# Risk-budget decumulation -- every weight carries the reason it exists.
#
# STATUS: implementable today from a French retail setup (a taxable account
#   plus the equity-only tax shelters). Same family as
#   dragon-decumulation-household, one generation further: the equity block
#   moves into the tax shelters as far as the RISK budget allows, the bond
#   overlay lost on the way is rebuilt with two issuers instead of one, and
#   every line is labelled by the kind of claim that justifies it.
#   Revised 2026-08: the wrapper logic written down (s. 0), the currency
#   leg of the replication trend line decided on measurement (s. 8), the
#   buffer held outside the weights (s. 14), the forward scenarios mapped
#   onto existing levers (s. 15), the trend sleeve re-examined against the
#   book's own worst months (s. 16).
#   Revised 2026-09: gold cut from 15 to 12 points on the price of the
#   insurance and on its risk share (s. 7), the three points moved to the
#   linkers after a head-to-head on where they should go (s. 2).
#
# Idea: start from the liability (a stream of real euros over ~40 years),
#   immunize the years where a bad sequence is unrecoverable, and spend the
#   surplus on mechanisms that pay a documented premium, not on assets that
#   merely backtested well.
#
# LABELS. Each weight below is tagged by what produced it:
#   DERIVED    falls out of a calculation (the linkers dose).
#   MECHANISM  a documented premium; the dose is a judgement call.
#   HEDGE      no premium at all; the dose is what the covered regime
#              demands (gold, long duration).
#   CONSTRAINT set by a wrapper's rules or by an assumed behavioral limit.
#
# ## Lineage
#
#   Browne's Permanent Portfolio (1981) -> Cole's Dragon (Artemis, 2020)
#   -> a three-line distillation (NTSG, trend, gold) ->
#   hydra-five-engines (one line per return engine) ->
#   dragon-decumulation-household (the same design across French wrappers)
#   -> here. The step this file adds is the liability: the earlier files
#   size sleeves against a portfolio, this one sizes them against a
#   spending stream, and the two answers differ. Since then the book has
#   been re-derived twice from scratch by blind designers (s. 0, s. 12)
#   and reconverged each time. Its weights have moved once since, in
#   2026-09: gold 15 -> 12, linkers 13 -> 16 (s. 7).
#
# ## 0. The wrappers: the shelter tranche is bounded by risk, never by tax
#
#   The setup assumed: a taxable account (CTO), a PEA and a PEA-PME
#   (equity only), and an employee savings plan (PEE) whose world-equity
#   FCPE is the one diversified fund it offers. World equity lives in the
#   PEE up to the ceiling the book's EQUITY budget sets, and not one euro
#   more. Why the PEE despite its fund charges:
#   1. Future gains pay the social levies only (18.6%), and only on exit,
#      instead of the 31.4% flat tax (PFU) paid along the way in a taxable
#      account: each euro of future gain keeps 81.4 cents, not 68.6.
#   2. The latent tax on the gain already accrued stays invested and
#      compounds for the holder: an interest-free loan from the state,
#      repaid pro rata at each withdrawal. That, more than the rate gap,
#      is the engine. Modelled: +16 to +30% of final net wealth per 100
#      kept in the plan over 20 years, for growth of 4, 6 or 8%/yr.
#   3. The bet is reversible AT TAX PARITY: the levies are flat, with no
#      progressivity, so leaving later costs the same rate as leaving
#      today. The converse is false: a euro taken out can never come back
#      (no new contributions once the employment ends). When in doubt,
#      keep it in, up to the equity budget.
#   CROSS-CHECK (2026-08): three blind designers from opposed schools,
#   without access to this file, recomputed the arbitrage and concluded
#   in the same terms: the plan beats the taxable account at every
#   horizon (break-even fund charge 1.83%/yr at 10 years, 1.14% at 20,
#   against 0.5 to 0.62% actually charged, a margin of two to three
#   times), and the tranche kept is sized by the equity budget, never by
#   tax. The doctrine of this section can be re-derived from nothing.
#   SPENDING ORDER in decumulation: taxable account first, then the PEE,
#   the PEA kept in reserve, a life-insurance contract up to its yearly
#   allowance once it is eight years old (s. 14). The PEE is the FIRST
#   DRAW whenever equity is overweight: selling its world fund pays the
#   quarter, rebalances and uses the cheaper exit in one move. To de-risk
#   without tax, switch inside the plan to its money-market fund; to
#   re-risk, the taxable account buys a world fund.
#   Annual watch on the wrapper: all-in charge (feeder plus master), the
#   account fees charged after departure, the quality of the fund range.
#   The position can be exited at any time at the flat rate: a revisable
#   decision, not a lock-in.
#
# ## 1. The numeraire: the risk-free asset is not cash
#
#   Merton, then Campbell & Viceira (Strategic Asset Allocation, 2002):
#   the risk-free asset is the one whose cash flow replicates the
#   LIABILITY. The liability here is real euros for decades. Cash is not
#   risk-free against it (it loses to inflation); a ladder of euro
#   inflation-linked bonds is.
#
#   Consequence 1, how to read the linkers line. Its low expected return
#   IS its function. It is the zero point from which every other line is a
#   deliberate departure that a premium has to pay for. Its job is not to
#   earn, but to guarantee that the floor years it covers arrive intact
#   whatever inflation does. Judge it like insurance, on service rendered,
#   never by comparing its return to equities.
#
#   Consequence 2, why 1-10y and not all maturities. Duration ~4 against
#   ~7-8 for an all-maturity fund: 2022 showed long linkers losing 25-35%
#   DURING an inflation shock (real-rate duration), exactly when they were
#   being counted on. Short maturities buy the indexation without the
#   real-rate bet. An all-maturity linker fund is a real-rate bet, not an
#   inflation hedge.
#
#   Consequence 3, measured rather than hoped (2026-08). Duration 4.5 is
#   still duration: four times less than the all-maturity fund, not zero.
#   In 2022 the line lost more than cash in real terms (-9.0% against
#   -6.6%) because real yields rose. Over 2021-2023 it beat cash by ~1.5
#   pt/yr real, and over twenty years its real drawdown is 10 points
#   shallower (-14.5% against -25.0%). What paid the inflation actually
#   lived through was trend and gold. Judge the line over a decade, never
#   on the year of the shock.
#
#   THE TAX LEAK ON INDEXATION. France taxes the NOMINAL gain, hence the
#   indexation itself. In a taxable account at 31.4% with 2.2% inflation,
#   a linker at ~1.8% real gross nets ~0.5% real (1.8 x 0.686 - 0.314 x
#   2.2); at 5% inflation the real net turns NEGATIVE (~-0.3%). A taxable
#   linker pocket is a structurally leaky inflation hedge, and that is a
#   tax fact, not a fund choice. Cushions, in order: any indexed annuity
#   (outside the tax base), gold and trend (which paid the lived
#   inflation), the option for the progressive scale in decumulation (at
#   an 11% marginal bracket, ~28.9% all-in instead of 31.4%), and the
#   line's short duration. Read this before any urge to grow the line:
#   every added point of linkers suffers the leak.
#
# ## 2. Sizing the linkers by horizon (DERIVED)
#
#   Sequence risk only destroys on the near years, where no recovery is
#   possible; distant years have the horizon working for them. So immunize
#   the beginning and take the risk on the rest. At a floor drawn near
#   ~2.5-3%/yr of capital and discounted at the real yield linkers
#   actually pay (~1%):
#     years 1-3    covered by the cash buffer, held OUTSIDE the weights
#                  (s. 14)
#     years 4-10   ~12-13% of capital          <- the floor of the dose
#     years 4-12   ~16%                        <- the dose retained
#     years 4-15   ~21%
#     years 4-40   ~57%: Bodie's answer, ruin impossible, growth
#                  abandoned. Refused.
#   A household that already owns indexed annuities (state pension,
#   indexed rent, a residual salary) subtracts their present value from
#   the floor first: owning them is what lets a floor worth ~45% of
#   capital be covered by 13 to 16% of linkers. Note that such an annuity
#   starting years out does NOT shrink this dose, because it starts after
#   the immunized window; the derivation is invariant to it, which is a
#   good reason not to reopen this line at every pension scare.
#
#   An independent recount by a blind liability-driven designer landed on
#   the same net liability and the same duration (~26 years). Its
#   corollary is worth keeping: a French state pension is already a
#   long-duration French SOVEREIGN claim, so a France-heavy linker pocket
#   stacked on top concentrates the issuer exactly where the plan's
#   political stress sits. The fund held is ~40% France (the all-maturity
#   index would be ~41% France, 27% Italy): acceptable, but an ANNUAL
#   REVIEW item. Should the pocket ever grow, cap France at ~50% of it
#   and top up with German or Spanish linkers.
