Maximum Adaptive Market Adherence (MAMA)

@techreport{disalvatore2026mama,
  title        = {Maximum Adaptive Market Adherence (MAMA): Liquidity, Leadership and Regime — a Rules-Cut Model Book for Liquid Large-Cap and ETF Markets},
  author       = {di Salvatore, S. and E1 (Emergent)},
  institution  = {Assets Bulletin Research},
  year         = {2026},
  month        = {October},
  type         = {Working Paper},
  number       = {v1.0},
  url          = {https://assetsbulletin.com/research/maximum-adaptive-market-adherence}
}

1Motivation — adherence, not forecast

“The Adaptive Markets Hypothesis … implies that investment strategies will also wax and wane, performing well in certain environments and performing poorly in other environments.”

The two earlier desk papers read the index. The Triaxial Regime Hazard reads the hazard that an equity drawdown regime begins — a calibrated base hazard scaled by fragility, macro and the event window, gated by an observed trigger — and Suppressed Hazard Convergence reports whether a drawdown is under way. TRH's P* is the desk's hazard read of a 5% or bigger SPY drop within 10 sessions, on closes — a hazard read, not a forecast. Neither says what a model book should hold, in which universe, or when. The usual way of closing that gap — a committee reading the odds and choosing names — imports the two weaknesses the reads were built to remove: unstated rules and unmeasured turnover. This paper states the method that closes it by rules a reader can replay, and names it Maximum Adaptive Market Adherence.

The name is the thesis. Adaptive is Lo's word: no single strategy works in every environment, so a book must change its risk with the regime and its names with the tape. Adherence is the discipline: the book follows the market as it is — where leadership stands today, how much index risk the tape carries today, whether the leading industry is in its own trend today — and never a forecast of any of them. Maximum is the standard: the reads are taken at every cut from the closes alone, the rules leave no discretionary residue except the one the editor signs, and whatever the stack cannot justify rests in bills rather than in a weaker name. The result is a tactical book in the leading industry of a liquid universe, sized by the regime, with a defensive sleeve held only in assets whose own momentum qualifies them now, with a guardrail around it between the scheduled cuts.

2Nearly three decades of market behaviour — the literature and what MAMA takes from it

The design is not invented; it is assembled from results that held across the nearly three decades in which the US equity market became what it is — index funds and ETFs as the marginal buyer, a handful of mega caps as the source of most of the market's wealth creation, four systemic drawdowns of different speed and shape, and sector rotations that run inside a healthy index for months. Five strands of the literature measured those facts; each contributes one principle to the method, and each has a gap the method had to fill operationally.

“the best-performing 4% of listed companies explain the net gain for the entire US stock market since 1926”

Two of these results shape the universe. Bessembinder's skewness says a book that wants the market's return must hold the names that create it — and they are large. Aggarwal & Wu's manipulation cases, Amihud's illiquidity premium and the post-publication decay of the size premium (McLean & Pontiff 2016) say that whatever a small-cap book earns, it earns in gap risk, in spread and in the company of informed sellers, and that a rules book replayed from public closes cannot earn it at all. Moskowitz & Grinblatt's industry momentum shapes the selection: leadership is a property of industries before it is a property of stocks, so a tactical book concentrated in the leading industry is the direct expression of the evidence, and a diversified book is a hedge against being wrong about it. Faber, Moreira & Muir and the regime literature shape the sizing: exposure conditioned on trend or volatility reduced the left tail in those studies at a cost in up years; that cost is the price of the defensive rule. Lo closes the loop: because the environment changes, the method must learn forward — never by re-reading its record with a new rule.

3Evidence from nearly three decades — replications on free daily data

Each claim of section 2 is replicated on adjusted daily closes from yfinance, 1998-12-01 → 2026-10-16, with rules fixed before the results were read (scripts/mama_research.py). Month-end rules use the last session of each month; everything is gross of costs; the sample is one sample. These are hypothetical replications on past data, gross of costs, on one sample. For each defensive rule we show what it cost next to how it would have behaved in drawdowns.

