Research: money management & fiqh sources

Date: 2026-08-18 · Prepared for: the operator · Status: findings and proposals only — nothing here changes sizing code, rails, or attestations. Every actionable item is gated the way this repo gates everything: measurement first, then a reviewed PR, then evidence before live.

Method. Eleven sources were read and mapped against keel’s actual architecture (execution/sizing.py, execution/guards.py, strategy/promotion.py, the experiments record): ten posts from Will McGinnis’s money-management series on the keeks betting library (2025-04 → 2026-03), Fortune’s Formula (Poundstone, 2005), and a 29-page Arabic research paper prepared for the International Islamic Fiqh Academy (Jeddah) 2019 electronic-transactions seminar: أنواع المعاملات الرقمية المشفرة (“Types of Encrypted Digital Transactions”) by Dr. Mu’taz Abu Jib and Prof. Ashraf Hashem (ARSI). Sources are listed at the end.

Executive summary

1. The most important finding is confirmatory, not new: applied to keel’s measured edges, the Kelly-optimal bet is zero or a small negative number — which is exactly what keel already does. No shipped rule family is net-positive at the venue’s taker fee (the honest result), so every Kelly-variant formula in this literature, run on keel’s own numbers, endorses keel’s refusal to trade live. Fortune’s Formula states the degenerate case plainly: on a fair coin, the Kelly bet is zero. The literature’s “Kelly needs accurate probability estimates” is keel’s promotion gate restated (edge floors + PBO + n≥100 pooled with a diversity floor).
2. Keel’s fixed-fractional risk sizing is the strongest member of the fixed-fraction family the series covers. keel risks a fixed fraction of equity over the stop distance (size = equity × risk_pct / |entry − stop|), not a flat fraction of bankroll per bet; the series’ own conclusion — optimal fixed fractions sit below Kelly, start at 1–2% — matches keel’s risk_pct = 0.01 with notional caps binding separately.
3. Two adoptions are worth building when evidence exists (R1 now, R2 later): a Kelly-diagnostic in promotion/simulate output (report-only), and a quarter-Kelly ceiling on the live path that stays dormant until a rule actually clears the promotion gate.
4. One experiment is worth running on the hourly profile (R3): drawdown-throttled sizing as a graduated complement to rail 11’s binary halt — measured through the trials ledger before any live-path proposal, with the series’ own “slower recovery” cost stated.
5. Three ideas should be explicitly rejected (R5): Optimal-f, streak-driven dynamic sizing, and a Merton/CRRA risk-aversion knob — each for reasons this repo’s own machinery already encodes.
6. The fiqh paper independently argues for keel’s compliance architecture. Its central conclusion — crypto-assets are a wide spectrum of materially different instruments, so no ruling should issue until the asset is precisely defined, per type, by qualified sources — is the fiqh-side statement of keel’s per-product, attested, fails-closed screening. Its recommendation to route rulings through AAOIFI/IFSB standards names the attestation sources keel’s fiqh-basis.md reading list should watch. It is a taxonomy-and-method paper, not a permissibility ruling, so it cannot stand alone as an attestation source.

Part 1 — keel’s existing stack, translated into the series’ vocabulary

Series concept	keel’s implementation	Verdict
Fixed fraction (bet = f × bankroll)	sizing.size: risk risk_pct (1%) of equity over stop distance; DCA uses budget sizing	Stronger variant — risk-defined, not stake-defined
Fractional Kelly (¼–½)	Not implemented — no edge estimate is trusted enough to size on	Correct while no rule clears the gate (see R1/R2)
Drawdown-adjusted Kelly ((1 − d/D) × bet)	Rail 11: binary halt at total 20% / weekly 8% drawdown ceilings	Binary version; graduated version is R3 (experiment first)
CPPI (floor + multiplier)	Rail 11 ceiling ≈ floor at 80% of high-water mark; halt at the floor	Same protective goal, halt semantics; documented framing is R4
Dynamic bankroll (streak modifiers)	Rail 16: consecutive-loss breaker (halts); no-martingale/no-stop-widening rails	Loss half exists as a halt; win-streak sizing rejected (R5)
Naive/flat baseline	simulate benchmarks against DCA (a fixed-budget naive strategy)	Methodological parity; optional extra arm in R6
Kelly’s estimation-error caveat	Promotion gate: edge floors, PBO/CSCV overfitting check, n≥100 pooled with ≥5-product × 10-trade diversity floor	The literature’s caveat, made structural
Ruin protection	Fixed-fraction multiplicative sizing + per-order/per-day caps + exposure $5k + concentration 50% + no leverage	Beyond the series’ model

One translation warning that matters when reading the series from keel’s side: the posts size a stake (fraction of bankroll wagered, binary win/loss); keel sizes a risk (fraction of equity lost if the stop holds, with notional bounded separately by caps). A keel trade’s notional can be a large multiple of its risk when the stop is tight — the README already warns “a tighter stop produces a LARGER position”. Kelly comparisons against keel must therefore be made on risk fractions, not notional.

