.24, 33.58, 33.83, 33.53, 33.66, 34, 34, 33.26, 33.06,    32.92, 32.61, 33.52, 33.19, 33.12, 33.23, 33.21, 33.3, 32.89, 33.09,    32.8, 32.45, 32.95, 32.54, 32.11, 32.1, 32.12, 32.14, 32.07, 32.33,    32.48, 32.59, 32.46, 32.11, 31.71, 32.03, 32.58, 32.78, 32.85, 32.5,    32.47, 32.71, 32.91, 33.45, 33.17, 33.18, 33.69, 34.18, 33.91, 33.42,    33.73, 33.55, 33.63, 33.6, 34.17, 34.11, 34.45, 34.04, 33.77, 33.88,    33.57, 33.57, 33.53, 34.16, 34.08, 33.88, 33.18, 33.3, 33.79, 34.15,    34.07, 34.44, 34.24, 34.55, 34.68, 34.18, 33.87, 33.67, 33.35, 33.74,    33.43, 33.47, 33.13, 33.25, 33.08, 32.74, 32.78, 32.75, 33.18, 32.65,    32.03, 32.44, 32.28, 32.07, 32.5, 32.37, 32.62, 33.58, 33.96, 34.12,    33.98, 33.53, 33.84, 33.64, 34.03, 34.11, 33.86, 33.73, 33.1, 33.11,    33.19, 33.34, 33.53, 34.03, 34.71, 33.93, 33.98, 33.9, 33.5, 33.02,    33.26, 33.15, 33.67, 33.63, 33.63, 34.1, 34.28, 34.21, 34.65, 35.18,    35.61, 35.56, 35.3, 35.01, 34.56, 34.77, 34.79, 34.9, 35.42, 35.68,    35.94, 36.42, 35.96, 35.43, 35.36, 34.93, 34.75, 35.11, 34.32, 34.46,    34.34, 34.45, 34.56, 34.55, 34.6, 34.19, 34.65, 35.17, 34.01, 33.58,    33.75, 33.91, 33.29, 33.49, 33.4, 33.8, 33.94, 33.55, 33.97, 34.34,    33.83, 34.5, 34.93, 34.81, 34.93, 35.42, 35.78, 36.17, 36.66, 36.21,    36.43, 36.84, 36.97, 36.4, 37.1, 36.89, 36.92, 36.4, 37.07, 36.82,    36.76, 36.67, 36.63, 36.16, 36.33, 36.37, 36.49, 36.59, 36.94, 37.26,    37.16, 36.37, 36.52, 36.15, 36.23, 36.17, 36.13, 37.07, 37.41, 36.81,    37.82, 37.8, 38.52, 38.25, 38.63, 38.96, 39.22, 39.59, 39.98, 39.77,    39.11, 38.35, 38.23, 38.39, 38.03, 38.21, 38.17, 39.02, 39.34, 40.07,    40.28, 40.99, 41.21, 41.85, 42.31, 42.1, 42.33, 42.5, 42.46, 43.09,    42.35, 42.04, 42.65, 42.89, 43, 41.63, 42.25, 42.16, 42.08, 41.97,    42.66, 43.17, 43.17, 43.85, 43.03, 43, 43.06, 42.22, 42.78, 42.61,    42.24, 42.2, 41.31, 40.9, 41.45, 41.62, 41.6, 41.2, 41.8, 42.07,    42.36, 42.26, 42.77, 42.74, 42.15, 41.47, 40.92, 40.57, 40.35, 40.19  ],  "entry_z": 2,  "exit_z": 0.5,  "cost_bps_per_leg": 5,  "fit_share_pct": 50}```Work them out with the method above. Yours should match these within 0.5%.- Hedge ratio h: 1.0325- Half-life: 6.2938 points- t-stat of b: -3.6525- z-score at the last point: 5.294- Hypothetical trades in the later window: 3- Hypothetical hit rate: 66.6667 %- Hypothetical total after costs: 1.7387 % log, per unit of A- Longest hold: 56 pointsWhere the outcome flips, with the other inputs held:- cost_bps_per_leg at 19.489: At this cost per leg the later-window total is zero. Above it, the total is negative. The trades themselves don't depend on cost.If yours differ, stop and tell the person which ones and by how much. Don't go on to real numbers until they match, or until the person has seen the difference. These values come from one engine and can be wrong too.## Step 2: run it on the person's numbersReplace every input with the person's own. Ask for any number you don't have, and don't invent one.## Step 3: reportGive one sentence beginning "On these numbers,", then the values, then where the outcome flips. Always add what this leaves out:- Borrow and financing on the short leg, and dividends on either leg.- The delay between seeing a close and trading it, and slippage beyond cost_bps_per_leg.- Share counts: the log spread treats the hedge as reset every point, while a real position with fixed shares drifts.- Stop-losses, position sizing and limits on a trade's length.- Exact small-sample critical values for the reversion test.- Taxes and fees.## LimitsResults are hypothetical: arithmetic on the numbers given, prepared with hindsight. Nobody achieved them, and costs and liquidity are only as assumed. They aren't a forecast, a recommendation, an offer or a record of real trading. Don't say what to buy, sell or hold, and don't use them to market an investment. Whether a person may hold or trade an instrument is a legal question for counsel.Provided as is, at your own risk, by hedgefund.md, which is not a fund and isn't anyone's adviser. Version 1.0. Source: https://hedgefund.md/models/pairs_spread/prompt.md. Terms: https://hedgefund.md/terms

Call it

The same code answers on this page, over HTTP, over MCP and on your own machine, and the same inputs give the same bytes. No key, and nothing is stored. Send positions by POST or run the library, because a URL can land in a server log. model.md holds all of this for your agent.