3.1 Size and liquidity — the four indices through four episodes

Over 26.4 years the small-cap index earned +8.4 % a year against +8.6 % for the large-cap index — less, at 24 % volatility against 19 %, with 1.7 times the share of sessions moving five percent or more. In every systemic episode it fell as far as the large-cap index and in the fast ones further (-41 % against -34 % in COVID). The concentrated technology index is the other lesson of the table: -83 % in the dot-com bust and 3112 sessions to recover, then the highest compound return of the four — the return of leadership is real and its unconditional drawdown is unacceptable, which is exactly why the book that holds it needs HOW MUCH and WHEN beside WHERE.

3.2 Industry leadership persists — the nine-sector rotation

Leadership persists at the industry level long enough to be followed monthly from public closes, and the rotated books fell less than the index in each episode tested, gross of costs — a sector that has led for a year is rarely the one that leads the market down. In this hypothetical test, the six-month variant matched equal weight in return with a shallower drawdown; the twelve-month variant had a higher compound return and a shallower drawdown than both. The live book reads leadership with a faster instrument — relative rotation against the index smoothed over 63 sessions, its momentum over 21 — and takes the consensus of three cross-sectional reads; this replication is the slow, public-data version of the same WHERE.

3.3 The defensive posture — the 10-month switch and what it costs

In this test, the switch would have behaved as intended in slow, systemic drawdowns. It cost returns in up years, when a trend rule is late to get back in. It also lagged in fast drops like COVID and 2022, when a monthly rule reacts too late and sometimes exits at the bottom. Gold hedged the 2008 and 2020 episodes and not 2022, duration hedged 2008 and not 2022, bills hedged all three and paid nothing in between — which is why the live book's defensive sleeve is a basket of assets that have hedged in different regimes, each carried only while its own momentum says it is hedging now, and why the bills line is a last resort rather than a default.

3.4 Concentrated technology against a diversified book — raw and managed

This is the case for a tactical technology book over a diversified one, and for sizing it. Diversification buys its drawdown by giving up half the return; conditioning the exposure of the concentrated book — on its own volatility here, on the regime and the leader's channel in the live method — buys most of the same drawdown while keeping most of the return. The live book does both: the regime sets how much of the book is in strength names (50 to 85 %), and the WHEN read decides how much of that is in the leading industry at all.

3.5 The stack as a proxy — the three reads together

The proxy is deliberately crude — nine sectors, a 10-month average for the regime and for each sector's trend, three bond and gold ETFs as the defensive sleeve, monthly — and it carries none of the live method's instruments: no TRH rung, no SHC date, no relative rotation, no channel by third, no volume read, no guardrail. In this crude, hypothetical proxy, the worst drawdown was about a seventh of the index's and the compound return about two points a year lower. Most of the gap came in sharp rebounds like 2023, when trend rules get back in late (Daniel & Moskowitz 2016). The live method reads risk daily, not monthly. Whether that narrows the gap is for the live record to show: the regime is read daily from TRH and SHC rather than monthly from a moving average, leadership from relative rotation rather than from six-month returns, and the leader's weight from its channel rather than from a binary trend.

4The method — three reads in a fixed order

4.1 The adherence universe

The book's pool is the two upper rungs of the ladder in Fig. 2: the mega caps and the large caps the desk follows — technology, the financial and health-care leaders — and the liquid sector, industry, country and factor ETFs; gold, silver and the international ETFs and ADR leaders as strength, never as a hedge. Nothing leveraged, one broad inverse at most, no thin story stocks. The rule is not taste: every read in the stack is taken from closes and volumes, and only in this universe do closes and volumes carry the information the reads assume (Blume, Easley & O'Hara 1994; Lee & Swaminathan 2000).

4.2 WHERE — leadership read cross-sectionally

RSᵢ = Pᵢ / P_SPY · ratio = 100 · RSᵢ / SMA₆₃(RSᵢ) · momentum = 100 · ratio / SMA₂₁(ratio)          (a relative-rotation read in the style of Julius de Kempenaer's Relative Rotation Graphs — our own approximation, not the proprietary calculation)
leading ⇔ ratio ≥ 100 ∧ momentum ≥ 100 · improving ⇔ ratio < 100 ∧ momentum ≥ 100 ∧ Δmomentum₅ > 0 · weakening · lagging
consensus = the names the three cross-sectional reads agree on (relative rotation · the hot-assets book · the radar sectors), ranked by agreement then score,
            at most two per theme, ten names at equal weight — read weekly on the book's clock (every scheduled cut and seven days after it)

