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Open research instrumentBreadth LabArithmetic, not a forecast

Portfolio breadth calculator

How much do strategies diversify when they move together?

How this tool works

More sleeves stops working, and you can see where. A book of equally weighted sleeves, each worth s, sharing a pairwise correlation rho, is worth s × sqrt(N / (1 + (N-1) × rho)). Take that to the limit and the ceiling is s / sqrt(rho), which does not contain N at all. Past a point, breadth is not the lever and correlation is. This is the most important arithmetic in this project and it decides whether its own objective is reachable. Canli Capital, the research house that publishes ALPHAC, runs this calculator free, with no account or key required.

What this is. Closed-form arithmetic under strong assumptions. It shows the SHAPE of the constraint breadth operates under. It is not a forecast of any book, and no output here is a performance claim.

The lab

solid: book Sharpe against N · long dash: the ceiling · short dash: your target

Book Sharpe
0.838
Ceiling at this correlation
2.692
Share of the ceiling captured
31.1%
Sleeves needed for the target
35 sleeves

What this says

3 sleeves give 0.838. Reaching 2 needs 35, and the ceiling at this correlation is 2.692, so the target is reachable but the margin is 0.692.

The live contract permits average pairwise correlation up to 0.15. This is what that permits the book to become.

The assumptions, which are strong

What it assumes

  • every sleeve carries the same Sharpe ratio
  • every sleeve is weighted equally
  • every pair of sleeves shares one correlation
  • correlations are stable, which is the assumption that fails first in a crisis

Real books have none of these. The lab is for the shape of the constraint, not for forecasting a book.

Where the numbers come from

The presets read this project's own published claims: the research-curve average pairwise correlation, the current and planned sleeve counts, and the declared forward Sharpe objective. 0.5 is used as the per-sleeve Sharpe in every preset. It is an illustrative round number, not a measured sleeve figure: no sleeve here has an established forward Sharpe.

The case it refuses

1 + (N-1)*rho must be strictly positive. At zero the equally weighted book has zero variance and an infinite Sharpe, which is refused rather than displayed. A tool that displays an infinite Sharpe for an impossible correlation is doing the opposite of its job.

Why it matters here

This project's live contract permits an average pairwise correlation up to 0.15. Load that preset and read the ceiling: it is the honest answer to whether the declared objective is reachable by adding sleeves, and it is not the answer anyone wants.

Sandbox contract. every input is stored in the URL, so a scenario is shareable and reproducible. no write path to any ledger, artifact, broker or published record exists. outputs are arithmetic under stated assumptions, never a forecast.

Rendered from breadth_lab_contract.json. Related: the Selection Risk Lab and the arithmetic of not fooling yourself. Run this same ceiling arithmetic against your own sleeve count and correlation through the validation API.