#
#   SWEEP VERSUS HEAD-TO-HEAD (2026-08). An isolated Monte-Carlo sweep of
#   the dose over {5, 10, 15, 20} pointed at the top of the range (20
#   bought -2.6 years at the floor in a lost decade for -0.16 pt/yr of
#   median). The full head-to-head against a book at 20 points of linkers
#   erased that edge once gold at 15 and small value at 14 stood opposite:
#   the extra linkers then cost more geometric return than they bought
#   floor years, the two other legs already covering the tail and being
#   better paid. The 13 held, the 10-20 range of s. 10 stays the reading,
#   and going above 13 takes a new head-to-head, never an isolated sweep.
#   The tax leak of s. 1 penalizes every extra point on top.
#
#   THE HEAD-TO-HEAD THAT TOOK THE LINE TO 16 (2026-09). Gold was cut from
#   15 to 12 (s. 7), three points needed a home, and the condition above
#   applied. Candidates: the linkers, world equity, euro 25+, and mixes of
#   them, on the 2005-2025 window and on a deep stand-in one (1987-2025),
#   replayed and then resampled under prudent priors. The gaps are small
#   (a few tenths of a floor year, 1 to 3% of the 5th-percentile terminal
#   wealth) but ordered. EQUITY is the worst home in the tail and the best
#   in the median: worst real drawdown -20.3% against -18.6% for the
#   linkers on the short window, and it raises the risk share of a sleeve
#   that already carries two thirds of the variance. EURO 25+ scores well
#   on priors but deepens a 2022 (-10.5% real against -9.2%) in the very
#   move that cuts a leg absorbing rate shocks (s. 6). THE LINKERS keep
#   the defensive share of the book, its lowest volatility of the set,
#   and the inflation leg like for like. What refused more linkers in
#   2026-08 was a gold line covering the tail and better paid; at four
#   times its median real price, that payment is precisely what is in
#   doubt. The tax leak of s. 1 applies to the three added points and is
#   accepted with open eyes.
#
# ## 3. The premia that actually exist
#
#   Risk is only paid for against a mechanism, never against a track record.
#   EQUITY     covariance with consumption. The widest premium, the
#              soundest mechanism. Anchor its expected return on CAPE
#              (~3% real from today's level), not on the historical mean.
#   TREND      the most robust documented anomaly: a century, every asset
#              class (Moskowitz, Ooi & Pedersen 2012; Hurst, Ooi &
#              Pedersen 2017). Mechanism: under-reaction plus risk
#              transfer. Correlation ~0 to equities, negative in crises.
#              CAVEAT: that century is gross of fees, on paper backtests.
#              Investable UCITS trend (0.8-1.3% plus replication error),
#              net, has a markedly thinner realized Sharpe and an enormous
#              manager dispersion. The premium exists; its NET SIZE is the
#              least certain input in the whole design. Measured on this
#              file's own backcast window (2005-2025, real EUR): the
#              replication leg earned ~3.8%/yr real and the direct-manager
#              leg ~1.2%, an excess over cash of ~3.6%/yr for the pair.
#              The dispersion is not hypothetical; it is the thing the
#              two-leg structure diversifies.
#   TERM       thin today. The line stands on its hedging demand (negative
#              beta to growth shocks), not on its yield.
#   SIZE/VALUE Fama-French, contested since 2000: weaker mechanism, hence
#              a minority share INSIDE the equity sleeve.
#   GOLD       zero real expected return (Erb & Harvey 2013). Not a
#              premium, an insurance, and LOGICALLY THE SAME STATUS as
#              long duration: held for its covariance with bad states of
#              the world. Size it by the regime it covers (section 7),
#              not by a "minimum polite allocation".
#
# ## 4. The risk budget, and the behavioral cap on trend
#
#   Capital shares are not risk shares, and this file is named after the
#   difference. Capital is 42/20/12/16/10 (equity / trend / gold / linkers
#   / duration). At the 15/13 split of gold and linkers it was first
#   written against, the design sat EX ANTE (standalone volatilities and
#   assumed correlations) at roughly 61/23/9/3/4 of variance.
#   MEASURED EX POST, the report's risk-budget block (Euler decomposition
#   of variance on the simulation's monthly contributions, over this
#   file's window, re-run 2026-09 at the current weights) says something
#   different and worth reading twice:
#     equity 68% of variance for 42 of capital and 57% of realized return
#     gold 11% for 12 and 18%
#     trend 11% for 20 and 15%
#     govt bonds 8% for 10 and 5%
#     linkers 4% for 16 and 4%
#   Two lessons. First, a book balanced in CAPITAL across regimes is still
#   an equity book in RISK: two thirds of the variance sits in one sleeve,
#   which is exactly what the defensive lines exist to blunt, and the
#   number to watch when the equity band drifts. Second, the ex-ante 23%
#   for trend was an overstatement: an Euler share prices MARGINAL
#   contribution, so a sleeve that moves independently of the book
#   consumes far less variance than its standalone volatility suggests.
#   Twenty points of trend cost 11% of the risk budget here; the cap below
#   is therefore a behavioral limit, not a risk-budget constraint, and
#   should be argued as one. Gold, meanwhile, is not free: it takes as
#   much variance as it takes capital, and in this window it earned it.
#   And a share measured over twenty years hides the present one: over
#   the twelve months to 2026-09, gold's realized volatility stood near
#   27%/yr against ~16% in the long run, and 15 points of it carried
#   about 40% of the book's variance (32% at 12 points; twelve monthly
#   observations, an order of magnitude). That is one of the reasons for
#   the cut of s. 7.
#   Re-run the block after any weight change (it is the "Risk budget" row
#   of the HTML report) rather than trusting the ex-ante figures above.
#
#   Within that budget, unconstrained optimization would push trend
#   toward 30-45 and gold lower. Refused, for two independent reasons:
#   (a) uncertainty on trend's NET premium (section 3): moving 14 points
#       of risk budget onto the least certain input is optimization under
#       another name;
#   (b) asymmetry of the errors under uncertainty about one's own
#       behavior. Nobody knows in advance how they will sit through a
#       2011-2019 flat stretch in a trend sleeve. A trend leg too small
#       costs a few basis points of missed diversification, invisible in
#       the floor metrics; a trend leg too big, abandoned at the bottom,
#       costs a permanent capitulation on a third of the book at the worst
#       possible moment. Stand where being wrong is cheap: 20.
#   REVISION PROTOCOL: revisable UPWARD on lived evidence only (keep a
#   decision journal through each flat or losing stretch), 20 -> 25 at an
#   annual review only, NEVER during a drawdown of the sleeve, and no cut
#   during a drawdown either. Mitigations: judge trend only at the whole
#   book level, never the line alone; look quarterly, not daily. Base
#   rate: Morningstar's "Mind the Gap" measures ~1-2%/yr lost to timing by
#   investors who all thought they were steady.
#   QUANTIFIED (2026-08): a decumulation Monte-Carlo sweep of the trend
#   weight over {7.5, 12, 17, 22} improves the floor metrics MONOTONICALLY
#   up to 22 in five of six return models (years at the floor in a lost
#   decade: 6.8 -> 2.8 going from 7.5 to 17); the only model that pays is
#   the flat-CTA decade, and only its median (-0.24 pt/yr), never its
#   tail. The regret asymmetry argued above is measured, not just pleaded,
#   and the upward-only revision protocol has numbers behind it. A trend
#   dose of 7.5 (the blind liability-driven designer's) leaves ~2 years
#   at the floor on the table in the bad worlds.
#
# ## 5. The bond tent that does not say its name
#
#   42 points of equity at the start is not "too defensive": it is a
#   rising equity glidepath (Kitces & Pfau 2014) taken deliberately inside
#   the retirement red zone (~5 years before, ~10 after the exit). The
#   defensive start is a TRAJECTORY, not a state: past year ~8, stop
#   refilling the linkers and let equity drift up by not rebalancing it
#   down. Write that in the household's rule page: "no DOWNWARD
#   rebalancing of equity after year 8". Consequence: any comparison of
#   expected return against a static book UNDERSTATES this one, because
#   the return given up is concentrated on the years where it buys the
#   most survival.
#   GUARDRAIL PLUMBING that goes with the tent: if the plan includes an
#   indexed income arriving mid-retirement (a state pension), REBASE the
#   guardrail reference rate at each income step (the exit itself, the
#   end of a bridge income, the first pension). Without the rebase, the
#   pension's arrival mechanically crushes the measured withdrawal rate
#   and a prosperity rule would raise spending for the wrong reason.
