# Cerberus (three heads) -- the S&P 500's return without the parts that break the holder # # STATUS: nearly buyable. Five of the six lines are UCITS funds a French # retail account can hold today; the sixth (GDE, 24%) is US-listed with # no PRIIPs KID, and its accessibility is this file's one standing # problem (the access ledger below is the state of the art). Cerberus is # the hydra's sibling, in the family and in the myth: Hydra and Cerberus # are both children of Typhon and Echidna, and this build is the same # engine philosophy regrouped into THREE EVEN HEADS of notional exposure. # Its job is the watchdog's: guard the floor while the owner sleeps. # # Idea: the S&P 500's 30-year return at half its volatility, a third of # its drawdown and a sixth of its time under water, packaged as three # balanced notional thirds (equity / trend / bonds+gold) with a minority # of direct US exposure. # # ## What 100 EUR actually holds (the exposure ledger) # # 17 NTSG -> 15.3 world equity + 10.2 sovereign futures (~7y duration) # 6 AVWS -> 6 global small-cap value equity # 28 MFEH -> 28 managed-futures trend (replication, EUR-hedged) # 16 AQR MF -> 16 managed-futures trend (direct TSMOM, EUR-hedged) # 24 GDE -> 21.6 US large-cap equity + 21.6 gold futures # 9 MTH -> 9 euro sovereigns at ~19y duration # ------------------------------------------------------------------ # Total ~43 equity + ~44 trend + ~41 bonds-and-gold = ~128% # # That last line IS the design: three even heads, one third of notional # each (34/34/32), the hard-ballast head split half nominal duration # (19.2 bonds) and half gold (21.6). The ~28 stacked points are financed # inside NTSG and GDE at roughly the T-bill rate; the frontier sibling # (hydra-five-engines-capital-efficient.txt) keeps the full case for # embedded leverage over margin, boxes and daily-reset ETFs. # # ## Where it stands in the hydra family # Same five engines as the hydras; what changed is the passport and the # currency doctrine. Three swaps against the frontier build: # - ZPRV -> AVWS: the small-value sleeve goes global (31% non-US) instead # of US-only. The frontier file measured the swap a wash on returns; # here the tie-breaker is the whole point of the build (minority US). # - RAEF -> the AQR flat-fee I class (IAE1FT): same fund, but a share # class whose published charge is real and durable. RAEF's 0.23% # ongoing figure is a discretionary management-fee waiver that can end # any day; IAE1FT's 1.26% is what the NAV actually pays, and the class # is reachable through ordinary brokers (IBKR carries it). # - ZROZ -> MTH: the deflation-duration head moves from a 27y USD # zero-coupon to a 19y euro sovereign book. Deliberate doctrine, not a # compromise: the USD flight-to-quality premise behind a Treasury # sleeve was re-examined on the very windows it is supposed to pay in # and did not survive the check, so the defensive duration stays in # the liability currency instead of paying dollar volatility on top of # the rate bet. # Net: direct US exposure is a minority stake, 40% by geography and 41% # by currency (EUR 54%), against a family habit of USD-heavy books. # # ## Regime map: what hurts, and which head answers # # Growth boom ~43% equity across three engines (NTSG world, # AVWS global small value, GDE US large). # Disinflation/recession NTSG's overlay (~10 points intermediate # duration) + MTH + trend rotating long. # Deflation crash (2008) MTH long-end convexity in euros + trend short # risk assets. # Inflation shock Trend long commodities/short bonds + 21.6 # points of gold via GDE. # Choppy stagflation Gold (trend whipsaws without a trend). # Prolonged equity bear Trend crisis alpha, 44 points of it. # # Measured coverage (share of weight): growth 43%, inflation 72%, # crisis 75%, deflation 19%. Deflation is the thin quadrant, as in the # frontier build (21%): the repair, if wanted, is MTH toward 15-20 (the # sweep below prices it at ~0.28 pts of CAGR per 5 points). # # ## The five engines (weights, and sane ranges from the per-line sweep) # # ENGINE 1 -- NTSG, equity + duration (17%; range 10-25). # 90% developed-world equities + 60% sovereign futures, UCITS # (IE00077IIPQ8). The sweep reads nearly flat Sharpe (1.05-1.07) across # 0-25 and a ceiling past ~25 (Sharpe 1.03 and falling, drawdown -21% by # 30): the ceiling is empirical. The floor is a priori, as in every # hydra: the sweep would happily hold 0% NTSG, but the worst-5y floor # thins (+0.65% at 0) and a 30-year plan needs the world-equity