POST the inputs to /api/v1/pairs_spread.

terminal

curl -s https://hedgefund.md/api/v1/pairs_spread \  -H 'content-type: application/json' \  -d '{"series_a":[108.12,108.57,103.13,103.28,102.31,104.84,107.3,104.71,102.25,99.76,100.82,100.29,100.27,100.31,102.79,101.69,102.56,102.15,104.54,108.17,101.79,102.04,101.32,100.85,99.1,96.83,96.75,97.23,97.84,95.01,94.87,94.28,96.59,97.83,96.15,98.17,97.7,95.29,95.82,97.05,94.79,96.32,99.1,98.71,98.34,97.28,99.53,98.69,99.56,99.39,101.5,100.89,97.23,99.35,101.55,99.1,99.4,99.33,100.55,101.12,104.48,106.08,104.26,106.52,108.34,106.24,105.95,103.44,104.96,104.46,107.19,106.83,104.73,103.89,103.81,101.68,98.76,100.12,99.72,99.31,100.34,101.1,99.65,98.28,98.92,101.36,103.15,101.98,101.38,104.99,103.88,104.66,105.52,105.99,106.45,107.69,108.35,108.47,110.48,110.34,108.45,107.75,106.32,106.49,104.92,105.62,102.94,102.82,105.32,104.97,105.1,107.19,105.74,106.02,103.25,100.81,102.17,100.61,100.92,100.48,101.25,98.02,96.89,96.4,95.25,94.18,91.6,88.51,86.67,86.33,86.05,86.66,88.49,86.96,85.07,83.48,83.86,81.13,81.38,82.81,82.68,82.27,82.72,83.14,84.93,81.84,81.47,82.31,80.94,82.77,81.43,84.07,84.72,84.85,85.56,85.16,85.77,85.72,83.98,83.23,84.4,83.87,81.29,79.32,79.95,81.29,81.97,81.18,81.22,82.95,80.72,82.22,83.5,82.05,83.4,79.65,79.95,78.02,75.87,76.43,75.68,75.07,74.33,71.12,72.01,71.81,72.53,72.69,72.44,73.33,73.83,74.64,76.35,76.9,77.04,75.98,74.18,73.75,73.68,73.89,74.15,71.69,71.78,71.49,69.96,69.68,68.7,69.15,67.31,70.81,70.64,70.09,70.53,70.31,70.64,70.55,71.25,72.45,73.08,73.54,74.42,74.52,73.21,72.9,72.16,71.05,72.46,72.75,71.08,69.57,70.58,68.45,71.43,71.92,71.79,71.11,71.26,70.03,68.98,68.85,68.32,67.81,68.03,67.15,66.12,65.89,67.07,66.25,65.5,67.16,68.57,68.93,68.13,68.69,67.88,69.03,70.61,71.4,70.77,69.29,70.9,72.13,74.27,73.7,74.35,73.28,75.06,75.77,73.85,72.74,72.29,72.79,72.3,73.63,75.22,75.3,75.55,74.1,73.82,74.8,74.92,75.89,75.9,76.07,77.1,76.49,73.32,72.95,73.4,76.44,75.78,75.48,73.77,74.6,74.87,73.37,71.53,70.76,70.91,72.12,71.81,72.47,70.81,69.78,69.7,69.03,68.65,68.14,70.17,69.15,66.99,68.4,68,68.91,71.28,70.05,70.53,73.98,73.15,73.56,73.25,71.05,72.55,74.1,73.66,72.63,72.48,71.59,70.58,70.61,71.85,72.14,71.41,73.37,75.11,72.43,72.28,71.8,70.66,69.93,70.07,69.56,70.48,69.65,69.98,70.38,71.84,72.18,73.81,74.64,74.69,73.64,73.3,72.48,72.83,73.7,74.26,75.16,76.51,76.56,78.76,79.02,76.71,76.34,75.73,74.2,73.22,74.02,71.63,71.26,70.51,70.74,71.14,72.48,73.16,71.83,73.75,74.17,72.31,71.53,70.86,69.51,69.51,70.29,70.48,72.24,71.45,70.35,70.79,71.27,71.14,72.51,73.33,73.48,72.58,73.31,74.91,77.81,79.32,77.92,79.36,80.13,80.86,78.81,80.84,79.97,80.07,77.41,77.89,77.68,78.59,77.79,78.2,76.06,75.64,74.62,75.52,76.54,76.14,76.9,77.87,74.2,75.83,75.53,76.46,75.92,75.37,79.44,80.92,78.71,82.66,81.17,83.28,80.79,81.99,84.3,84.99,86.34,87.32,87.88,86.42,84.29,84.95,86.3,86.79,87.05,86.43,87.47,89.55,91.81,91.3,92.07,93.51,95.49,96.59,95.44,96.95,98.63,98.6,101.11,100.11,98.41,99.38,101.46,101.24,98.48,97.44,97.48,96.36,95.08,98.74,99.78,98.94,101.19,98.97,98.83,98.96,96.84,97.82,98.12,96.49,97.01,93.21,92.38,94.76,94.14,95.32,96.07,96.83,97