BL-EC-004: Capital Scale, and the Three-Clause Test
BIJECTIVE LABS
BL-EC-004: Capital Scale, and the Three-Clause Test
Status: RELEASED
Classification: PUBLIC
Revision: 1
Date: 2026-09-07
1. The declared scale
The programme was designed around working capital of 1,000 to 2,000 USD.
That figure was chosen, not imposed by circumstance, and it was held fixed so
that four months of results stayed comparable. It is the fifth parameter of the
operating envelope in BL-FM-002, and it does more work than any of the others
because it determines three things at once.
It fixes the fee tier. Both venues price on volume. At this scale neither
progression is reachable, so the cost floor in BL-EC-001 is a constant rather
than something to trade toward.
It fixes the minimum viable position. Exchange minimums and tick sizes stop being negligible. A strategy whose per-trade edge is a few basis points on a position of a few hundred dollars is measuring quantities smaller than the rounding.
It determines which mechanisms are reachable at all. Some strategies have a capital floor built into their instruments rather than into their economics, and below that floor they are not available regardless of how good the signal is.
2. The three-clause test
The programme's economic assessment, recorded on 2026-07-28 and unchanged since, is a single sentence with three clauses:
No mechanism satisfies measured edge, cost clearance, and capital fit simultaneously.
Each clause fails differently and the distinction is what makes the assessment usable rather than merely discouraging.
| Clause | What fails it | Rows |
|---|---|---|
| Measured edge | The effect is not there | 18 rows, axis idea |
| Cost clearance | The effect is there and smaller than the round trip | 7 rows, axis cost |
| Capital fit | Both hold and the instrument is out of reach | 3 rows, axis capital or venue |
A reader with more capital changes the third column and part of the second. They do not change the first, which is 18 of the 37 settled verdicts.
3. The clearest capital-bound case
The fragility-conditioned volatility premium is the row where the mechanism is strongest and the capital constraint is unambiguous.
| Measurement | Value |
|---|---|
| Variance risk premium, BTC | +8.10 volatility points, t=22.0, n=1,277 days |
| Days positive | 75.3 pct |
| Variance risk premium, ETH | +3.98 volatility points, t=7.7 |
| Hedged overlay simulation | +1.51 pct mean, t=2.43, n=42 |
A t-statistic of 22 is among the most robust measurements in this archive.
What closed it:
| Requirement | Value |
|---|---|
| Margin per contract | 6,345 USD |
| Loss profile | Unbounded on the short leg |
| Simulated drawdown, optimistic hedged | -10.5 pct |
| Simulated drawdown, pessimistic hedged combination | -27.4 pct |
| Simulated drawdown, unhedged | -79.8 pct |
| Capital required to run with managed risk | 50,000 to 100,000 USD |
Margin of 6,345 USD against declared capital of 1,000 to 2,000 is not a near miss. A single contract is three times the account.
The verdict is CLOSED on capital and venue, classified ENVELOPE-BOUND. The
premium is not in question. The operator was the wrong size for the instrument
that prices it.
4. Why this is a design parameter rather than a shortfall
A reader could take section 3 as an argument that the programme was under-resourced. That reading is available and it is wrong, for a reason worth stating.
The capital scale was set to make the research honest at the size the strategies would actually run. A programme that researches at one scale and deploys at another has an unmeasured gap between the two, and every cost figure it produces is optimistic by an amount nobody has quantified.
Setting the scale first, declaring it, and measuring against it produces verdicts that are correct for that scale and explicitly conditional. The alternative produces verdicts that are wrong at every scale.
The volatility premium result illustrates the payoff. Because the scale was declared in advance, the finding is not "we could not make this work". It is: the premium measures at t=22, the instrument requires 6,345 USD per contract, managed risk needs 50,000 to 100,000, and here is the drawdown profile at each hedging assumption. A reader at that scale has a research result rather than an apology.
5. What changes above the declared scale
Three things, in order of how much they change.
Venue access. The options desk that prices the magnitude class becomes reachable. That is the single largest unexplored route in the record, and it is a capital and business question rather than a research one.
Fee tier. At 5,000,000 USD of monthly volume the Bybit schedule improves, and
several cost-bound rows in BL-EC-001 section 7 move. Reaching that volume
requires either capital or a strategy that trades far more than anything this
programme validated, which is circular unless the capital comes first.
Position granularity. Minimum sizes and tick rounding stop distorting small-position economics, which mainly affects the cross-sectional strategies where the panel is wide and each leg is small.
What does not change: the 18 rows that died because the mechanism is not there.
6. What was not measured
Capacity, in the sense of how much capital each surviving mechanism could absorb before its own transacting degraded the result. No strategy ran at a size where that was testable.
The record therefore cannot say at what scale any of these strategies stop
working from above. It can only say at what scale they were unavailable from
below. BL-EC-005 states this constraint on each row.
7. Cross-references
BL-FM-002 section 6 declares the parameter. BL-EC-001 for the fee tier it
fixes. BL-P2-001 doors 4 and 5a. BL-SD-038 and BL-SD-047 for the
volatility rows. BL-P2-003 section 2.2 for the magnitude class this constraint
blocks.
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