presence. # # ENGINE 2 -- AVWS, global small-cap value (6%; range 0-10). # Size and value premia in the value-weighted form, global edition # (IE0003R87OG3), carrying the non-US tail ZPRV lacks. The most # expensive risk in the book, empirically: each 5 points buys ~0.13 pts # of CAGR and costs ~1.4 pts of drawdown and ~0.4 pts of worst-5y; by # 20% the worst-5y is negative. The ceiling is empirical and tight. # # ENGINES 3a/3b -- trend, TWO models (28% + 16%; 44 total). # The largest head, and knowingly above the frontier file's 40-point # comfort edge and its ~22-per-leg cap. The overweight leg is carried on # the manager's record, not the share class's: MFEH (LU3359622902, # 0.75%/yr) is DBi's SG CTA replication, the same engine that has run # DBMF since 2019 with the longest replication record in the business, # and the class adds only an EUR hedge on top. Engine 3b is AQR's direct # TSMOM (Managed Futures UCITS, flat-fee I class IAE1FT LU2622190622, # EUR-hedged). Both legs hedged: an unhedged managed-futures sleeve is # trend plus a long-dollar position (the frontier file measures the # dollar leg at +3 pts of volatility for no return). The sweep is # monotone in Sharpe up to 45% on either leg, which is exactly the # in-sample flattery of a shared reconstruction the family's blind-spot # notes warn about: the 44-point total and the 28/16 split are a priori. # # ENGINE 4 -- GDE, gold stacked on equity (24%; range 15-30). # 90% S&P 500 + 90% gold futures (US97717Y5684). The CAGR engine: the # sweep pays +0.39 pts of CAGR and +0.48 pts of worst-5y per 5 points, # at ~0.5 pts of volatility each. The floor is empirical: below ~15 the # worst-5y goes negative and the build no longer matches the index's # return, i.e. Cerberus stops being Cerberus. Sharpe peaks at 5-15 and # volatility makes the ceiling call. NOT UCITS; see the access ledger. # # ENGINE 5 -- MTH, euro deflation duration (9%; range 5-20). # Amundi Euro Government Bond 25+Y (LU1686832194, 0.07%/yr, ~19y # duration): recession/deflation convexity in the liability currency. # The sweep prices each 5 points at ~0.28 pts of CAGR for ~0.35 pts less # volatility and a slowly rising worst-5y, up to a cliff past ~35 where # 2022-style duration losses dominate (drawdown -23%, recovery 3.9y at # 45%): both ends of the range are empirical. The euro book carries # OAT/BTP spread risk (31% France, 15% Italy): see blind spot (a). # # ## GDE access ledger (the one standing problem, measured 2026-08) # No UCITS stacks gold on equity today. What exists, in order: # - HOLD GDE ANYWAY: requires an account that clears PRIIPs, i.e. MiFID # professional opt-up (2 of 3: 500k EUR portfolio, trading frequency, # professional experience) or a non-EU account. The options-exercise # route that unlocks big US ETFs does not work here: GDE has no liquid # option chain. # - SYNTHESIZE IT, UCITS-only: 24 GDE -> 10.8 CL2 (Amundi MSCI USA 2x # Daily, FR0010755611, PEA-eligible) + 13.2 IGLN (physical gold, # IE00B4ND3602). Measured on the shared 2009-2026 window: CAGR 10.28% # vs 10.84%, volatility 8.70% vs 9.58%, Sharpe 1.13 vs 1.09, same # -19.5% drawdown, worst-5y +0.18% vs +0.95%. The -0.56 pts of CAGR # buy the passport; read them as a floor, not the full price: the # window starts mid-2009 and never charges CL2's daily-reset decay a # 2000-02-style chop, and 8.4 points of gold notional are missing # (gold at 1x cannot fund both halves from 24 points of capital). # - DE-STACK IT (12 IGLN + NTSG raised to 29): refuted. CAGR 9.03% # (-1.6 pts), worst-5y -0.22%: it breaks both properties the build # exists for. Documented so nobody retries it. # - WATCH LIST: a WisdomTree Efficient Gold UCITS stays the clean # unlock. Two live signals: Return Stacked announced a UCITS rollout # with HANetf targeted at 2026 (nothing shipped as of 2026-08), and # their RSSX (US stocks + gold/bitcoin 100/100, US-listed 2025-05) is # a near-GDE with a bitcoin kicker; a UCITS RSSX would do this job. # # ## Currency # EUR 54% / USD 41% / other 5% of look-through exposure: both trend legs # are EUR-hedged share classes and the whole duration head is euro # sovereigns, so the dollar remains only where it is paid for (the # equity premium inside NTSG and GDE). Hedging is not free forward (the # USD-EUR carry gap, ~1.5%/yr at 2026-08 rates); the build accepts that # as the price of a defensive book that pays in the liability currency. # AVWS quotes in EUR on Xetra but that is cosmetic (its basket is ~55% # USD); no hedged class