.44,99.83,98.6,98.62,99.63,99.79,96.51,94.69,95.14,97.03,97.8],"series_b":[49.48,49.95,48.68,48.5,47.89,48.74,48.72,48.11,47.72,47.66,47.54,47.91,47.56,47.96,48.9,47.8,48,47.66,48.13,48.9,47.31,47.11,46.71,47.1,46.57,46.21,46.27,46.92,46.84,46.3,46.18,46.12,46.42,46.52,45.5,46.03,45.57,44.92,45.16,45.88,45.45,45.76,45.87,45.87,45.23,45.04,45.18,44.15,44.88,44.96,45.34,45.15,44.38,45.51,46.42,46.47,46.63,46.35,46.56,46.7,47.62,48.34,47.23,48.19,49.03,49.04,48.64,47.73,48.02,48.34,48.73,48.19,48.18,47.76,47.49,46.96,46.32,47.01,47.34,47.55,47.2,47.21,47.24,46.6,46.43,47.22,47.99,48.39,48.06,48.97,48.89,49.08,49.08,49.83,48.86,48.68,49.11,48.84,48.47,48.82,47.94,47.29,46.95,47.17,46.85,46.77,46.49,46.22,46.96,47.67,47.21,47.67,47.09,46.86,46.32,45.58,46.06,45.82,45.34,45.44,45.27,45.23,45.01,45.2,44.96,44.63,43.41,42.05,41.35,40.59,40.4,40.69,41.18,40.71,40.23,39.89,40.17,39.21,38.92,39.2,39,38.82,38.86,39.24,40.06,39.56,38.76,39.24,39.03,39.51,38.99,40.23,40.52,40.55,40.48,40.14,40.44,40.33,39.89,39.63,39.86,39.64,39.15,37.96,38.23,38.6,38.81,38.65,38.49,39,37.95,38.07,38.41,37.93,37.76,36.58,36.79,36.05,36.07,35.88,35.83,35.46,35.3,34.57,34.57,34.11,34.43,34.53,34.36,34.98,35.13,35.29,35.61,35.75,35.59,35.18,34.42,33.74,33.49,33.38,33.36,32.68,32.49,32.41,32.21,31.79,31.78,32.25,31.67,32.53,32.43,32.12,31.81,31.89,31.81,31.62,31.9,32.42,32.79,33.37,33.79,34.24,33.58,33.83,33.53,33.66,34,34,33.26,33.06,32.92,32.61,33.52,33.19,33.12,33.23,33.21,33.3,32.89,33.09,32.8,32.45,32.95,32.54,32.11,32.1,32.12,32.14,32.07,32.33,32.48,32.59,32.46,32.11,31.71,32.03,32.58,32.78,32.85,32.5,32.47,32.71,32.91,33.45,33.17,33.18,33.69,34.18,33.91,33.42,33.73,33.55,33.63,33.6,34.17,34.11,34.45,34.04,33.77,33.88,33.57,33.57,33.53,34.16,34.08,33.88,33.18,33.3,33.79,34.15,34.07,34.44,34.24,34.55,34.68,34.18,33.87,33.67,33.35,33.74,33.43,33.47,33.13,33.25,33.08,32.74,32.78,32.75,33.18,32.65,32.03,32.44,32.28,32.07,32.5,32.37,32.62,33.58,33.96,34.12,33.98,33.53,33.84,33.64,34.03,34.11,33.86,33.73,33.1,33.11,33.19,33.34,33.53,34.03,34.71,33.93,33.98,33.9,33.5,33.02,33.26,33.15,33.67,33.63,33.63,34.1,34.28,34.21,34.65,35.18,35.61,35.56,35.3,35.01,34.56,34.77,34.79,34.9,35.42,35.68,35.94,36.42,35.96,35.43,35.36,34.93,34.75,35.11,34.32,34.46,34.34,34.45,34.56,34.55,34.6,34.19,34.65,35.17,34.01,33.58,33.75,33.91,33.29,33.49,33.4,33.8,33.94,33.55,33.97,34.34,33.83,34.5,34.93,34.81,34.93,35.42,35.78,36.17,36.66,36.21,36.43,36.84,36.97,36.4,37.1,36.89,36.92,36.4,37.07,36.82,36.76,36.67,36.63,36.16,36.33,36.37,36.49,36.59,36.94,37.26,37.16,36.37,36.52,36.15,36.23,36.17,36.13,37.07,37.41,36.81,37.82,37.8,38.52,38.25,38.63,38.96,39.22,39.59,39.98,39.77,39.11,38.35,38.23,38.39,38.03,38.21,38.17,39.02,39.34,40.07,40.28,40.99,41.21,41.85,42.31,42.1,42.33,42.5,42.46,43.09,42.35,42.04,42.65,42.89,43,41.63,42.25,42.16,42.08,41.97,42.66,43.17,43.17,43.85,43.03,43,43.06,42.22,42.78,42.61,42.24,42.2,41.31,40.9,41.45,41.62,41.6,41.2,41.8,42.07,42.36,42.26,42.77,42.74,42.15,41.47,40.92,40.57,40.35,40.19],"entry_z":2,"exit_z":0.5,"cost_bps_per_leg":5,"fit_share_pct":50}' \  | jq '{summary, flags, flips, not_modeled, inputs_hash}'