#   The same tent seen from the liability: when the pension arrives the
#   net liability drops sharply, which frees part of the base for equity.
#   The upward drift past year 8 is not only a trajectory choice; it
#   falls out of the balance sheet.
#   Name the mechanical loss honestly: against a build centered on a
#   stacked 90/60 core, notional exposure falls from ~130% to ~116%,
#   because cheap embedded leverage was handed back when the equity moved
#   into the shelters. If the floor metrics ever suffer for it, recover
#   leverage at the margin with +1-2 points of long duration (duration is
#   cheap leverage), never with more equity.
#
# ## 6. The deflation leg: two issuers, the dollar left unhedged
#
#   The bond overlay lost with the stacked core is rebuilt by TWO long
#   duration lines, half and half, so the whole leg does not sit on one
#   sovereign complex. This is the only place in the book where the dollar
#   is an asset rather than a risk:
#   1. Two engines add up. In a growth crisis the dollar rises (haven) AND
#      Treasuries rise (flight to quality); a euro holder collects both.
#      2008 measured: about +26% for the unhedged US line against about
#      +7% for euro 25+. The euro sovereign drags its spread risk in
#      exactly when it is needed (2011 showed it again).
#   2. Hedging pays nothing: a EUR-hedged US bond earns the euro rate. The
#      carry buys the removal of currency variance, nothing else.
#   3. The currency risk taken in exchange is small and BOUNDED: 5 points
#      of dollar against an all-euro floor (linkers, euro long duration,
#      the cash buffer, the hedged trend leg).
#   CAVEAT, written for the future reader: the "crisis means USD and
#   Treasuries rally together" playbook assumes a crisis NOT centered on
#   the United States. The 2025 tariff episodes showed the dollar and long
#   Treasuries falling in concert when the shock is US fiscal and
#   institutional: the line can then lose on both legs at once. That is
#   precisely why it is capped at 5 and never averaged up. And 2025 was
#   not the first failure, only the first watched live: in the 1990
#   oil-shock recession (US-centered: S&L, recession, dollar sliding
#   against the mark) the unhedged US line printed -6.7% in EUR while the
#   euro long line printed +5.9%. Both times, the half that paid was the
#   liability-currency half. The two-issuer split is not diversification
#   cosmetics; it is what has actually carried the leg through both of
#   its measured failures.
#   Accepted corollary: outside crises the line moves with EURUSD,
#   visible volatility with no expected return attached. That is the
#   premium on an insurance that pays twice when it pays.
#   DISAGREEMENT INSTRUCTED AND SETTLED (2026-08). The blind from-scratch
#   book preferred to carry its duration INTERMEDIATE and multi-currency,
#   through a stacked 90/60 core, rather than very long and in capital.
#   Its isolated test was real: at equal equity exposure, intermediate
#   multi-currency duration beats a lone euro 25+ line in 2022 (-9.1%
#   against -10.9% real) and on floor years. But the full head-to-head
#   settled it for THIS file: with gold at 15 and trend at 20 opposite,
#   this book measures 2022 at -8.6% real, better than the challenger's
#   -9.4%, and dominates on all six models. The lesson cuts both ways:
#   what helped in the isolated test was the PROFILE (intermediate,
#   multi-currency), not the leverage; and the long pair is defensible
#   only BECAUSE gold and trend absorb the rate shock. Should either of
#   those legs ever be cut, reopen the question of the duration's shape.
#   REOPENED AS ASKED (2026-09), gold going from 15 to 12 (s. 7). The cut
#   moves the book's 2022 by about -0.3 point real; sending the three
#   freed points to euro 25+ would have moved it by -1.6. The long pair
#   stands at 10 points, and this is why the freed points did not go to
#   duration (s. 2).
#
# ## 7. Gold at 12: the dose follows the price of the insurance
#
#   WHY NOT A TOKEN DOSE. Cutting gold to a minimum ("no premium, minimum
#   dose") while keeping long duration for its hedging demand applies the
#   same logic selectively. The regime gold covers (long stagflation,
#   monetary debasement) is the worst-covered regime in the whole book
#   (Neville, Draaisma, Funnell, Harvey & van Hemert, JPM 2021): long
#   duration LOSES there (2022), and trend is slow to turn and is exactly
#   the sleeve capped for behavioral reasons above. Gold and trend are the
#   only two legs of that regime; weakening both at once is incoherent.
#   The dose is what the regime demands GIVEN that the other leg is
#   capped, and 10 is its floor (s. 10).
#   HEAD-TO-HEAD CHECK (2026-08, gold then at 15): a leaner variant at 9
#   points of gold was dominated by this file across six decumulation
#   return models, INCLUDING one where every sleeve is capped at prudent
#   forward priors (gold at 1%/yr real). Gold is paid by its covariance
#   with bad states, not by its 2005-2025 tailwind (~9%/yr real, not to be
#   extrapolated). An isolated weight sweep cannot see this (8 vs 11 reads
#   as noise); only the full head-to-head, in the tails, does.
#   WHY 12 AND NO LONGER 15 (2026-09). An insurance has a price, and the
#   dose follows it. Four measurements, none of them a forecast:
#   1. THE REAL PRICE. Gold deflated by US CPI stood in 2026-09 at 3.97
#      times its 1968-2026 median (4.46 in euros on French CPI), against
#      2.6 at the 1980 peak and 2.5 in 2011. The evidence that a high real
#      price announces a low ten-year return (Erb & Harvey 2013; "Is There
#      Still a Golden Dilemma?", 2024) is WEAK: two independent episodes,
#      and a counter-example running since 2020 (+9%/yr real from a start
#      at 2.35 times). A reason to stop adding, not a reason to sell.
#   2. THE RISK SHARE. At 15 points gold carried about 40% of the book's
#      variance over the twelve months to 2026-09 (s. 4).
#   3. THE PAYOFF BY STARTING PRICE, real returns in EUR. In the stress
#      episodes gold entered below 1.5 times its median, it paid: +71%
#      over 1973-74, +33% from 2007-11 to 2009-02. In those it entered
#      above 2, it mostly did not: -46% from 1980-02 to 1982-06, -31% in
#      2013, -1% in 2022 (the inflation shock itself), -18% from 2026-02
#      to 2026-06. Exceptions: the 2011 euro crisis (+15%) and the 2025
#      tariff shock (+7%). A small sample, one sign.
#   4. THE CARRY. Gold hedges NEGATIVE REAL RATES rather than inflation as
#      such (1980-82, 2013 and 2022 are the three times real yields rose
#      against it). With ten-year real yields near 2.8% in dollars in
#      2026-09, holding a zero-yield asset had not cost as much in twenty
#      years.
#   WHAT THE SIMULATIONS CAN AND CANNOT SAY. A decumulation Monte-Carlo
#   that lowers gold's mean and keeps its co-movements finds the low dose
#   better by construction, so it proves little. Read as a break-even it
#   is more useful: in the tail (5th-percentile terminal wealth), 15
#   equals 10 when gold earns about +1%/yr real on the 2005-2025
#   co-movements, 0% on 1972-2025, -1% on 1987-2025; above, 15 wins,
#   below, 10. The stake is a few percent of terminal wealth either way,
#   and history adds a nuance: when gold gave back its premium (-83% real
#   over 1980-2001) the rest of the book was thriving, so a 1980 cohort
#   replayed on a representative schedule never cut its spending, at any
#   dose. With equity as dear as it was in
#   2026 that comfort cannot be assumed twice, and the one scenario where
#   the dose really bites is equity AND gold deflating together, against
#   15. Hence a small move, inside the range, made by NOT BUYING the last
#   points rather than by selling.
#   THE ONE-OFF IN THE 1970s RECORD. Part of what gold did over 1972-1980
#   was the release of a price administered at $35 since 1934, a spring
#   that cannot be compressed again (s. 12). Taking it out (gold
#   recentred to a zero real return inside the high-inflation regime, its
#   co-movements kept) roughly halves the edge of 15 over 10 in that
#   regime without cancelling it: ruin 1.9% against 2.6%, equal floor
#   years. What remains is covariance; dose on it, not on the level gain.
#   RULE. Target 12, band 9 to 15: sell back to 12 above 15 points, buy
#   only below 9. Go back toward 15 if the real price returns under about
#   three times its median with volatility back near its long-run level,
#   or if real yields turn negative again. No dose indexed on the price
#   itself: replayed in real time since 1972 (expanding median), such a
#   rule moves neither the return nor the drawdown, and bands do the same
#   work without a median to estimate.
#   WHERE THE THREE POINTS WENT: the linkers, s. 2.