exists, and at 6 points it would move the book's # currency mix by ~2 points: not worth an instrument change. # # ## Blind spots # (a) A euro-sovereign stress (2011): MTH is then exposure, not hedge # (31% France, 15% Italy; no Bund-only long ETF exists). The USD # zero-coupon dodged this one and caught dollar volatility instead; # this build chose its side of that trade. # (b) DEFLATION is the thin quadrant (19% of weight): a bust that trend # misses leans on 9 points of MTH plus NTSG's overlay. # (c) 44 points of capital in trend, above the family's 40-point # live-record edge, and the deep history of both legs shares one # reconstruction: the backtest cannot price model divergence and # flatters the sleeve. Treat it as a regime study, not a promise. # (d) Product risk: GDE is small and young; MFEH is younger and smaller # still (~EUR 11m, weeks of live NAV, Xetra only, France # registration to verify before buying). DBMFE (LU2951555403) is the # same book unhedged if MFEH is unreachable; the frontier file # prices that fallback at +3 pts of sleeve volatility. # (e) Fee stack: 0.53%/yr weighted, the trend legs being 0.75% and # 1.26%. That is the price of published charges that are real # (RAEF's 0.23% is a waiver, not a fee schedule). # (f) Embedded financing: the ~28 stacked points pay T-bill inside the # funds; when cash is at 5% that is ~1.4%/yr of drag before the # overlays earn anything (2022-23). # # ## Honesty note on the WEIGHTS # The engine roles are theory-first; the percentages are backtest- # informed and then hand-rounded to the three-thirds shape. The measured # edge should be expected to shrink out of sample; the three-heads # geometry, the ranges above and their empirical/a-priori labels are the # part built to survive. The per-line sweep (rest renormalized, # 1996-2026) is re-runnable with: # ./pofo -sweep examples/portfolios/cerberus-three-heads.txt # # ## Measured profile (this toolkit, EUR, common window 1996-03 -> 2026-08) # CAGR 10.61%, volatility 9.55% (8.66% monthly), Sharpe 1.07, Sortino # 1.50, Ulcer 4.2, max drawdown -19.5%, worst recovery 2.0y, worst # rolling 5y +0.95%, median 5y 9.18%, up/down-capture 38/33%, beta vs # S&P 0.32, CWARP +19.1, weighted charges 0.53%/yr. The S&P 500 in EUR # over the same window: 10.76% CAGR at 20.9% volatility, -63.8% max # drawdown, 13.2y worst recovery, worst rolling 5y -9.84%. That is the # claim in the title, measured: the index's return (10.61 vs 10.76) at # 46% of its volatility, 31% of its drawdown, 15% of its time under # water, and a positive worst-5y against the index's -9.8%. # Vs the frontier hydra (same window): 0.16 pts less CAGR, 0.34 pts # less volatility, same Sharpe (1.07 vs 1.05), same drawdown, and a # better CWARP (+19.1 vs +18.7), for +0.20%/yr of fees: the three-thirds # regrouping costs almost nothing against the frontier the family says # is unreachable without GDE. # Vs the buyable hydra: +1.11 pts of CAGR, +0.41 pts of worst-5y, one # recovery year less (2.0y vs 2.8y real): that gap is what GDE's # accessibility problem is worth, and why the access ledger above # exists. # # ## Practical notes # - Rebalance quarterly; the sane ranges define how far drift can run. # - The AQR leg is a FUND, not an ETF: check platform availability and # minimums (IBKR carries IAE1FT; the EUR class avoids manual FX). # - CHECK BEFORE BUYING MFEH: size, spread and France registration (see # blind spot (d)); DBMFE is the fallback. # - GDE makes this file 76% buyable today; the synthesis line in the # access ledger is the 100% UCITS fallback, priced. # # Siblings: hydra-five-engines-capital-efficient.txt (the frontier build # and the family's rationale ledger), hydra-five-engines-ucits.txt (the # fully buyable five-engine build). #meta rebalance:90 #meta sim:on 17 NTSG # Engine 1, equity + duration: WisdomTree Global Efficient Core 90/60 (NTSG, IE00077IIPQ8, UCITS) 6 AVWS # Engine 2, value factor: Avantis Global Small Cap Value (AVWS, IE0003R87OG3, UCITS) 28 MFEH # Engine 3a, trend replication, EUR-hedged: iMGP DBi Managed Futures R EUR HP (MFEH, LU3359622902, UCITS; unhedged class DBMFE LU2951555403) 16 LU2622190622 # Engine 3b, second trend model, direct TSMOM: AQR Managed Futures UCITS, flat-fee EUR-hedged I class IAE1FT (LU2622190622) 24 GDE # Engine 4, gold stacked on equity 90/90: WisdomTree Efficient Gold Plus Equity (GDE, US97717Y5684, US-listed; access ledger above) 9 MTH # Engine 5, euro deflation duration: Amundi Euro Government Bond 25+Y (MTH, LU1686832194, UCITS)