The tool is pairs_spread on https://hedgefund.md/mcp.

terminal

curl -s https://hedgefund.md/mcp \  -H 'content-type: application/json' -H 'accept: application/json' \  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"pairs_spread","arguments":{"series_a":[108.12,108.57,103.13,103.28,102.31,104.84,107.3,104.71,102.25,99.76,100.82,100.29,100.27,100.31,102.79,101.69,102.56,102.15,104.54,108.17,101.79,102.04,101.32,100.85,99.1,96.83,96.75,97.23,97.84,95.01,94.87,94.28,96.59,97.83,96.15,98.17,97.7,95.29,95.82,97.05,94.79,96.32,99.1,98.71,98.34,97.28,99.53,98.69,99.56,99.39,101.5,100.89,97.23,99.35,101.55,99.1,99.4,99.33,100.55,101.12,104.48,106.08,104.26,106.52,108.34,106.24,105.95,103.44,104.96,104.46,107.19,106.83,104.73,103.89,103.81,101.68,98.76,100.12,99.72,99.31,100.34,101.1,99.65,98.28,98.92,101.36,103.15,101.98,101.38,104.99,103.88,104.66,105.52,105.99,106.45,107.69,108.35,108.47,110.48,110.34,108.45,107.75,106.32,106.49,104.92,105.62,102.94,102.82,105.32,104.97,105.1,107.19,105.74,106.02,103.25,100.81,102.17,100.61,100.92,100.48,101.25,98.02,96.89,96.4,95.25,94.18,91.6,88.51,86.67,86.33,86.05,86.66,88.49,86.96,85.07,83.48,83.86,81.13,81.38,82.81,82.68,82.27,82.72,83.14,84.93,81.84,81.47,82.31,80.94,82.77,81.43,84.07,84.72,84.85,85.56,85.16,85.77,85.72,83.98,83.23,84.4,83.87,81.29,79.32,79.95,81.29,81.97,81.18,81.22,82.95,80.72,82.22,83.5,82.05,83.4,79.65,79.95,78.02,75.87,76.43,75.68,75.07,74.33,71.12,72.01,71.81,72.53,72.69,72.44,73.33,73.83,74.64,76.35,76.9,77.04,75.98,74.18,73.75,73.68,73.89,74.15,71.69,71.78,71.49,69.96,69.68,68.7,69.15,67.31,70.81,70.64,70.09,70.53,70.31,70.64,70.55,71.25,72.45,73.08,73.54,74.42,74.52,73.21,72.9,72.16,71.05,72.46,72.75,71.08,69.57,70.58,68.45,71.43,71.92,71.79,71.11,71.26,70.03,68.98,68.85,68.32,67.81,68.03,67.15,66.12,65.89,67.07,66.25,65.5,67.16,68.57,68.93,68.13,68.69,67.88,69.03,70.61,71.4,70.77,69.29,70.9,72.13,74.27,73.7,74.35,73.28,75.06,75.77,73.85,72.74,72.29,72.79,72.3,73.63,75.22,75.3,75.55,74.1,73.82,74.8,74.92,75.89,75.9,76.07,77.1,76.49,73.32,72.95,73.4,76.44,75.78,75.48,73.77,74.6,74.87,73.37,71.53,70.76,70.91,72.12,71.81,72.47,70.81,69.78,69.7,69.03,68.65,68.14,70.17,69.15,66.99,68.4,68,68.91,71.28,70.05,70.53,73.98,73.15,73.56,73.25,71.05,72.55,74.1,73.66,72.63,72.48,71.59,70.58,70.61,71.85,72.14,71.41,73.37,75.11,72.43,72.28,71.8,70.66,69.93,70.07,69.56,70.48,69.65,69.98,70.38,71.84,72.18,73.81,74.64,74.69,73.64,73.3,72.48,72.83,73.7,74.26,75.16,76.51,76.56,78.76,79.02,76.71,76.34,75.73,74.2,73.22,74.02,71.63,71.26,70.51,70.74,71.14,72.48,73.16,71.83,73.75,74.17,72.31,71.53,70.86,69.51,69.51,70.29,70.48,72.24,71.45,70.35,70.79,71.27,71.14,72.51,73.33,73.48,72.58,73.31,74.91,77.81,79.32,77.92,79.36,80.13,80.86,78.81,80.84,79.97,80.07,77.41,77.89,77.68,78.59,77.79,78.2,76.06,75.64,74.62,75.52,76.54,76.14,76.9,77.87,74.2,75.83,75.53,76.46,75.92,75.37,79.44,80.92,78.71,82.66,81.17,83.28,80.79,81.99,84.3,84.99,86.34,87.32,87.88,86.42,84.29,84.95,86.3,86.79,87.05,86.43,87.47,89.55,91.81,91.3,92.07,93.51,95.49,96.59,95.44,96.95,98.63,98.6,101.11,100.11,98.41,99.38,101.46,101.24,98.48,97.44,97.48,96.36,95.08,98.74,99.78,98.94,101.19,98.97,98.83,98.96,96.84,97.82,98.12,96.49,97.01,93.21,92