Leadership is a property of the cross-section, so it is read against the index rather than from a name's own return: a name is leading or improving when its relative strength and relative momentum say so on the completed close, and that read is what the growth sleeve's gate (section 5.2) consults for every slot. Above the single-name read sits the desk consensus — the names three independent cross-sectional reads agree on — taken weekly with the volume behind each name: relative volume on the last session, the ten-session up/down volume ratio and the status of any breakout over the prior six-month high (confirmed on RVOL ≥ 1.2, light below 1.0, failed when a close above it within ten sessions is followed by a close back below). The consensus is information between the cuts and a source tier inside them; it becomes the book only through the AB Defensive Guardrail (section 5.6).

4.3 HOW MUCH — the regime sizes the sleeves

G(rₜ, φₜ, σₜ) = DEFENSIVE  if rₜ ∈ {HIGH, SEVERE} ∨ φₜ = Phase 3 ∨ σₜ ∈ {ACTIVE, CONVERGED, REALIZED}
               = GUARDED    if rₜ ∈ {MODERATELY ELEVATED, ELEVATED} ∨ φₜ = Phase 2
               = CALM       otherwise                     rₜ the TRH rung · φₜ the cycle phase · σₜ the SHC state, on the close before the cut

The governor is a lookup, not a fit, and the budgets are the whole of the adaptivity. A DEFENSIVE read does not veto a name — the reads are good at how much and poor at which, and a veto on names in a regime with a handful of observations is the kind of rule a backtest cannot support (section 8). It cuts the growth budget from 85 to 50, raises the defensive sleeve from 5 to 20 and swaps two growth slots for the XDTE + SOXY income pair, so that a cautious book holds an income pair while it waits. The direction of dependence is one way: the index reads govern the book and the book never feeds the reads, which makes the book's record by regime a third validation surface for TRH and SHC (section 7).

4.4 WHEN — the leader's channel, where position outranks momentum

channel  = from the most recent 100-session closing high: floor = min close since, ceiling = max close since, as known on the cut day (never the later floor)
state    = TREND (a new high within 15 sessions) · RANGE (thirds between the rails) · AT THE FLOOR (a new range low on ordinary volume) · BREAK (a new range low on RVOL ≥ 1.2)
weight   : trend → full slot · range: upper third 0 · middle ½ · lower ½, full only on a bounce confirmation (an up-close on RVOL ≥ 1.0) · floor → held, no adds · break → 0, read between cuts

Six-month strength is slow by construction and a healthy index can hide a long sideways range in its leading industry. In our sample (SMH, May to Oct 2026) a name in the upper third more often retested the lows than broke out, whatever momentum said — so inside the growth sleeve the weight of the leading industry follows its state, not its rank, and the sleeve budget HOW MUCH set is untouched: the weight the state frees rests in bills by rule. Section 6.3 reconstructs the semiconductor leader from the end of its last trend under an always-on slot, the momentum rule and this range rule.

5The book — how the method is cut

5.1 Cadence, shape, execution

The book is decided on the close of the last session before the 2nd and the 16th of each month, every line entered at that closing price in exact fractional shares, and released at 6:00 PM ET with the regime and the rule behind each line, live for the next session. It carries 12 to 17 lines — ten growth names, the bills line and up to five defensive slots in CALM; eight growth, the income pair, bills and the defensive sleeve otherwise; the editor's disclosed decision (section 5.7) may add one line — published in weights and percentages only. Between the dates it changes only through the layers of section 5.6.

5.2 The growth sleeve — relative strength behind the rotation gate

screen(i) ⇔ Pᵢ > SMA₅₀(i) > SMA₂₀₀(i) ∧ ¬macd_bear_x(i) ∧ ¬bb_atr_stretch(i) ∧ RSI₁₄(i) < cap(tape, βᵢ)       cap: strong tape 85 · weak 70 · weak & β ≥ 1.5 → 65
rank by  R₁₂₆(i) = Pᵢ,ₜ / Pᵢ,ₜ₋₁₂₆ − 1   inside each source tier:  held (hysteresis, ≤ slots + 2) → M8 in accumulation → the desk consensus (≤ 2) → the semis ETF while it rotates in
         → rotation in (≤ 2, improving quadrant) → six-month leaders → desk shadow / hot assets · one name per theme · equal weight rounded to 0.5 %, residual to bills
gate (d-187):  enter(i) ⇔ read(i) ∈ {leading, improving} · hold(i) ⇔ read(i) ∈ {leading, improving} ∨ (weakening ∧ Δmomentum₅ > 0) · leave otherwise — hysteresis never outranks the read

“The optimal strategy is characterized by two principles: (1) aim in front of the target, and (2) trade partially toward the current aim.”