#   WHAT GOLD DOES NOT COVER (1990, measured on the deep-history stand-in
#   variant, s. 12): gold is a DOLLAR asset, and in an inflation shock
#   where the dollar falls it can lose double digits for a euro holder.
#   Through the 1990 oil-spike recession, the worst drawdown of the whole
#   forty-year test, gold printed -13.0% in EUR (only -3.1% in USD; the
#   rest is the dollar) while hedged trend printed +16.0% and was the one
#   leg that paid. Read the division of labor precisely: TREND catches the
#   shock as it happens (long energy, short bonds: +16% in 1990, +15% in
#   2022 for the net index); GOLD covers the monetary aftermath and the
#   debasement decade, on its own clock. Judging gold on the shock year
#   is the same mistake as judging the linkers on 2022.
#
# ## 8. What 100 EUR actually holds (the exposure ledger)
#
#   42 equity (of which 14 small value)
#   + ~26.5 nominal duration in 7y-equivalent terms (the euro 25+ line at
#     ~20y duration counts ~2.9x its 5 points, the US 20+ at ~17y ~2.4x)
#   + 20 trend + 12 gold + 16 linkers  = ~116% of exposure, no margin.
#   Against a stacked-core build, equivalent duration is HIGHER (~26.5 vs
#   ~16 points) and concentrated on the very long end: more convex per
#   euro, and better matched to a euro liability for the euro half.
#   Accept the consequence: a ~20y duration line will print -30% in
#   another 2022. That is the line doing its job, and the anti-panic rule
#   must name it explicitly ("do not sell duration after a rate shock").
#   Currency: ~17 points of EFFECTIVE dollar, measured on the whole book
#   at 15 points of gold (EURUSD beta -0.167; per line: the replication
#   trend line -1.04, the US 20+ line -0.93, gold -0.20, small value
#   -0.11), two points above the sum of the lines, not eight; the three
#   points since moved from gold to euro linkers take it to about 16, by
#   those same per-line betas. The ~5 of the US duration line are a
#   crisis asset WANTED and capped (s. 6). The ~10 riding the replication
#   trend line are a POSITION, not a side effect: its EUR share class is
#   UNHEDGED, the NAV carries EURUSD on the whole position (beta -0.94 on
#   real NAVs, correlation only 0.68 with the hedged class of the same
#   sub-fund). Plus the USD inside the global small-value fund; the floor
#   stays in euros. The dollar budget of s. 6 therefore holds, which
#   changes nothing to the cap of 5 on the US line nor to the rule
#   against any further dollar line.
#   THE CURRENCY LEG IS KEPT, AND THAT IS A MEASURED DECISION (2026-08).
#   The hedged class exists (MFEH, LU3359622902, same sub-fund, same
#   0.75%/yr). What the dollar brings the sleeve, backcast 1996-2026:
#   +0.24 pt/yr of CAGR for +2.78 pts of volatility, +18.4 pts in 2008,
#   +18.3 in the 2022 rate shock, -7.9 in the 2025 tariff shock. Hedging
#   lowers the book's volatility, but that is not the statistic bought
#   here: on the drawdown and on the BOOK's worst months hedging degrades
#   (worst drawdown -20.7% against -19.8%, worst 12 months -17.9% against
#   -16.2%), EVEN AT ZERO CARRY, for 0.22 pt/yr of CAGR. No rate gap
#   makes the hedge win, so carry is not the criterion; and the hedge buys
#   nothing where it was hoped for (its gain in the book's worst months is
#   0.00 pt/month, measured). The price is real and accepted: in a 1990
#   (hedged trend +16%, dollar -12% against the mark) the unhedged half
#   of the sleeve hands most of its crisis alpha back to the currency,
#   exactly in the regime where trend is the only leg that pays (s. 7).
#   That is the price of its +18 points in 2008 and in 2022. Reopen only
#   if the book's total dollar exposure ever exceeded ~30 points.
#
# ## 9. Regime map: what hurts a spending household, what answers
#
#   Growth boom            42 points of equity: presence. The small value
#                          share diversifies the mega-cap concentration a
#                          world index carries.
#   Deflation crash        The two long duration lines are bought for this
#                          and nothing else, one in the liability currency,
#                          one collecting the haven dollar on top. Trend
#                          rotates long bonds as the move extends.
#   Disinflation/recession Duration again, plus trend; the linkers keep
#                          their value and pay the floor meanwhile.
#   Trending inflation     Trend short bonds and long commodities (Neville
#                          et al. 2021) plus the linkers accruing the index
#                          by contract. The 2022 configuration.
#   Choppy inflation       Gold and the linkers' accrual. The worst covered
#   (stagflation)          regime and the retiree killer: trend is slow to
#                          turn, duration loses outright. Section 7. The
#                          1990 measurement (deep-history stand-in) adds a
#                          twist: when the shock comes with a FALLING
#                          dollar, gold fails too (in EUR) and trend
#                          alone answers; see section 7.
#   Long equity bear       Trend crisis alpha (Hurst, Ooi & Pedersen 2017);
#                          linkers and duration are what gets spent while
#                          equity is underwater, which is what stops the
#                          sequence from becoming permanent.
#   US-centered fiscal     The uncovered corner, deliberately: the unhedged
#   shock                  US leg can lose on both its legs at once (2025),
#                          hence the cap of 5. Gold is the only answer.
#
# ## 10. Sane ranges, and what leaving them costs
#
#   Ranges are derived from the roles above, then checked against the
#   backtest, never read off it.
#   Equity 42 (35-50). Below 35 the growth engine no longer carries a
#     40-year horizon; above 50 the equity variance share (already ~65%)
#     leaves the other lines nothing to blunt, which defeats the tent.
#   Trend 20 (15-25). Below 15 the sleeve stops moving the book after
#     fees; 25 is the behavioral ceiling of section 4, not a risk one.
#   Gold 12 (10-20). Below 10 the stagflation regime loses one of its only
#     two legs; above 20 a zero-real-return asset is funded out of the
#     growth engine. Inside the range the dose follows the price of the
#     insurance (s. 7): 15 until 2026-09, 12 since.
#   Linkers 16 (10-20). 10 covers roughly the floor to year 8, 16 to year
#     12, 20 to year 15; beyond that the book drifts toward Bodie's
#     abandoned-growth corner.
#   Long duration 10, split 5/5 (8-14 total, the unhedged US leg NEVER
#     above 5). The total rebuilds the overlay lost with the stacked core;
#     the split is issuer diversification, the cap is section 6.
#   Small value 14 inside the 42 of equity (10-18). A contested mechanism
#     gets a minority share of the sleeve, about a third here.
#
# ## 11. Blind spots, stated rather than discovered later
#
#   NO LONG VOLATILITY, the dragon's fifth leg. A crash that completes in
#     days (February 2018, March 2020) is covered by nothing here: trend
#     needs weeks to reposition, gold is unreliable in the first sessions,
#     duration only helps if the shock is deflationary. Accepted because
#     listed long-vol vehicles bleed structurally and a household cannot
#     run an option book with discipline. UPGRADED FROM ASSUMED TO
#     MEASURED (2026-08): a 3-point long-vol sleeve was simulated in the
#     decumulation Monte-Carlo; near-neutral under generous assumptions
#     (-4%/yr bleed, +90% payoff on a <=-30% equity year), NEGATIVE under
#     a realistic one (-10%/yr bleed, +60%). And the retail UCITS shelf
#     was surveyed: the listed VIX-roll product lost ~99% since 2012, the
#     genuine tail funds are institutional-access. Trend buys roughly
#     three times the protection at positive carry. The crash in days is
#     carried by the buffer (s. 14).
#   NO BROAD COMMODITIES beyond gold: an energy shock is reached only
#     through the trend sleeve, which has to catch it first. ALSO MEASURED
#     (2026-08): a 2-point broad-commodity sleeve was tested head-to-head
#     and dragged every model (-2.2%/yr real over 2005-2025, and a prudent
#     prior only caps upside tailwinds, it never lifts a drag).
#   NO CAT BONDS, NO AAA CLOs: the retail UCITS shelf, surveyed 2026-08,
#     offered nothing accessible at a sane cost. Closed.
#   THE EQUITY SLEEVE IS A US MEGA-CAP BET in disguise (world cap weight),
#     and small value is only a partial answer to it.
#   CONCENTRATION IN NAMES, not just in assets: two managers carry the
#     whole trend sleeve, one of them priced at NAV rather than traded,
#     and the sheltered world fund is swap based. Counterparty and manager
#     risk are the price of the wrapper and of the diversification.
#   TAXES ARE OUTSIDE THE BACKTEST entirely, while they are half the
#     argument for where each line is held (s. 0).
#   THE FLOOR IS IN EUROS and much of the equity is not: a long EUR
#     appreciation is a real drag that no line here offsets.