Part 2 — Findings per source

Kelly criterion (f* = (p·b − q)/b). Maximizes log-wealth growth; bet more with bigger edge, nothing without one; full Kelly is volatile and brutally sensitive to estimation error. keel reading: the formula’s inputs (p, b) are exactly what keel refuses to estimate loosely — and at keel’s measured edges the numerator is ≤ 0.

Keeks 0.3.0 / Merton share (f* = μ/(γσ²), γ = 1 Kelly-like, γ = 2 “empirically typical”). The CRRA framing is the honest generalization of “how much risk do you actually want”. Its own simulation: γ = 2 keeps 84% of returns with 61% less volatility. keel reading: γ is a parameter with no evidence to tune it here; keel’s fixed 1% risk is dynamically more conservative than any γ at thin edges. Rejected as a knob (R5), retained as vocabulary.

Fractional Kelly (f × f*; G(f) ≈ r + f·K − f²K/2; half Kelly ≈ 75% of growth at half variance). The standard practical concession to estimation error; recommended 25–50% for individuals, 10–20% for professionals. keel reading: this is the shape of R2 — a ceiling, never a target, and only once an edge survives the gate.

Drawdown-adjusted Kelly ((1 − d/D) × Kelly). Linear de-risking toward zero at the maximum acceptable drawdown D. Costs: suboptimal growth, slower recovery, parameter sensitivity. keel reading: rail 11 already guarantees the D-bound by halting; the question R3 poses is whether graduating toward the halt beats jumping to it — measurable on the hourly profile.

Optimal-f (Vince). Maximize TWR = Π(1 + f·Rᵢ) over the actual trade history, numerically. The posts’ own caveats: unreliable under ~30–50 trades, “often more aggressive than Kelly”, use a 50–70% safety factor. keel reading: backward-looking growth maximization on a small sample is what the PBO/CSCV gate exists to catch. Rejected (R5).

Fixed fraction (bet = f × bankroll). Simple, no estimates, ruin-proof, slow recovery, ignores edge strength. keel reading: keel’s default posture, done more precisely. The series’ “start at 1–2%” matches risk_pct = 0.01.

CPPI (bet = m × (bankroll − floor)). Floor protection with multiplier exposure; gap risk can breach the floor; cash drag. keel reading: rail 11’s ceiling is a floor at 80% of high-water mark with halt-at-floor semantics; keel’s gap risks (thin books, weekend moves) are mitigated by the #350 spread gate and zero leverage. Framing worth stating in the runbook (R4).

Dynamic bankroll management (base × streak modifier, bounded). Win-streak raises, loss-streak cuts over a 3–5 lookback. The post’s own cons: overreaction to variance, overconfidence on lucky streaks, parameter sensitivity, backtesting difficulty. keel reading: loss-streak protection already exists as rail 16’s halt; win-streak sizing is the psychology the repo’s own hourly caveat warns about — ~250 sequential same-regime trades are not independent draws, so a streak is not evidence of anything. Rejected (R5).

Naive strategy / strategy comparison. Flat betting as a baseline; the comparison post maps risk tolerance → strategy and honestly shows its simulations are single-seed, cost-free, and binary-outcome. keel reading: keel’s DCA benchmark already plays the naive-baseline role, and keel’s own cost-faithful measurements dominate the series’ simulation-based claims. The series’ methodological honesty (state the baseline, same random seed) is worth imitating in any R3 experiment design.