Selection is mechanical relative strength, where discretion is weakest and the literature is oldest (Levy 1967; Jegadeesh & Titman 1993), in a strict source order so that the desk's own reads enter first and the consensus converges the two books without replacing one with the other. Equal weight follows DeMiguel, Garlappi & Uppal (2009); one name per theme keeps the sleeve from becoming one trade under ten tickers; the hold band is the book's turnover control on the growth side and the ablation of section 6 set its width. The rotation gate is the WHERE read made operational: a gate, not a source — the pool, the ranking and the tier order are unchanged, so the book stays the tactical book it was built to be; the gate only says when a name may hold a slot. It is symmetric (the read that keeps a weakening sector out re-admits it the moment it turns improving) and disclosed name by name at every cut.

5.3 The defensive basket — weight only on confirmed momentum

confirmed(j, t) ⇔ all five checks hold at t ∧ at t − 1      (two consecutive closes to enter · two consecutive failures to leave)
weight = 4 % a slot · best 3-month return first · one name per theme AND per macro cluster (metals · currencies · crypto · duration & credit · equity inverse / vol · trend · commodities · international · defensive equity) · Σ ≤ defensive budget

The basket holds 58 assets that have hedged equity drawdowns in different macro regimes. None hedges every regime and each costs carry when it is not hedging (Baur & Lucey 2010; Israelov 2019) — section 3.3 shows gold, duration and bills taking turns — so the rule asks each name, on the close before the cut, whether it is hedging now, twice. Whatever budget is not confirmed rests in the bills line; an unconfirmed hedge is never replaced by a weaker one. A linear inverse line is capped at 8 % and only one; long volatility enters only on an SHC touch.

5.4 The bills line — a last resort

excess = bills_line − bills_budget(regime)        (unconfirmed defensive sleeve + unfilled growth + rounding residual)
offered to defensive names rotating in vs SPY — utilities · staples · health care · real estate · low-volatility and dividend ETFs · defensive mega caps —
candidate(j) ⇔ quadrant(j) ∈ {improving, leading} ∧ Δmomentum₅(j) > 0 ∧ Pⱼ > SMA₅₀(j) ∧ R₂₀(j) > 0 ∧ theme(j) ∉ themes(book)
slots = min(3, ⌊scope ÷ 4 %⌋, 16 − lines) · scope: the excess by default · + ½ bills budget on a TRH 'temporary dips' read · 0 while the rule's own record reads UNDER REVIEW

The regime's bills budget — 10, 15 or 20 % — is a decision and stands. The blind excess above it is not a decision; it is what remains when defensive-sleeve names fail their checks and growth slots go unfilled, and the method offers it to defensive-equity names that are rotating in against the index, in 4 % slots, with the scope set by the market read and by the rule's own record — never by the pick. It is the first rule in the book to carry its own kill switch.

5.5 Volume last — the first trading day of the month

RVOLᵢ = Vᵢ,ₜ / mean(Vᵢ,ₜ₋₂₀ … Vᵢ,ₜ₋₁) · peer read beside it (sector ETF · SOXX for semis · SPY for ETFs and defensive names)
confirmed ⇔ RVOL ≥ 1.20 · thin ⇔ RVOL < 0.80 · against ⇔ RVOL ≥ 1.30 ∧ r₁ ≤ −1 %  →  thin ∨ against: half the slot, a borderline name dropped, the freed weight to bills
refill: the next name already through every earlier filter, one per theme, that itself reads neutral or confirmed on the day — volume never promotes a name that failed a filter

On the first trading day of the month new capital goes to work and it shows in volume before it shows in price (Ogden 1990). The finished composition is read against that flow last: it may confirm, trim or drop, and refill a freed slot only from names the stack had already chosen — never invent one. The mid-month cut records the same read and acts on none of it; the edition is held while the day-one bar is incomplete.