#   CONSIDERED AND REJECTED: all-maturity linkers (a real-rate bet, not an
#     inflation hedge), EUR-hedged long Treasuries (distributing, and the
#     hedge pays the euro yield anyway), keeping a stacked 90/60 core in
#     the taxable account (restores leverage but wastes the shelters), a
#     single trend manager (manager risk on the least certain premium),
#     cash instead of linkers (see section 1).
#   CONSIDERED, MEASURED AND REJECTED (2026-08, on the long-window
#     stand-in variants of s. 12): a broad-commodity sleeve, 4 points
#     carved out of gold as a standing oil-shock hedge. Over 1996-2026 it
#     costs 0.21 points of CAGR a year, deepens the real drawdown from
#     -19.4% to -21.8% (it loses a third of its value across 2008) and
#     drops the worst rolling 5y from 0.80% to 0.28%, for about +0.6
#     points in 2022: a premium paid every year for a hedge that pays once
#     a decade, and whose exposure the trend sleeve already RENTS when it
#     trends (+16% in 1990, +15% in 2022 for the net index). An oil shock
#     is a spike that reverses (WTI +112% June-October 1990, then -29% in
#     1991), not a state to hold. Also measured and refused: floating-rate
#     cash in place of part of the linker line (nil effect: 13 points at
#     duration 4.5 weigh 0.6 duration-points on the whole book).
#
# ## 12. Backtesting this file
#
#   RE-DERIVED AND STRESSED (2026-08). As an adversarial check, the same
#     liability was handed to three blind designers from opposed schools
#     (liability-driven, all-weather risk-balanced, capital-efficient
#     return-stacking), plus an instrument-universe survey, WITHOUT access
#     to this file. Their synthesis reconverged on this architecture: the
#     same two trend vehicles, the same euro linkers fund, the same
#     "equity budget first, tax wrapper second" doctrine, ~116% notional.
#     The head-to-head decumulation Monte-Carlo that followed (monthly
#     real-return panel 2005-2025, 5000 paths, six return models including
#     capped prudent priors, floor-years / first-cut / terminal-wealth
#     metrics) kept THIS file dominant over the blind challenger on every
#     model, prudent priors included (lost decade: 2.3 mean years at the
#     floor vs 5.0, P90 11 vs 23; prudent priors: 3.2 vs 3.9). The
#     drivers, at the weights of 2026-08: the small-value tilt, gold at
#     15 (12 since 2026-09, s. 7), and two drags on the
#     challenger's side (broad commodities, an oversized near-zero-real
#     linkers block). Ruin stayed <= 0.1% for both, which ruin saturates
#     near zero for any sane book, which is why section 13 steers on floor
#     years rather than on a ruin probability.
#   THE WINDOW'S TAILWINDS, to keep in mind when rereading it (real,
#     2005-2025): world equity 6.6%/yr, the Europe small-value manager
#     10.3 (real manager alpha, but not an index: manager risk), gold 9.2,
#     replication trend 3.8, direct trend 1.2, the euro linkers 0.1, euro
#     govt bonds 0.4, US 20+ 1.8, euro cash -0.9, broad commodities -2.2.
#     The prudent-priors model clips exactly these tailwinds and the
#     domination holds: the verdict is not the window's alone.
#
#   WHAT THE WINDOW CAN AND CANNOT SAY. The common period starts 2005-11,
#     bounded by the linkers line. It contains 2008, 2011, 2020 and 2022,
#     and therefore says something about deflation crashes and about a
#     trending-inflation year. It contains no 2000-02 and no 1970s, so the
#     regime this book fears most, a long choppy stagflation, is ABSENT
#     from the sample: the gold and trend doses rest on outside evidence
#     (section 7), not on these twenty years. Measured over the window,
#     pre-tax and before any withdrawal (2026-09, current weights): CAGR
#     ~7.7%, volatility ~7.4%, worst drawdown ~-19%, worst rolling 5y
#     ~+0.6%/yr, weighted ongoing charges 0.58%. Read the drawdown and
#     the worst 5y, not the CAGR.
#     For ruin probabilities rather than a single path, feed the file to
#     `pofo -fire`, which resamples instead of replaying.
#   THE LONG WINDOWS (2026-08, on measured stand-in variants of this book,
#     1996-03 and 1986-12, since retired). Same weights, the youngest
#     lines swapped for deeper stand-ins and the swap MEASURED first:
#     linkers -> cash (effect ~nil); the two trend funds -> the BTOP50
#     index EUR-hedged at about half its risk (-0.74 pt of CAGR); small
#     value -> a US small-cap value index (+1.2 pts of volatility). Every
#     substitution error points DOWN: read the deep variant as a FLOOR.
#     (1) The dotcom test passes: 2000-03 to 2003-03 at -13.5% against
#     MSCI World's -55.2% in EUR, +2.5% cumulative over 2000-2002 against
#     -44.5%, +60% over 2000-2007 against -13%.
#     (2) The forty-year worst drawdown is NOT 2008 and not the dotcom
#     bust: it is 1989-06 to 1991-06 (-20.7%, pessimistically measured),
#     oil spike plus recession plus rates plus a FALLING DOLLAR, i.e.
#     exactly the regime section 7 names as worst covered. The design
#     predicted where its weakness would be and four decades of data put
#     it there. 1990 in EUR, line by line: world equity -27.4, gold -13.0,
#     US 20+ -6.7, euro 25+ +5.9, cash +8.3, hedged trend +16.0 (the one
#     leg that paid; hence s. 7, s. 8 and the annual check of s. 13).
#     (3) The passage is paid in advance: 1997-1999 the book compounds
#     +58% against the index's +115%, three straight years of trailing by
#     12 to 24 points BEFORE the three years that repay it. Nobody holds
#     that without having written down, in advance, that it is the plan:
#     it is the trend protocol of s. 4 at the scale of the whole book.
#     (4) 1994, the bond crash: US 20+ -17.0, euro 25+ -10.4, gold -11.2
#     in EUR, the three hedges falling TOGETHER; trend +1.7 and cash +7.1
#     the only shelters, the book -4.6%. No offsetting leg exists in that
#     regime: what decides the damage is the starting carry (s. 13).
#     (5) THE CORE ALONE THROUGH 1972-1982 (the 82 points that have a deep
#     history, renormalized, no trend and no linkers; DM numeraire,
#     deflated by German CPI; US small value as stand-in): +6.7%/yr REAL
#     over the decade against -0.3 for world equity, 1973-74 at -33.7%
#     real against -58.3. The honest reading is uncomfortable: ALL of the
#     rescue comes from gold (+46% and +48% in DM in 1973 and 1974, +113%
#     in 1979, the only line positive with cash through the shock), and
#     that gold was leaving an administered price of $35: a compressed
#     spring unique in history, not reproducible. Both duration lines
#     cost for TEN YEARS (the US line negative in DM almost every year
#     until its +69% of 1982); cash was a real floor only for a mark
#     holder (+1.65%/yr real); for a French holder -0.1%/yr real BEFORE
#     tax on the nominal (s. 1, the tax leak: clearly negative after).
#     Conclusion for the younger assets: trend and linkers are not
#     gadgets, they are the SECOND and THIRD legs of the regime the core
#     crossed only thanks to a historical accident of gold, which is the
#     role s. 7 assigns them, now dated on the decade that matters.
#     (6) COHORTS WITH REAL CASH FLOWS: historical start dates replayed
#     with a representative schedule (a bridge income, then an indexed
#     pension; real withdrawals at a target, a base 10% below and a floor
#     20% below, plus a flexible rule dropping from target to floor while
#     underwater; French CPI, German before the euro). NO RUIN anywhere,
#     even at the rigid target: not 2000, not 2007, not 1989, not 1972-73
#     on the core without trend or linkers. Worst real troughs: 0.80 of
#     the start (2001 and 2007 cohorts), 0.64 (1973, core alone, an upper
#     bound on the damage). The spending LEVEL barely moves the trough
#     (0.83 / 0.84 / 0.85 for 2000 at target, base, floor): the trough
#     belongs to the markets. Years at the floor under the flexible rule:
#     0 in most cohorts, 4-5 for the worst modern starts (2000-2001), 7
#     for 1972-73 on the core alone. Ten years in, the 2000 cohort at
#     target is back at par (1.05): hence the 4-10 tent and a full buffer
#     at the start.
#     The objective has THREE terms, not two: consumption (the target), a
#     spending floor, and a WEALTH floor late in life, the self-insurance
#     against longevity and long-term care that also buys sleep (of the
#     order of ten years of floor spending still in the account around
#     90; an order of magnitude, not a rule). Terminal wealth has utility
#     UP TO that level, not beyond. Hence: (a) the rigid target costs
#     nothing, historical terminals (x2.1 to x4.9 over 30 years) clearing
#     any serenity floor by far; it would bite only on paths worse than
#     all of history. (b) An upward ratchet is CONDITIONAL: raise spending
#     only if the projected real path keeps the serenity runway past ~90
#     (amortize toward the serenity floor at ~95, not toward zero). (c)
#     The deferred annuity of s. 13 is the tool of the BAD tail only: it
#     manufactures a guaranteed runway when capital has drifted low; in
#     the median the visible stock does the serenity job better. (d) A
#     steering metric for the reviews: real wealth P5 at ~90 against the
#     serenity floor. Caveats: withdrawals are pre-tax, and the cohort
#     ranking follows the ENTRY valuation: a start at a high CAPE
#     resembles the 1996-2000 starts, not the post-crash ones.