.38,94.76,94.14,95.32,96.07,96.83,97.44,99.83,98.6,98.62,99.63,99.79,96.51,94.69,95.14,97.03,97.8],"series_b":[49.48,49.95,48.68,48.5,47.89,48.74,48.72,48.11,47.72,47.66,47.54,47.91,47.56,47.96,48.9,47.8,48,47.66,48.13,48.9,47.31,47.11,46.71,47.1,46.57,46.21,46.27,46.92,46.84,46.3,46.18,46.12,46.42,46.52,45.5,46.03,45.57,44.92,45.16,45.88,45.45,45.76,45.87,45.87,45.23,45.04,45.18,44.15,44.88,44.96,45.34,45.15,44.38,45.51,46.42,46.47,46.63,46.35,46.56,46.7,47.62,48.34,47.23,48.19,49.03,49.04,48.64,47.73,48.02,48.34,48.73,48.19,48.18,47.76,47.49,46.96,46.32,47.01,47.34,47.55,47.2,47.21,47.24,46.6,46.43,47.22,47.99,48.39,48.06,48.97,48.89,49.08,49.08,49.83,48.86,48.68,49.11,48.84,48.47,48.82,47.94,47.29,46.95,47.17,46.85,46.77,46.49,46.22,46.96,47.67,47.21,47.67,47.09,46.86,46.32,45.58,46.06,45.82,45.34,45.44,45.27,45.23,45.01,45.2,44.96,44.63,43.41,42.05,41.35,40.59,40.4,40.69,41.18,40.71,40.23,39.89,40.17,39.21,38.92,39.2,39,38.82,38.86,39.24,40.06,39.56,38.76,39.24,39.03,39.51,38.99,40.23,40.52,40.55,40.48,40.14,40.44,40.33,39.89,39.63,39.86,39.64,39.15,37.96,38.23,38.6,38.81,38.65,38.49,39,37.95,38.07,38.41,37.93,37.76,36.58,36.79,36.05,36.07,35.88,35.83,35.46,35.3,34.57,34.57,34.11,34.43,34.53,34.36,34.98,35.13,35.29,35.61,35.75,35.59,35.18,34.42,33.74,33.49,33.38,33.36,32.68,32.49,32.41,32.21,31.79,31.78,32.25,31.67,32.53,32.43,32.12,31.81,31.89,31.81,31.62,31.9,32.42,32.79,33.37,33.79,34.24,33.58,33.83,33.53,33.66,34,34,33.26,33.06,32.92,32.61,33.52,33.19,33.12,33.23,33.21,33.3,32.89,33.09,32.8,32.45,32.95,32.54,32.11,32.1,32.12,32.14,32.07,32.33,32.48,32.59,32.46,32.11,31.71,32.03,32.58,32.78,32.85,32.5,32.47,32.71,32.91,33.45,33.17,33.18,33.69,34.18,33.91,33.42,33.73,33.55,33.63,33.6,34.17,34.11,34.45,34.04,33.77,33.88,33.57,33.57,33.53,34.16,34.08,33.88,33.18,33.3,33.79,34.15,34.07,34.44,34.24,34.55,34.68,34.18,33.87,33.67,33.35,33.74,33.43,33.47,33.13,33.25,33.08,32.74,32.78,32.75,33.18,32.65,32.03,32.44,32.28,32.07,32.5,32.37,32.62,33.58,33.96,34.12,33.98,33.53,33.84,33.64,34.03,34.11,33.86,33.73,33.1,33.11,33.19,33.34,33.53,34.03,34.71,33.93,33.98,33.9,33.5,33.02,33.26,33.15,33.67,33.63,33.63,34.1,34.28,34.21,34.65,35.18,35.61,35.56,35.3,35.01,34.56,34.77,34.79,34.9,35.42,35.68,35.94,36.42,35.96,35.43,35.36,34.93,34.75,35.11,34.32,34.46,34.34,34.45,34.56,34.55,34.6,34.19,34.65,35.17,34.01,33.58,33.75,33.91,33.29,33.49,33.4,33.8,33.94,33.55,33.97,34.34,33.83,34.5,34.93,34.81,34.93,35.42,35.78,36.17,36.66,36.21,36.43,36.84,36.97,36.4,37.1,36.89,36.92,36.4,37.07,36.82,36.76,36.67,36.63,36.16,36.33,36.37,36.49,36.59,36.94,37.26,37.16,36.37,36.52,36.15,36.23,36.17,36.13,37.07,37.41,36.81,37.82,37.8,38.52,38.25,38.63,38.96,39.22,39.59,39.98,39.77,39.11,38.35,38.23,38.39,38.03,38.21,38.17,39.02,39.34,40.07,40.28,40.99,41.21,41.85,42.31,42.1,42.33,42.5,42.46,43.09,42.35,42.04,42.65,42.89,43,41.63,42.25,42.16,42.08,41.97,42.66,43.17,43.17,43.85,43.03,43,43.06,42.22,42.78,42.61,42.24,42.2,41.31,40.9,41.45,41.62,41.6,41.2,41.8,42.07,42.36,42.26,42.77,42.74,42.15,41.47,40.92,40.57,40.35,40.19],"entry_z":2,"exit_z":0.5,"cost_bps_per_leg":5,"fit_share_pct":50}}}' \  | jq '.result.structuredContent | {summary, flags, flips, not_modeled, inputs_hash}'

