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docs(kb): explore source-84 leads — drawdown taper (kept) + Merton γ (promoted) - #129

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docs(kb): explore source-84 leads — drawdown taper (kept) + Merton γ (promoted)#129
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Measures the two candidate leads flagged in KB source-84 §84.16, in the KB's "settled by measurement" style. Adds a stdlib-only study (explore_leads.py, +18 tests → 56 in the dir) and a report, and folds the verdicts back into source-84 §84.4/§84.6/§84.16 + the README index row.

Halal/educational framing preserved — the Kelly family studied as the math of capital allocation, not betting; nothing is wired into keel's execution path.

Lead 1 — dynamic drawdown taper (1−d/D)·f*KEEP as ceiling/diagnostic (not built)

  • Barely engages on keel's 1% base (drawdown rarely reaches even D=0.15; breaker-trips 0% either way) — confirming its value isn't protecting the tiny base.
  • Its payoff is unlocking a higher base: tapered quarter-Kelly at D=0.15 (below keel's 20% hard breaker) dominates both flat-1% on growth (4.27× vs 2.08×, profile A) and untapered ¼-Kelly on safety (median DD 14.9% vs 22.75%; hard-breaker trips 99.8%→0%).
  • Strictly conditional: dominance needs D < the 20% breaker (fails at D≥0.25 and in the p-over-estimated world); a half-Kelly base is too large for any taper to rescue. Only pays off if the base is ever raised off 1% — which §58.11/§84.14 argue against. Parked, with a number.

Lead 2 — Merton γ μ/(γσ²)PROMOTE to diagnostic (not a risk_pct change)

  • keel's implied γ ≈ 24 (floor edge) / ≈ 34 (stronger edge) — 24–34× more risk-averse than full Kelly (γ=1), 12–17× past textbook γ≈2. A crisp "how sub-Kelly are we" number.
  • A single fixed γ is edge-and-variance-aware: γ=24.24 sizes the stronger/lower-variance edge at 1.39% vs the floor's 1.00%, automatically — which flat-1% cannot do.
  • Effective λ = 4.00% / 3.76% of full Kelly, matching keel-1%'s own ~4% figure; ruin stays 0% under the p-over-estimated stress (graceful, like fractional Kelly).

Test plan

  • uv run pytest docs/superpowers/analysis/bankroll_sizing/ -q → 56 passed
  • uv run ruff check docs/superpowers/analysis/bankroll_sizing/ → clean
  • uv run python docs/superpowers/analysis/bankroll_sizing/explore_leads.py regenerates the report (deterministic)

🤖 Generated with Claude Code

…(promoted)

Measures the two candidate leads flagged in KB source-84 §84.16, "settled by
measurement" style. New stdlib-only study explore_leads.py (+18 tests, 56 total
in the dir) writing reports/2026-07-23-drawdown-taper-and-merton-exploration.md.

- §84.4 dynamic drawdown taper → KEEP as ceiling/diagnostic (not built): barely
  engages on keel's 1% base; its value is unlocking a HIGHER base — tapered
  quarter-Kelly at D<20% (below keel's hard breaker) dominates both flat-1% on
  growth (4.27x vs 2.08x) and untapered quarter-Kelly on safety (hard-breaker
  trips 99.8%→0%). Strictly conditional on D<breaker; half-Kelly base too large.
  Only pays off if the base is ever raised off 1%, which §58.11/§84.14 oppose.
- §84.6 Merton γ → PROMOTE to diagnostic (not a risk_pct change): keel's implied
  γ ≈ 24 (floor) / ≈ 34 (stronger edge) — 24–34× more risk-averse than full Kelly.
  A fixed γ is edge-and-variance-aware (sizes the stronger edge 1.39% vs 1.00%)
  where flat-1% cannot be; effective λ = 4.00%/3.76% matches keel-1%'s ~4%-of-Kelly.

Updates source-84 §84.4/§84.6/§84.16 + the README index row with measured outcomes.
Deterministic; 56 tests pass; ruff clean.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
@eaitbrahim
eaitbrahim merged commit 8a7a309 into main Jul 23, 2026
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eaitbrahim deleted the explore/drawdown-taper-merton branch July 23, 2026 09:19
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