#     (7) READING THE `pofo -fire` MODEL LADDER FOR THIS BOOK. The models
#     are a DELIBERATE ladder from optimistic to grim; the trap is to read
#     the last column as a probability. Ruin measured with the same kind
#     of schedule (40 years, 5000 paths):
#       model                        rigid target   floor   flexible
#       Student-t, CAPE (central)        4.3%        0.4%     1.2%
#       Broad-sample (60/40 dom.)       11.8%        6.1%     8.3%
#       Lost decade (mu at CAPE)        41.7%       18.7%    27.8%
#     The CENTRAL CAPE column is the planning column, consistent with the
#     cohorts and with the head-to-head. The BROAD-SAMPLE model ignores
#     this book BY CONSTRUCTION: a domestic 60/40 in ~10-year blocks of
#     ONE country's history, calibrated on the ~2.26% safe rate of
#     Anarkulova, Cederburg & O'Doherty; its ruins are failures of states
#     (Austria, Japan, Germany), not of allocations, and its 6.1% at the
#     floor puts that floor AT the most pessimistic literature's safe
#     rate. The gap down to ~0 on the book's own models is international
#     diversification plus the hedge legs, which it cannot see: its job is
#     to bound, not to predict. The LOST DECADE x CAPE column counts the
#     compression TWICE (the CAPE anchor already prices the compression
#     decade, the sticky bear subtracts it again, and the equity mean is
#     applied to all of the book while 58 points are not priced off CAPE):
#     ~1.2-1.5%/yr blended real over 40 years, a stated stress, never an
#     expectation. Never reopen the weights on the strength of that
#     column. The floor passes even the hardest external model at the
#     literature's threshold; the target is carried by the flexible rule
#     and by what these models do not model.
#     Deep-variant caveats: euro duration before 1999 is a euro-area
#     aggregate at pre-convergence coupons (~11%, Italy ~13.5%), so its
#     +5.9% of 1990 would be -0.4% for a pure Bund: do not conclude that
#     euro long bonds absorb rate shocks. The 1980s BTOP50 rests on a
#     handful of programmes (its +57.6% of 1987 is one concentrated
#     record). The small-value stand-in adds ~9 points of USD the real
#     book does not carry, part of the -20.7% of 1990.
#   ERESMONDEM is the 75/25 blend of two Xtrackers MSCI World ETFs less the
#   FCPE's 0.41%/yr wrapper charge (0.56%/yr all-in per its KID), real NAV
#   from 2024-03, backcast from 1971. Never write an FCPE's QS-prefixed
#   code in a portfolio file: the fund has no public listing and an ISIN
#   search returns an unrelated asset; use the catalog id.
#   DTLA has a clean total-return backcast from 1962. Its EUR-hedged
#     cousin DTLE (IE00BD8PGZ49) is set aside twice over: a distributing
#     class (coupons taxed every year in a taxable account) whose public
#     series is a
#     PRICE return that ruins any backtest, and the hedge converts the US
#     yield into the euro yield anyway. Use DTLETR to look at the hedged
#     segment's total return.
#   CHSN backcasts cleanly to 2005-11, which is what bounds this file's
#     common window. A US TIPS 1-10 stand-in is not a substitute: US CPI
#     base, different series.
#   THE DIRECT TREND SHARE CLASS is chosen on fee PLUMBING, not on past
#     returns, and the reasoning generalises to any multi-class fund
#     (details in pofo docs/specs/aqr-mf.txt). Every EUR class of that fund
#     holds the same portfolio, so comparing two of them on NAV measures
#     their fee difference and never the manager. What each levies INSIDE
#     its NAV: 0.23%/yr for the cheapest class, 0.78% plus 10% of the
#     gains above cash for the performance-fee one, 1.26% flat for the one
#     held here. The flat class wins on two grounds. Its whole cost sits
#     in the quoted price, so the backtest above is what a holder gets.
#     And a performance fee bills the most in the years trend explodes,
#     which are the crash years this sleeve exists to pay the floor
#     through: at +40% it takes 3.7 points against 1.26, surrendering a
#     quarter of the very crisis alpha it was bought for. The cheapest
#     class is cheapest only because its management fee is WAIVED at the
#     manager's sole discretion, revocable without notice, and leaving
#     after a revocation realises a taxable gain. Break-even between the
#     flat and performance-fee classes: an excess of 4.8%/yr over cash.
#   WEIGHTS ARE INTEGERS on purpose. Half a point is worth less than the
#     drift between two rebalancings, and far less than the width of the
#     sane ranges. They are rounded off a design logic, never optimized
#     (DeMiguel, Garlappi & Uppal, RFS 2009: twenty years of data do not
#     estimate means well enough to beat equal weighting out of sample).
#
# ## 13. Running rules
#
#   - Rebalance on bands, executed in the taxable account; spending IS
#     rebalancing. Inside the shelters the only trades available are
#     equity for equity and, in the PEE, a tax-free switch to its
#     money-market fund (s. 0), so no move between the book's sleeves
#     happens there.
#   - Always use limit orders on the thin LISTED lines (linkers, the
#     replication trend ETF, euro 25+). The direct trend fund is not
#     listed at all: it deals at the day's NAV on an early-afternoon
#     cut-off and settles three days later, so there is no price to
#     limit, and a rebalance that pairs the two trend legs has to budget
#     for the one-day lag between them.
#   - One management day per quarter: withdrawal, bands, journal.
#   - Annual review: trend 20 -> 25 on lived evidence only (section 4);
#     the unhedged US leg never above 5 (section 6); the total expense and
#     fund range of each shelter; re-run the withdrawal simulation with
#     current capital and age. Also check that BOTH trend managers still
#     trade energy and commodities, not only financials: in the oil-shock
#     regime the trend sleeve is the only leg that answers (1990, 2022),
#     and a CTA that has drifted to purely financial futures silently
#     vacates that post. The replication leg stays in its UNHEDGED class
#     (s. 8): reopen that only past ~30 points of total dollar exposure,
#     never on a move in rates.
#   - A YOUNG OR SMALL SHARE CLASS (the direct trend class today): the
#     spread is a non-issue (a one-off ~20-40 bps on a 10-point line is
#     2-4 bps of the book, and orders are limited anyway). The real risk
#     is the CLASS CLOSING, and it forks. Closed by MERGER into a sister
#     class of the same sub-fund, it should benefit from the tax deferral
#     French law grants fund mergers (art. 150-0 B CGI, cost basis kept;
#     confirm in the BOFiP when it happens). Closed by FORCED REDEMPTION,
#     it is a taxable sale at 31.4% on the accrued gain, plus days out of
#     the market and a repurchase elsewhere. The expected cost therefore
#     scales with the latent gain at closure, hence an ASYMMETRY: at the
#     INITIAL purchase (gain starting at zero, worst case ~0.03-0.06% of
#     the book if the class dies within 1-2 years by forced redemption) a
#     small class is ACCEPTABLE; an assets threshold of 50-100 M only
#     makes sense for a SWITCH out of a line already held, which would
#     crystallize its gains as well. What must prove itself is the CLASS,
#     not the sub-fund: check its size, and check that the broker really
#     serves it to a French resident (France registration is required
#     only of French brokers).
#   - Duration vulnerability is read off the STARTING long yield, not
#     rebalanced away: at 8-11% coupons the 1990 rate shock left euro long
#     bonds positive; from ~1% carry the same shock in 2022 cost -38%.
#     The current euro long yield is the gauge of how bad the next 1994
#     would be; it changes what to expect, never the weights.
#   - Steering metrics: years spent at the floor, median year of the first
#     cut, median terminal wealth, real wealth P5 at ~90 (s. 12). NOT the
#     Sharpe of a 20-year backtest: its second decimal is estimation
#     noise, and a pre-tax backtest is structurally blind to the wrapper
#     arbitrage this design rests on (18.6% deferred against 31.4%).
#   - Rebase the guardrail reference at each income step (s. 5).
#   - Test the progressive-scale option against the flat tax EVERY year
#     of decumulation: at an 11% marginal bracket, scale plus social
#     levies minus the deductible CSG is ~28.9% all-in against 31.4%.