5.6 The guardrail — the layers between the scheduled cuts

EMERGENCY EDITION (d-168):  fire(T) ⇔ rung(T) ∈ {HIGH, SEVERE} ∧ SHC(T) ∈ {ACTIVE, REALIZED} · notice at 6:00 PM ET · cut DEFENSIVE if fire(T+1) · de-risk only · ≥ 3 sessions apart
AB DEFENSIVE GUARDRAIL (d-193) — the Divergence Key, three legs on one completed close:
   (a) composition   the desk consensus carries ≤ 2 growth names of 10  ∧  the live growth sleeve is ≥ 60 % in leader-cluster names
   (b) the leader    SOXX / SMH in the lower third of its channel, or in break down
   (c) money moving  the antagonist sector's breakout confirmed on volume  ∨  the daily shadow replacing ≥ ½ the growth sleeve on two closes  ∨  the consensus leading the book by ≥ 3 pts fortnight-to-date over ≥ 3 sessions
   turned → ten consensus names take the growth sleeve at equal weight (two per theme, fixed income one theme, bills never) inside the regime's budget; the defensive sleeve, income, bills unchanged
   held to the scheduled cut · once per fortnight · not inside the last two sessions before a cut · ≥ 3 sessions after any emergency or guardrail edition · not while P* ≥ 0.60 or SHC is triggered
THREE KEYS (d-191):  SHC triggered ∧ TRH no longer reading temporary dips ∧ the leader's floor broken on volume → the leader cluster leaves the growth sleeve on that close; SOXY stays, ladder paused

The scheduled cadence is deliberately slow — two cuts a month, each on a close — and the guardrail sets out how the book can change between cuts. Each layer is information until the next confirms it: the weekly consensus read is notice; the antagonist sector's breakout read with volume is confirmation (section 6.4 measures why volume is the test); the AB Defensive Guardrail is the interim rung — when the consensus has moved defensive while the growth sleeve is still in the leader cluster, the leader sits low in its channel and the money is seen moving, the book becomes the ten consensus names at equal weight until the scheduled cut, in lieu of the tactical selection; the three-key step-down from the leading industry follows when the index reads and the channel agree the drawdown is realizing. Every layer works on completed closes, never intraday, never on the book's own P&L; the desk may disarm the Guardrail and hasten but never invent the emergency channel.

5.7 The editor's decision, the income ladder, the learning loop

Three further rules complete the book. The editor's decision (d-189): the rules cut first; the editor may keep, add or exclude named lines for one cut date, each with its reason, funded from or returned to the bills line, stamped in the edition note — never silent, never retroactive, its size from the environment and never from a loss to recover. The SOXY ladder (d-192): the semiconductor covered call is income first and beta second — base 5 % in GUARDED and DEFENSIVE, adding 1.25 % a cut from bills while the leader reads lower third or at the floor up to 7.5 %, unwinding a step while it reads upper third or trend, paused on a break. The learning loop (d-155, d-175): once a fortnight has closed, the Review Engine judges every pick, the full composition sleeve by sleeve and each rule against the counterfactual frozen at the cut, in the market context of the period; each rule carries its record since the entry that adopted it (too early · holding · strengthening · under review) and an under-review rule proposes its own change. The engine never changes a pick or a weight: evidence → proposal → reconstruction ablation → the desk's decision → a dated entry in the register below. The method improves forward; its record is never rewritten and never re-read with a new rule.

6Evidence from the desk's own reconstructions

6.1 Data and method

Daily adjusted closes, opens and dividends of the growth pool (89 names), the defensive basket, the income pair, the bills vehicles, SPY and QQQ from January 2024. The reconstruction starts fully in cash on Jan 2, 2025 (every figure a percentage of the book), cuts at the close before every 2nd and 16th and executes at the next open; dividends are reinvested in the paying name; SPY total return is computed on the same basis. Three proxies stand in for reads that did not exist before launch: the regime is read off the tape (SPY below its 200-day or ≥ 8 % off its high → DEFENSIVE; ≥ 4 % off, QQQ RSI > 70 or below the 50-day → GUARDED), the M8 accumulation tier is a rules proxy, and an SHC touch is never assumed. The pool is the desk's pool as it stands today — a look-ahead by construction. The line is gross of costs; a drag of 5 bps a side is modelled and reported beside it, never netted into it.