One file with no dependencies, and nothing is sent anywhere.

terminal

curl -fsSL https://hedgefund.md/hedgefund.mjs -o hedgefund.mjs   # read it before you run itnode hedgefund.mjs template pairs_spread > mine.json           # replace every number in itnode hedgefund.mjs run pairs_spread mine.json | jq '{summary, flags, flips, not_modeled, inputs_hash}'

Made-up numbers that run as they stand. Replace every one.

pairs_spread.json

{  "series_a": [    108.12, 108.57, 103.13, 103.28, 102.31, 104.84, 107.3, 104.71, 102.25, 99.76,    100.82, 100.29, 100.27, 100.31, 102.79, 101.69, 102.56, 102.15, 104.54, 108.17,    101.79, 102.04, 101.32, 100.85, 99.1, 96.83, 96.75, 97.23, 97.84, 95.01,    94.87, 94.28, 96.59, 97.83, 96.15, 98.17, 97.7, 95.29, 95.82, 97.05,    94.79, 96.32, 99.1, 98.71, 98.34, 97.28, 99.53, 98.69, 99.56, 99.39,    101.5, 100.89, 97.23, 99.35, 101.55, 99.1, 99.4, 99.33, 100.55, 101.12,    104.48, 106.08, 104.26, 106.52, 108.34, 106.24, 105.95, 103.44, 104.96, 104.46,    107.19, 106.83, 104.73, 103.89, 103.81, 101.68, 98.76, 100.12, 99.72, 99.31,    100.34, 101.1, 99.65, 98.28, 98.92, 101.36, 103.15, 101.98, 101.38, 104.99,    103.88, 104.66, 105.52, 105.99, 106.45, 107.69, 108.35, 108.47, 110.48, 110.34,    108.45, 107.75, 106.32, 106.49, 104.92, 105.62, 102.94, 102.82, 105.32, 104.97,    105.1, 107.19, 105.74, 106.02, 103.25, 100.81, 102.17, 100.61, 100.92, 100.48,    101.25, 98.02, 96.89, 96.4, 95.25, 94.18, 91.6, 88.51, 86.67, 86.33,    86.05, 86.66, 88.49, 86.96, 85.07, 83.48, 83.86, 81.13, 81.38, 82.81,    82.68, 82.27, 82.72, 83.14, 84.93, 81.84, 81.47, 82.31, 80.94, 82.77,    81.43, 84.07, 84.72, 84.85, 85.56, 85.16, 85.77, 85.72, 83.98, 83.23,    84.4, 83.87, 81.29, 79.32, 79.95, 81.29, 81.97, 81.18, 81.22, 82.95,    80.72, 82.22, 83.5, 82.05, 83.4, 79.65, 79.95, 78.02, 75.87, 76.43,    75.68, 75.07, 74.33, 71.12, 72.01, 71.81, 72.53, 72.69, 72.44, 73.33,    73.83, 74.64, 76.35, 76.9, 77.04, 75.98, 74.18, 73.75, 73.68, 73.89,    74.15, 71.69, 71.78, 71.49, 69.96, 69.68, 68.7, 69.15, 67.31, 70.81,    70.64, 70.09, 70.53, 70.31, 70.64, 70.55, 71.25, 72.45, 73.08, 73.54,    74.42, 74.52, 73.21, 72.9, 72.16, 71.05, 72.46, 72.75, 71.08, 69.57,    70.58, 68.45, 71.43, 71.92, 71.79, 71.11, 71.26, 70.03, 68.98, 68.85,    68.32, 67.81, 68.03, 67.15, 66.12, 65.89, 67.07, 66.25, 65.5, 67.16,    68.57, 68.93, 68.13, 68.69, 67.88, 69.03, 70.61, 71.4, 70.77, 69.29,    70.9, 72.13, 74.27, 73.7, 74.35, 73.28, 75.06, 75.77, 73.85, 72.74,    72.29, 72.79, 72.3, 73.63, 75.22, 75.3, 75.55, 74.1, 73.82, 74.8,    74.92, 75.89, 75.9, 76.07, 77.1, 76.49, 73.32, 72.95, 73.4, 76.44,    75.78, 75.48, 73.77, 74.6, 74.87, 73.37, 71.53, 70.76, 70.91, 72.12,    71.81, 72.47, 70.81, 69.78, 69.7, 69.03, 68.65, 68.14, 70.17, 69.15,    66.99, 68.4, 68, 68.91, 71.28, 70.05, 70.53, 73.98, 73.15, 73.56,    73.25, 71.05, 72.55, 74.1, 