Fortune’s Formula (Poundstone). The history: Kelly (1956, Bell Labs), Shannon, Thorp’s blackjack and Princeton-Newport, and the cautionary counter-example — LTCM, which leverage plus estimation overconfidence destroyed when a half-Kelly posture would not have been. Reviewers’ distillation matches the math: the formula “reduces the risk of ruin” only for those with a genuine edge; on a fair coin the Kelly bet is zero. keel reading: keel’s posture — no leverage, sizing on actual cash, no live trading without a proven edge — is the book’s lesson operationalized. The “dark side” chapter (the formula serving insider edges) underlines why keel claims no edge and measures instead.

The Fiqh Academy paper (Abu Jib & Hashem 2019). A taxonomy of encrypted digital instruments — mined currencies (Bitcoin-generation), utility tokens (Filecoin’s ICO worked example), security/ equity tokens (tZERO), protocol/platform tokens, asset-backed types — classified also by chain type (public/private), issuing authority, and backing. Its principal finding: the term “digital currencies” spans instruments so different in structure, characteristics, and substance that no ruling should issue until the asset under consideration is defined precisely and comprehensively (تعريفاً دقيقاً جامعاً مانعاً), type by type; the new generations demand deeper Shariah study than the first generation received. Its two recommendations: (1) a standing committee of jurists, Shariah researchers, and fintech-literate economists to rule per type; (2) Shariah standards for these assets via AAOIFI and the IFSB, analogous to existing standards for tangible/intangible assets. keel reading: this is keel’s compliance model argued from the fiqh side — classification is per-instrument, supplied by qualified attribution, never inferred; an absent classification is a rejection, not a default pass. See Part 4.

Part 3 — Recommendations (ranked)

R1 — Kelly diagnostic in promotion and simulate output (adopt now; report-only)

Compute, from a backtest’s own fills, the empirical win rate p and payoff ratio b = avg_win / avg_loss, derive f* = (p·b − q)/b, and print in rules promote / rules backtest / simulate reports: kelly_f_star = …; risk_pct 1% = …% of f* (and f* ≤ 0: no edge to size on when negative). Zero behavior change; it makes the sizing-versus-edge relationship visible at exactly the moment a human decides whether to promote, and it restates the honest result in sizing vocabulary. Small, testable, one PR.

R2 — Quarter-Kelly ceiling on the live path (spec now; implement only when a rule promotes)

When a rule first clears the promotion gate, its live risk fraction should be capped at min(risk_pct, 0.25 × f*_forward) — quarter-Kelly, the series’ individual-investor recommendation — computed on forward (paper/live) fills, not the backtest that earned the promotion, and re-derived as evidence accrues. Fail-closed like rails 12/13/17: no computable f* → the cap falls back to risk_pct. Until any rule promotes, this is dead code; writing the spec now (this document) is enough, and implementation should wait for the first credible live candidate so the knob ships with an edge to bind it.

R3 — Drawdown-throttled sizing on the hourly profile (experiment first, via the trials ledger)

Test, in paper only: between a soft floor (e.g. 8% drawdown) and rail 11’s existing 20% ceiling, scale effective risk as (1 − d/D) × risk_pct, with rail 11’s halt unchanged at the ceiling. Record as a threshold_nudge trial in the experiments ledger; judge on drawdown distribution, recovery time, and forgone winners over ≥ n=100 pooled signals. Stated costs, from the series itself and from keel’s own caveat: slower recovery, parameter sensitivity, and a throttle tuned on same-regime sequences. No live-path proposal unless the measured trade-off is decisively favorable.

R4 — State the live account’s floor semantics in CPPI terms (documentation only)

The operator runbook should say what rail 11 already implies: the 20% total-drawdown ceiling is a hard floor at 80% of the high-water mark; below it, exposure is zero (CPPI with halt-at-floor semantics, multiplier effectively 0 past the floor — deliberately not the m > 0 continuous form, which re-risks into a drawdown). Include the gap-risk note and its mitigations (no leverage, #350’s spread gate, per-order caps). One paragraph, no code.

R5 — Explicit rejections (recorded so they are not re-proposed every time this literature is read)

• Optimal-f. Backward-looking TWR maximization on ≤ 100-trade samples is overfitting bait; the PBO/CSCV gate already plays the “is this history real” role with sequence-aware methodology; the source itself concedes unreliability under 30–50 trades and prescribes a 50–70% safety factor — a fudge factor, not a control.
• Streak-driven dynamic sizing. Raising size on win streaks optimizes for the psychology of confidence, not for evidence; keel’s own hourly caveat (sequential same-regime trades are not independent draws) makes a streak exactly the non-evidence it would size on. The protective half already exists as rail 16’s consecutive-loss halt.
• A Merton/CRRA γ knob. A continuous risk-aversion parameter with no data to tune it adds a knob whose every setting is a guess; keel’s fixed 1% risk with hard caps is already more conservative than any plausible γ at current edges. Revisit only if forward evidence ever makes γ identifiable — the same bar R2 sets.