#   - Harvest realized losses in the taxable account each December (ten
#     year carry-forward in France): on a book of 7+ decorrelated lines
#     there is almost always a loser to purge, worth ~0.15-0.25%/yr.
#   - SURVIVOR FALLBACK, written in advance: a two-page notice plus a
#     three-line replacement book (35 world equity / 45 euro linkers 1-10
#     / 20 gold, rebalanced once a year), switched AUTOMATICALLY if the
#     managing spouse dies, no waiting for a good market moment. Measured
#     cost of the simplicity: ~-0.2 pt/yr real and the loss of the
#     conditional hedges (a 2022 at ~-14% real instead of ~-9). A design
#     nobody can run when its designer is gone is a design flaw.
#   - DEFERRED LIFE ANNUITY decision point: mandatory review at ~75, buy
#     if capital has drifted more than ~25% below its median trajectory.
#     Late annuitization is the cheapest longevity insurance for the
#     beyond-the-horizon tail: mortality credits become significant, and
#     French taxation of purchased annuities improves sharply with age at
#     purchase (30% of the annuity taxable when bought after 70).
#   - REGISTER OF FOREGONE RETURN, against the unease of being "nibbled":
#     every return given up is entered here with what it buys, so the
#     total is seen rather than felt. Deliberate ones, pre-tax:
#       the PEE fund charge on 23 points, ~-0.12%/yr: buys the 18.6 vs
#         31.4 tax wedge plus the float of s. 0 (modelled at over 1%/yr
#         of net-of-tax equivalent);
#       giving up the stacked core, -0.07 to -0.14%/yr of notional handed
#         back (130 -> 116), the intermediate multi-currency duration
#         profile that won the isolated test (s. 6), and the attachment
#         to a design one liked (a real behavioral cost: a book one likes
#         is held better). Against it: the tax wedge (a stacked core fits
#         no shelter), a HIGHER equivalent duration in exchange (s. 8),
#         and a head-to-head this book wins BECAUSE gold and trend absorb
#         what the intermediate profile absorbed.
#     Total deliberate: ~0.3-0.4%/yr pre-tax. Identified against it: loss
#     harvesting +0.15-0.25, the cheaper Europe small-value class +0.05,
#     the progressive scale in low-bracket years (~2.5 points of tax),
#     and the PEE wedge. NET CLEARLY POSITIVE: cents pre-tax against tens
#     of cents after tax and in the tail. Two reading rules: (a) "losses"
#     measured against vehicles a French retail holder cannot buy are not
#     decisions but the price already paid for the setup, never counted
#     twice; (b) the item that really eats return is behavioral (Mind the
#     Gap, 1-2%/yr): one capitulation costs more than ten years of all the
#     items above, and avoiding it is what they buy.
#     RULE: a new sacrifice is accepted only if it improves a measured
#     steering metric OR its net-of-tax gain exceeds its pre-tax cost; the
#     DISCRETIONARY budget is capped at ~0.5%/yr pre-tax, beyond which
#     something is removed before anything is added.
#
# ## 14. The buffer held outside the weights
#
#   The weights cover the invested book. Two reserves live apart, and
#   neither is ever counted in the weights or in the solvency of any line
#   above:
#   THE BUCKET, years 1-3 of spending (net of any bridge income), in two
#     halves.
#     The FAST half: a euro overnight-rate money-market ETF (XEON,
#       LU0290358497) in the taxable account. The first draw: settles
#       next day, no duration risk, the short rate capitalized.
#     The SLOW half: the capital-guaranteed euro fund of a French
#       life-insurance contract, zero unit-linked. Its gains pay 17.2% of
#       social levies (life insurance was left out of the 2026 rise to
#       18.6%), and after eight years a couple's yearly allowance
#       (EUR 9,200 of gains free of income tax) applies. The sizing is
#       DERIVED: that allowance is worth at most 9,200 x (31.4 - 17.2)%,
#       ~EUR 1,300 a year over the taxable account, which a 0.5%/yr
#       unit-linked charge consumes past ~EUR 250,000 of units. Hence a
#       PURE euro fund, and a SMALL contract.
#   THE PRECAUTION: regulated savings accounts (Livret A, LDDS), outside
#     the market and outside the plan.
#   Rules: the bucket is drawn only when the book is in a real drawdown
#   deeper than 10%; the money-market half first, the euro fund second;
#   refilled as a priority once the book is back within 5% of its peak.
#   It is what carries the crash that completes in days (s. 11), which no
#   line of the book covers.
#   Considered and REJECTED: replacing part of the bucket by a contingent
#   lombard credit line. It is revocable, its capacity is correlated with
#   the very crisis it would serve, and its rate floats. Free optionality
#   is acceptable as a second line if it costs nothing; never a
#   substitute.
#
# ## 15. Forward readings, 2026: each scenario lands on a written lever
#
#   Forecasts cannot add a line; their one use is to check that no
#   plausible scenario demands a lever this file does not already hold.
#   Checked, scenario by scenario, each mapped onto the regime map of
#   s. 9 and onto its measured anchor:
#   A. AN AI-BUBBLE BUST (a slow deflationary crash). Anchor: 2000-02,
#      +2.5% cumulative against -44.5% for world equity (s. 12). The
#      analogue is structurally sound: the same valuation gap between
#      mega-cap growth and value as in 2000, and the 14 points of small
#      value are the SPECIFIC asset of the rotation that followed. The
#      2026 twist: if inflation stays sticky (tariffs, energy capex) the
#      Fed cuts little and the scenario takes the shape of 2022, not of
#      2001: duration helps less, trend and gold carry. Expected: flat to
#      -10% real. Levers: small value, trend, bands.
#   B. A DOLLAR DEVALUATION WITH RISING US RATES ("sell America"). Anchors:
#      2025 (tariffs) and 1990 (the US 20+ line -6.7% in EUR). Gross
#      dollar sensitivity ~35-40 points (5 US duration, ~10 replication
#      trend, ~20 of US equity, part of small value): a 20% devaluation is
#      ~-7 points of translation plus the de-rating. Against it: gold IS
#      the asset of monetary distrust, the euro long line collects the
#      flight to the Bund, and short dollar is the cleanest trend trade
#      there is (a slow, trending scenario by nature). Expected: -5 to -10%
#      real. This is the scenario that weighs most on the currency leg of
#      the trend sleeve (s. 8), and the only one that could one day reopen
#      the hedged class; it is read on the book's TOTAL effective dollar
#      exposure (~17 points measured), never on the rate gap.
#   C. A AND B TOGETHER (US bust, a Fed unable to cut, a falling dollar).
#      The true worst corner. Rough arithmetic: equity -40% locally and
#      -15% of currency on ~40 points is ~-20 points; against it gold +4,
#      trend +3-5, the euro long line +1, linkers stable. Net -13 to -19%
#      real: THE ORDER OF THE MEASURED 1990 (-20.7%, pessimistic, s. 12).
#      The tent is sized for it: bucket for years 1-3 plus linkers for
#      4-10 means no forced sale for ten years. No new lever needed.
#   D. AN ENERGY SHOCK (wars plus the power demand of AI). Anchors: 2022
#      (book ~-2%) without a weak dollar, 1990 with one. No physical
#      commodities (measured and rejected, s. 11): the regime rests on the
#      linkers (they accrue the HICP by contract, energy included) and on
#      trend, which RENTS the exposure if it lasts months. A two-week
#      spike that reverses is caught by nobody, and it reverses (WTI in
#      1990: +112%, then -29%).
#   The scenarios missing from the intuitive list, the first being the
#   most important:
#   E. THE MELT-UP. The logical sequel of "a soft market is hard to
#      imagine" is 1998-99, not the crash: three years of AI at +40%/yr
#      with this book trailing by 12-24 points a year (1997-99 measured:
#      +58% against +115% cumulative, s. 12). Nobody sells this book at
#      the bottom of a crash; it gets sold at the top of a mania, out of
#      boredom. RISK NUMBER ONE, behavioral, and the sentence is already
#      written (s. 4; s. 12, point 3).
#   F. A FRENCH OR EURO DEBT CRISIS. The only scenario that attacks the
#      FLOOR itself (the linkers and the euro long line are France- and
#      Italy-heavy). Measured kit, 2011: US 20+ +37.1% in EUR, gold +13.1,
#      euro 25+ +7.6 all the same. The mirror justification of the dollar
#      leg, and the scenario where its cap at 5 has a COST, accepted with
#      open eyes.
#   G. FINANCIAL REPRESSION (inflation at 4-6%, rates held below it, for
#      a decade, no crash). The historical way out of public debt at 110%
#      of GDP, hence likely. It is the scenario where the TAX LEAK on
#      indexation (s. 1) becomes the central subject, and the one that
#      most justifies the wrapper architecture (s. 0). Cushions listed in
#      s. 1; gold and trend carry the real return.