73.66, 72.63, 72.48, 71.59, 70.58, 70.61,    71.85, 72.14, 71.41, 73.37, 75.11, 72.43, 72.28, 71.8, 70.66, 69.93,    70.07, 69.56, 70.48, 69.65, 69.98, 70.38, 71.84, 72.18, 73.81, 74.64,    74.69, 73.64, 73.3, 72.48, 72.83, 73.7, 74.26, 75.16, 76.51, 76.56,    78.76, 79.02, 76.71, 76.34, 75.73, 74.2, 73.22, 74.02, 71.63, 71.26,    70.51, 70.74, 71.14, 72.48, 73.16, 71.83, 73.75, 74.17, 72.31, 71.53,    70.86, 69.51, 69.51, 70.29, 70.48, 72.24, 71.45, 70.35, 70.79, 71.27,    71.14, 72.51, 73.33, 73.48, 72.58, 73.31, 74.91, 77.81, 79.32, 77.92,    79.36, 80.13, 80.86, 78.81, 80.84, 79.97, 80.07, 77.41, 77.89, 77.68,    78.59, 77.79, 78.2, 76.06, 75.64, 74.62, 75.52, 76.54, 76.14, 76.9,    77.87, 74.2, 75.83, 75.53, 76.46, 75.92, 75.37, 79.44, 80.92, 78.71,    82.66, 81.17, 83.28, 80.79, 81.99, 84.3, 84.99, 86.34, 87.32, 87.88,    86.42, 84.29, 84.95, 86.3, 86.79, 87.05, 86.43, 87.47, 89.55, 91.81,    91.3, 92.07, 93.51, 95.49, 96.59, 95.44, 96.95, 98.63, 98.6, 101.11,    100.11, 98.41, 99.38, 101.46, 101.24, 98.48, 97.44, 97.48, 96.36, 95.08,    98.74, 99.78, 98.94, 101.19, 98.97, 98.83, 98.96, 96.84, 97.82, 98.12,    96.49, 97.01, 93.21, 92.38, 94.76, 94.14, 95.32, 96.07, 96.83, 97.44,    99.83, 98.6, 98.62, 99.63, 99.79, 96.51, 94.69, 95.14, 97.03, 97.8  ],  "series_b": [    49.48, 49.95, 48.68, 48.5, 47.89, 48.74, 48.72, 48.11, 47.72, 47.66,    47.54, 47.91, 47.56, 47.96, 48.9, 47.8, 48, 47.66, 48.13, 48.9,    47.31, 47.11, 46.71, 47.1, 46.57, 46.21, 46.27, 46.92, 46.84, 46.3,    46.18, 46.12, 46.42, 46.52, 45.5, 46.03, 45.57, 44.92, 45.16, 45.88,    45.45, 45.76, 45.87, 45.87, 45.23, 45.04, 45.18, 44.15, 44.88, 44.96,    45.34, 45.15, 44.38, 45.51, 46.42, 46.47, 46.63, 46.35, 46.56, 46.7,    47.62, 48.34, 47.23, 48.19, 49.03, 49.04, 48.64, 47.73, 48.02, 48.34,    48.73, 48.19, 48.18, 47.76, 47.49, 46.96, 46.32, 47.01, 47.34, 47.55,    47.2, 47.21, 47.24, 46.6, 46.43, 47.22, 47.99, 48.39, 48.06, 48.97,    48.89, 49.08, 49.08, 49.83, 48.86, 48.68, 49.11, 48.84, 48.47, 48.82,    47.94, 47.29, 46.95, 47.17, 46.85, 46.77, 46.49, 46.22, 46.96, 47.67,    47.21, 47.67, 47.09, 46.86, 46.32, 45.58, 46.06, 45.82, 45.34, 45.44,    45.27, 45.23, 45.01, 45.2, 44.96, 44.63, 43.41, 42.05, 41.35, 40.59,    40.4, 40.69, 41.18, 40.71, 40.23, 39.89, 40.17, 39.21, 38.92, 39.2,    39, 38.82, 38.86, 39.24, 40.06, 39.56, 38.76, 39.24, 39.03, 39.51,    38.99, 40.23, 40.52, 40.55, 40.48, 40.14, 40.44, 40.33, 39.89, 39.63,    39.86, 39.64, 39.15, 37.96, 38.23, 38.6, 38.81, 38.65, 38.49, 39,    37.95, 38.07, 38.41, 37.93, 37.76, 36.58, 36.79, 36.05, 36.07, 35.88,    35.83, 35.46, 35.3, 34.57, 34.57, 34.11, 34.43, 34.53, 34.36, 34.98,    35.13, 35.29, 35.61, 35.75, 35.59, 35.18, 34.42, 33.74, 33.49, 33.38,    33.36, 32.68, 32.49, 32.41, 32.21, 31.79, 31.78, 32.25, 31.67, 32.53,    32.43, 32.12, 31.81, 31.89, 31.81, 31.62, 31.9, 32.42, 32.79, 