6.2 The rules-cut book, January 2025 → today

The rotation gate on the same reconstruction (engine v2.5 → v2.6 variants, scripts/ab_v26_rotation_gate_research.py, Jan 2, 2025 → Oct 13, 2026, 43 cuts, gross of costs): the book without the gate returned +53.4 % at a Sharpe of 1.18 with a −18.9 % drawdown, β 0.91 and an up / down capture of 126 / 122; an entry-only gate +59.9 % · 1.31 · −17.8 %; the hard gate as built — entry gated and held names leaving on rotation out — +59.2 % · Sharpe 1.37 · −15.8 %, β 0.80, capture 115 / 106, with the semiconductor ETF in the sleeve at 10 of 43 cuts rather than 14. The hard gate gives back half a point of return against the entry-only variant and buys three points of drawdown and fifteen points of down-capture for it — the trade the rule was written to make. One sample, one pool. Why these returns differ from R1: R1 runs the current engine (v2.7) and stops at the launch close, Oct 1, 2026, where the live record takes over; the gate study ran the v2.5 / v2.6 engine twelve sessions further, to Oct 13, 2026, across the first two live weeks in which the semiconductor-led book gave back about four points against a roughly flat index — a different engine and a different end date.

6.3 WHEN on the record — the semiconductor leader's channel

From the end of its last trend (2026-05-26) to 2026-10-14 the semiconductor leader moved -6.2 % end to end through a 504–669 range with a -24.6 % drawdown inside it. Under each cut the figure shows the rails as they were known that day and the close by third. One 6.5 % slot held always-on returned -0.30 % points of book over the period, the momentum rule -0.41 %, the range rule — zero in the upper third, half in the middle, full in the lower third on a bounce — +0.49 %: position outranked momentum in a range, as section 4.4 states. A reading on one leader over one range; the rule is applied forward from its entry.

6.4 Volume as the test — 751 ETF breakouts since mid-2024

Two readings. Most breakouts fail — two in three close back below the level within ten sessions — which is why no breakout is a trigger anywhere in the method. And the ones on light volume fail more and go nowhere: 72 % against 59 %, a median +0.6 % against +1.8 % over the next twenty sessions. That is the confirmation layer of the guardrail: an antagonist sector breaking out on light volume while leader names return to the consensus is a rotation that is not confirmed, and the leader may resume.

6.5 The live record

7Relationship to TRH and SHC

TRH reads the drawdown hazard; SHC reports whether one is under way — whether the suppression that keeps that hazard from realizing is exhausted, and when; MAMA says what a rules book holds given both, in which universe, and when. The dependence is one way — the reads govern the book, the book never feeds the reads — so the pairing is not circular, and the book's record by regime (R2) is the reads' own scorecard in allocation space: a DEFENSIVE cut that held up better than the index is evidence for the rung, one that cost is evidence against it. The three papers share one standard: rules set before results, every threshold stated, every method entered dated and applied forward, one sample read as a reading and not a law.

8Limitations and the validation programme

“The higher the number of configurations tried, the greater is the probability that the backtest is overfit.”

The replications of section 3 are on one history with thresholds taken from the literature, gross of costs, on ETFs whose own histories begin between 1999 and 2004; the IWM read starts in May 2000 and the gold switch in 2004. The desk reconstruction of section 6 is twenty-one months on a pool with look-ahead, a tape proxy for the regime and a rules proxy for the M8 read, with forty-odd ablation variants across three runs on that one sample — the situation Bailey & López de Prado (2014) describe, so no Sharpe on this page is an estimate. The volume step and the defensive fill have no reconstruction at all; their thresholds are design choices from the literature, which is why each may only remove weight or hand a slot to a name the stack had already chosen, and why the fill carries a kill switch. The leader's channel is one leader over one range; the breakout study is 751 events in one universe over two years. The Guardrail and the three keys have no reconstruction either — the consensus reads have no history before launch — so their first evidence is live, and the Review Engine judges them from their first edition as frozen counterfactuals. Costs are modelled at a flat 5 bps a side. The programme is the one TRH and SHC carry: the live record accumulates under rules fixed in advance, each rule's status moves on at least four fortnights and proposes on at least eight, and every number on this page is a statistical observation published by a financial publisher — not a forecast, not a track record, not advice.

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