#   H. THE SOFT MARKET ruled out by assumption. A 2011-2019 (trend in the
#      desert, equities lukewarm): ~3-4%/yr real, no disaster, but the
#      regime where the temptation to cut trend peaks; the protocol of
#      s. 4 is written for it. Leaving it out of one's forecasts is
#      exactly how it hurts.
#   CONCLUSION, to reread before any urge to "position" the book: no
#   scenario above demands a new line or a different weight; each lands on
#   a lever already written. That is a design result, not an evasion: the
#   book exists to make forecasting unnecessary. The uncovered corner
#   remains the crash in days (s. 11), and the buffer carries it (s. 14).
#
# ## 16. The trend sleeve: the panel, and why these two lines
#
#   IN ONE SENTENCE: THE DIRECT MANAGER PAYS THE ACCIDENT MONTH, THE
#   REPLICATION LINE HOLDS THE LONG REGIME. Two managers, two hedging
#   horizons, both measured on this book: that is the 50/50, and why
#   neither line replaces the other.
#   JUDGMENT RULE, valid for any future candidate: MEASURING A SLEEVE
#   AGAINST ITSELF IS NOT MEASURING IT AGAINST THE BOOK. A ranking built
#   on the pair with the replication line alone names a different winner
#   from the one the whole book names, where the other sleeves already do
#   part of the work. The test is behavior in THE BOOK'S WORST MONTHS.
#   And the criterion that matters is not the correlation to equities:
#   the book's 25 worst months are NOT equity crashes (2013-06, 2015, the
#   2022 rate shock, the 2025-03 dollar). The right test is a candidate's
#   mean return over the decile of months where THE BOOK bleeds, and its
#   hit rate there (2026-08, monthly NAVs, 1984-2026 where available):
#     candidate                  bottom decile   hit rate   quintile
#     AQR MF (= the class held)  +2.44 %/month      86%      +1.09
#     AlphaSimplex               +1.52              43%      -0.79
#     Winton                     +1.27              71%      +0.00
#     Campbell                   +1.19              57%      +0.79
#     Metori Epsilon             +0.95              43%      -0.62
#     PIMCO TRENDS               +0.91              43%      -0.20
#     Man Trend Alternative      +0.91              43%      -0.80
#     DBMF (USD model)           +0.85              57%      -0.03
#     BlueTrend                  +0.81              43%      -1.02
#     DBMFE (the class held)     +0.73              43%      -0.02
#     Quantica                   +0.43              57%      -1.20
#     the book itself            -2.81               .       -1.89
#   AQR ranks first on three of the five axes tested (decile, quintile,
#   quintile hit rate), and by far: +2.44% in the month the book loses
#   2.81, 60% more than the runner-up. The two axes it does not win are
#   down-beta (BlueTrend does better) and the mean over the gloomy
#   quadrants, where ten lines of sixteen beat it. 2022 shows the
#   difference between the two legs: DBMFE wins the year but ELSEWHERE
#   than in the holes, AQR makes the same year while losing almost
#   nothing in the months the book bends. The counterpart, measured too:
#   DBMFE is the BEST accessible line in the gloomy quadrants (+0.57
#   against +0.33 for AQR). The two legs do different jobs, which is the
#   second, measured, justification of the 50/50.
#   VERDICTS (the file is closed after three rounds; do not reopen it
#   without a named mechanism):
#   - The direct class CONFIRMED as leg 2, 50/50 with DBMFE for manager
#     risk: a 5/15 split would dominate on the short window, but such a
#     tilt was already tested and refuted, and it costs drawdown (-21.3%
#     against -19.8% on the deep history). Fallback if the class cannot
#     be subscribed: IAET (LU1662498721), same portfolio and manager, at
#     the price of its performance fee (s. 12).
#   - REMOVING the sleeve costs a worst drawdown of -21.1% and a worst
#     12 months of -18.0% against -19.8% and -16.2%, and 0.10 of Sharpe,
#     at equal CAGR (tested on five ways of reallocating the 20 points).
#     The sleeve is not a return bet; it is paid in the tail. The gap is
#     real, and narrower than first claimed.
#   - CAMPBELL (IE00BKYBHJ61) rejected as the pair (probability of beating
#     the incumbent 0.07 to 0.27 depending on the metric), despite its
#     0.50 correlation, the lowest of the panel. The deciding bill: 15%
#     performance fee with no hurdle, 1.44%/yr of transaction costs, 6.0%
#     /yr of total cost in the KID, and an unfunded total-return swap
#     with a single bank. The wrong shape of bill for a floor: it charges
#     most in the year the sleeve must pay. It stays in the catalog, with
#     its backcast, as a witness.
#   - WINTON rejected: 0.79 correlation with DBMFE, a near clone; the pair
#     DEGRADES Sharpe and worst 12 months against DBMFE alone. Its lack of
#     any performance fee does not redeem that.
#   - QUANTICA (POSITIVE equity beta, 2.21% of performance fee taken over
#     the year), BLUETREND (below its 2015 high, assets -64% in two and a
#     half years), MAN, ALPHASIMPLEX, METORI (decorrelated WITHOUT
#     convexity): all rejected.
#   - CFM: a closed regret. The one paying class that could be measured
#     shows -2.82 of alpha; the attractive number came from a zero-fee
#     class.
#   - Access fallbacks and near misses: FOLOW (LU3307218399, a 0.60%
#     retail ETF, no minimum) was ten weeks old with a small asset base in
#     2026-08, to re-examine in a year; Aspect, Nomura and DUNN failed on
#     minimum, empty class or performance fee. FORTEM (Irish managed
#     futures with a standing convexity overlay and, rarely, NO
#     performance fee) is ON WATCH: not yet launched in 2026-08, no EUR
#     class, a USD 5 M minimum, no public NAV; to revisit in 2027.
#   - MFEH is not a second manager: it is the hedged class of the SAME
#     sub-fund as DBMFE (0.99 correlation with DBMF, same DBi engine), a
#     currency decision on leg 1, settled in s. 8.
#   ANNUAL CLASS REVIEW: two public oracles suffice. The broker's own
#   product search by ISIN with the residence filter (what it really
#   serves a French resident), and the AMF's GECO register (what is
#   registered in France). The trap of the first: the fee it shows is the
#   prospectus rate, not the KID's.
#
# Siblings: dragon-decumulation-household.txt (same wrappers, one
#   generation earlier, stacked core kept), hydra-five-engines-ucits.txt
#   (one line per engine), cerberus-three-heads.txt (the same engine
#   philosophy regrouped into three even heads). The long-window numbers
#   quoted above come from measured stand-in variants of this book, back
#   to 1996-03 and 1986-12, since retired; the years 1-3 buffer this file
#   holds outside its weights is section 14.
#meta rebalance:90
#meta sim:on

# ---- Taxable account (everything the shelters cannot hold) ------------
5	MTH             # euro deflation duration: Amundi Euro Govt Bond 25+Y Acc (LU1686832194) | HEDGE, liability currency (s. 6)
5	DTLA            # US deflation duration: iShares $ Treasury 20+yr Acc (IE00BFM6TC58) | HEDGE, accumulating and unhedged: crisis dollar, capped at 5 (s. 6)
10	DBMFE           # trend, replication method: iMGP DBi Managed Futures EUR (LU2951555403; UNHEDGED class kept on measurement, ~10 pts of USD ride the NAV, s. 8; the hedged sister MFEH LU3359622902 is not bought) | MECHANISM, dose capped by error asymmetry (s. 4); holds the long regime (s. 16)
10	IAE1FT          # trend, direct method: AQR Managed Futures UCITS IAE1FT EUR-hedged (LU2622190622, 1.26%/yr flat, all of it inside the NAV, no performance fee, EUR 100k minimum; fallback IAET LU1662498721, same portfolio) | MECHANISM, a second manager against manager risk; pays the accident month (s. 16); on the share-class choice see s. 12
12	IGLN            # gold: iShares Physical Gold ETC (IE00B4ND3602; the USD and EUR listings are the same ETC and the same exposure, gold, not dollar) | HEDGE, the stagflation regime, dosed on the price of the insurance (s. 7); physical ETC only, never an ETN
16	CHSN            # euro linkers 1-10y: UBS Core BBG Euro Inflation Linked acc (LU1645380442) | NUMERAIRE / DERIVED, floor years 4-12 (s. 1-2); all-maturity IBCI (IE00B0M62X26) rejected as a real-rate duration bet
5	AVWS            # global small value: Avantis Global SCV (IE0003R87OG3, 0.39%) | MECHANISM, weak, hence a minority share; EUR-quoted, USD unhedged

# ---- Tax shelters (equity only by law) --------------------------------
23	ERESMONDEM      # world equity FCPE, 0.56%/yr KID charge (s. 12) | MECHANISM; block sized by the equity budget, never by the tax edge (s. 0)
5	WPEA            # world equity: iShares MSCI World Swap PEA (IE0002XZSHO1; alt CW8 LU1681043599) | MECHANISM + wrapper CONSTRAINT
7	LU1832174962    # Europe small value: Independance AM Europe Small (for the shelter that cannot hold a world fund; an institutional class exists at 1.40%/yr vs 1.95%, LU1832175001, minimum permitting) | CONSTRAINT + weak mechanism
2	LU0131510165    # France small/mid value: Independance AM France Small Mid | CONSTRAINT; folding it into the Europe line is equivalent