33.37,    33.79, 34.24, 33.58, 33.83, 33.53, 33.66, 34, 34, 33.26, 33.06,    32.92, 32.61, 33.52, 33.19, 33.12, 33.23, 33.21, 33.3, 32.89, 33.09,    32.8, 32.45, 32.95, 32.54, 32.11, 32.1, 32.12, 32.14, 32.07, 32.33,    32.48, 32.59, 32.46, 32.11, 31.71, 32.03, 32.58, 32.78, 32.85, 32.5,    32.47, 32.71, 32.91, 33.45, 33.17, 33.18, 33.69, 34.18, 33.91, 33.42,    33.73, 33.55, 33.63, 33.6, 34.17, 34.11, 34.45, 34.04, 33.77, 33.88,    33.57, 33.57, 33.53, 34.16, 34.08, 33.88, 33.18, 33.3, 33.79, 34.15,    34.07, 34.44, 34.24, 34.55, 34.68, 34.18, 33.87, 33.67, 33.35, 33.74,    33.43, 33.47, 33.13, 33.25, 33.08, 32.74, 32.78, 32.75, 33.18, 32.65,    32.03, 32.44, 32.28, 32.07, 32.5, 32.37, 32.62, 33.58, 33.96, 34.12,    33.98, 33.53, 33.84, 33.64, 34.03, 34.11, 33.86, 33.73, 33.1, 33.11,    33.19, 33.34, 33.53, 34.03, 34.71, 33.93, 33.98, 33.9, 33.5, 33.02,    33.26, 33.15, 33.67, 33.63, 33.63, 34.1, 34.28, 34.21, 34.65, 35.18,    35.61, 35.56, 35.3, 35.01, 34.56, 34.77, 34.79, 34.9, 35.42, 35.68,    35.94, 36.42, 35.96, 35.43, 35.36, 34.93, 34.75, 35.11, 34.32, 34.46,    34.34, 34.45, 34.56, 34.55, 34.6, 34.19, 34.65, 35.17, 34.01, 33.58,    33.75, 33.91, 33.29, 33.49, 33.4, 33.8, 33.94, 33.55, 33.97, 34.34,    33.83, 34.5, 34.93, 34.81, 34.93, 35.42, 35.78, 36.17, 36.66, 36.21,    36.43, 36.84, 36.97, 36.4, 37.1, 36.89, 36.92, 36.4, 37.07, 36.82,    36.76, 36.67, 36.63, 36.16, 36.33, 36.37, 36.49, 36.59, 36.94, 37.26,    37.16, 36.37, 36.52, 36.15, 36.23, 36.17, 36.13, 37.07, 37.41, 36.81,    37.82, 37.8, 38.52, 38.25, 38.63, 38.96, 39.22, 39.59, 39.98, 39.77,    39.11, 38.35, 38.23, 38.39, 38.03, 38.21, 38.17, 39.02, 39.34, 40.07,    40.28, 40.99, 41.21, 41.85, 42.31, 42.1, 42.33, 42.5, 42.46, 43.09,    42.35, 42.04, 42.65, 42.89, 43, 41.63, 42.25, 42.16, 42.08, 41.97,    42.66, 43.17, 43.17, 43.85, 43.03, 43, 43.06, 42.22, 42.78, 42.61,    42.24, 42.2, 41.31, 40.9, 41.45, 41.62, 41.6, 41.2, 41.8, 42.07,    42.36, 42.26, 42.77, 42.74, 42.15, 41.47, 40.92, 40.57, 40.35, 40.19  ],  "entry_z": 2,  "exit_z": 0.5,  "cost_bps_per_leg": 5,  "fit_share_pct": 50}

Inputs

Input	Type	Range	Required	What it is
series_a	array	40 to 2000 items	yes	Prices of A, oldest first, above zero. 40 to 2000 points.
series_b	array	40 to 2000 items	yes	Prices of B, same dates and length as series_a.
entry_z	number	0.1 to 10	yes	The walk opens a hypothetical trade when the z-score is past this size. Must be above exit_z.
exit_z	number	0 to 9	yes	The walk closes a hypothetical trade once the z-score is back inside this size. 0 means at the mean.
cost_bps_per_leg	number	0 to 1000	yes	Cost per leg, in basis points. A round trip pays four legs.
fit_share_pct	number	20 to 80	no	Share of the points used to fit. The rest is walked. Default 50.

Hypothetical, and on made-up numbers until you replace them. Nobody traded this, and nothing here is on offer.