R6 — Optional: a fixed-fraction benchmark arm in simulate (low priority)

simulate already benchmarks against DCA. Adding a flat 2%-of-equity-per-signal arm (the series’ baseline discipline: same fills, same costs, same seed-equivalent determinism) would let future threshold experiments state their baseline the way the comparison post does. Nice-to-have; not scheduled.

Part 4 — The fiqh source and keel’s compliance architecture

The Abu Jib & Hashem paper’s central methodological demand — define the instrument precisely, per type, before ruling; different types are materially different things — is satisfied in keel by construction: keel assets attest records a classification per (venue, product_id) with an attributed human source, screening computes only market facts, and an absent attestation is a rejection (KB §28.4/§65.5; compliance/screen.py). The paper’s call for per-type rulings by qualified bodies names the kind of source an attestation should cite: AAOIFI/IFSB standards as they issue, academy seminar resolutions, or a qualified scholar’s attributed position — never a code-derived guess.

Recommended actions, all operator-level:

1. Add the paper to docs/fiqh-basis.md’s reading list as supporting the taxonomy-per-asset method (it is a method paper for the Fiqh Academy’s seminar, not a permissibility ruling, so it supports attestations’ framing rather than serving as one).
2. Watch AAOIFI/IFSB for crypto-asset Shariah standards — the paper’s recommendation #2. When such a standard issues, it becomes the natural attributed source for allowlist attestations, and fiqh-basis.md should record its arrival.
3. No screening changes. The paper confirms the existing split (computed market facts vs attested classification); nothing in it argues for new rails or new inference.

Part 5 — What this review deliberately does not change

No sizing formula, rail, gate, or attestation changes as a result of this document. The honest result stands unmodified: at measured edges, every Kelly-variant in this literature says what keel already practices — do not bet. The adoptions proposed (R1 now, R2 later, R3 as a paper experiment, R4 as a paragraph) are instrumentation and documentation around that posture, not departures from it.

Sources

1. McGinnis, W. — Kelly Criterion (2025-04-01): https://mcginniscommawill.com/posts/2025-04-01-kelly-criterion/
2. McGinnis, W. — keeks 0.3.0 release (Merton share; 2025-10-15): https://mcginniscommawill.com/posts/2025-10-15-keeks-0_3_0-release/
3. McGinnis, W. — Fractional Kelly (2026-01-16): https://mcginniscommawill.com/posts/2026-01-16-fractional-kelly/
4. McGinnis, W. — Drawdown-Adjusted Kelly (2026-01-23): https://mcginniscommawill.com/posts/2026-01-23-drawdown-adjusted-kelly/
5. McGinnis, W. — Optimal-f (2026-01-30): https://mcginniscommawill.com/posts/2026-01-30-optimalf/
6. McGinnis, W. — Fixed Fraction (2026-02-06): https://mcginniscommawill.com/posts/2026-02-06-fixed-fraction/
7. McGinnis, W. — CPPI Bankroll Management (2026-02-13): https://mcginniscommawill.com/posts/2026-02-13-cppi/
8. McGinnis, W. — Dynamic Bankroll Management (2026-02-20): https://mcginniscommawill.com/posts/2026-02-20-dynamic-bankroll-management/
9. McGinnis, W. — Naive Strategy (2026-02-27): https://mcginniscommawill.com/posts/2026-02-27-naive-strategy/
10. McGinnis, W. — Strategy Comparison (2026-03-06): https://mcginniscommawill.com/posts/2026-03-06-strategy-comparison/ (series code: keeks, https://github.com/wdm0006/keeks)
11. Poundstone, W. — Fortune’s Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street (Hill & Wang, 2005).
12. أبو جيب، معتز & هاشم، أشرف — أنواع المعاملات الرقمية المشفرة (“Types of Encrypted Digital Transactions”), research paper for the International Islamic Fiqh Academy (Jeddah) Seminar on Electronic Transactions, 9–11 September 2019 (ARSI). Local copy: ~/Documents/eBooks/Tradings/QtlrYLgYY_260818_124605.pdf.