Suppressed Hazard Convergence (SHC)

@techreport{disalvatore2026shc,
  title        = {Suppressed Hazard Convergence (SHC): Dating the Realization of an Elevated Equity Drawdown Hazard from Suppression Capacity and Price Pressure},
  author       = {di Salvatore, S. and E1 (Emergent)},
  institution  = {Assets Bulletin Research},
  year         = {2026},
  month        = {September},
  type         = {Working Paper},
  number       = {v0.1},
  url          = {https://assetsbulletin.com/research/suppressed-hazard-convergence}
}

1Motivation — the missing ex-post layer

Every axis of the Triaxial Regime Hazard is ex-ante: the calibrated hazard, the observed trigger and the fragility prior describe conditions before a drawdown regime; the event window and the macro multiplier scale the same odds. When the posterior P* sits at HIGH and the tape prints two red sessions, the framework can still say nothing about whether the event it prices has started, since when, or whether it has ended. In drawdown theory (Magdon-Ismail & Atiya 2004; Chekhlov, Uryasev & Zabarankin 2005) a drawdown begins at the running peak, not when it is noticed — but by that definition every 1 % wobble off a high is a drawdown. Three things must therefore be separated: when the drawdown started (the peak), when it converged (the mechanism that was holding it back gave way), and when it realized (the threshold the hazard prices). SHC is that state machine. It is an observer: it never alters P*, the verdict or any rule of the illustrative model book.

The intuition is two forces. Pressure is the hazard wanting to realize — hedging demand, inverse-index accumulation, skew, breadth decay; TRH's trigger axis sees it as positioning. Suppression is the tape being held up — volatility sold for premium, dealers long gamma pinning price, systematic strategies that add exposure while realized volatility is low, index masking by the largest names. While suppression exceeds pressure, an elevated hazard leaks out as a slow pullback and every dip reverses. The pullback runs inside a tunnel. When the suppressors' capacity is exhausted, they flip from stabilizers to amplifiers — dealers short gamma, volatility-targeting deleveraging, short-volatility covering — and price travels the remaining distance to the threshold quickly. The −5 % close is the consequence; the touch is the cause becoming visible.

2Literature and the gap

None of the four families treats suppression as a measurable, consumable capacity set against price in one geometry; none defines the observable moment the amplifier flips sign as a dated event; none conditions propagation on fragility. And Guttal et al.'s negative result — rising variance but no critical slowing down before index crashes, hence “stochastic transitions, not tipping points” — is left unexplained. SHC takes the fuel (Brunnermeier & Sannikov) and the ignition (Barbon & Buraschi) and makes them operational at daily frequency with free data, the way TRH made TVTP regime switching operational by decomposing the hazard.

3The model

Price pressure. Let Pₜ be the SPY close and Mₜ its running maximum over the last 250 sessions. The drawdown is ddₜ = (Mₜ − Pₜ)/Mₜ and

D(t) = 100 · min(1, ddₜ / 5 %)        (0 at the peak · 100 at the realization threshold)

Suppression capacity. Five daily observables are each mapped to [0, 1] (1 = intact, 0 = exhausted) and combined with fixed weights; weights renormalize when a series is unavailable.

S(t) = 100 · Σᵢ wᵢ · cᵢ(t)        tunnel width  W(t) = S(t) − S̲        touch ⇔ min₍₃ sessions₎ S ≤ S̲ = 40  ∧  D(t) ≥ D̲ = 60

After a touch the detector re-arms only when S has recovered above S̲ + 15 for five sessions or D has returned to zero, so one convergence is counted once. Propagation is a touch followed by the −5 % close within 15 sessions of the same episode. Realization is defined by price alone; the touch tags the mechanism: an episode whose −5 % close is preceded by a touch is a convergence, one that reaches −5 % without a prior touch is a grind — the second exit of the tunnel, in which price walks down while volatility stays contained.

4Data and method

Daily closes of SPY, VIX, VIX3M, VVIX, SKEW and the inverse basket SH, PSQ, SDS, SQQQ, January 2007 to the latest session (VIX3M and VVIX histories begin in 2006–07). Episodes are contiguous spells below the 250-session running peak; those reaching ≥ 5 % are the realized sample, those bottoming between 2 % and 5 % are the non-realizing control. Lead time is the number of sessions from the touch to the −5 % close. Pre-peak fragility is a price-only proxy in the spirit of Danielsson et al. — the percentile of 60-session realized volatility over the trailing five years (inverted), the calm duration since the last realized episode, and the 200-day extension — measured at the peak so the decline cannot contaminate it. Early-warning statistics follow Scheffer et al.: Kendall's τ of rolling-20 variance and lag-1 autocorrelation over 60-session windows ending (a) at the peak, (b) the session before the −5 % close, (c) at the deepest close of non-realizing pullbacks and (d) at quiet control dates at least 45 sessions from any peak or realization. All thresholds are reported on a grid; nothing is fitted in-sample beyond the choice of the default pair.

5Results

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6Reading the results

The touch is a confirmation mechanism. It precedes or coincides with 86 % of realized drawdowns with a median lead of 3.5 sessions, against 38 % of pullbacks that were absorbed; but roughly half of all touches are themselves absorbed. SHC therefore dates and tags — it does not forecast, and it is deliberately kept out of P*.

The early warning is first-moment, not second-moment. Before the peak there is no critical slowing down in price and no drift in S — consistent with Guttal et al. Inside the tunnel, S drains in 84 % of the episodes that realize and in half of the pullbacks that do not; at the −5 % close the median capacity left is about 32, while pullbacks that were absorbed bottomed with about 44 still intact. The tipping-point literature looked for rising variance and autocorrelation in price; the signal lives in the level of the stabilizer being consumed. That is the reconciliation: markets do not slow down before a drawdown realizes, they lose the mechanism that was holding them.

Grinds are the deeper exits. The four episodes that realized without a touch — 2011, 2012, September 2020, January 2022 — reached −5 % with roughly 50 points of capacity still intact and ran deeper at the median. When volatility never breaks, positioning never washes out. This is the observation the fragility bridge should eventually explain; with a price-only fragility proxy the propagation split runs in the predicted direction (fragile 63 % vs resilient 47 %) but is not significant.

7A recorded episode — worked example

The framework is only useful if it can be replayed on the tape it was built from. Below, any of the 28 realized episodes can be selected; the default is the February–March 2020 convergence. Today's observation — state, capacity components, the live chart — is deliberately not shown here: it belongs to the Pro desk, where it is read alongside the TRH verdict; the paper shows what was recorded, not what is happening.

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8Relationship to TRH

TRH gives the odds; SHC says whether the suppression that keeps those odds from realizing is exhausted, and dates the moment. The two are kept separate on purpose: folding the observed outcome into the hazard would be circular. The pairing yields the labels TRH's validation programme requires — each session's P* can be resolved against the forward path, and each realized episode carries its peak, touch, confirm and recovery dates — and it supplies a third axis of comparison, forecast severity band (trigger axis) against realized band. Governance of the verdict by the realization state is deferred until the observer has run live for several weeks.

9Limitations

The sample is one index and 28 events; the touch thresholds are a reported grid, not an estimate; the components of S are equal-spirited proxies for mechanisms — dealer gamma, volatility-target flows, short-volatility crowding — that are only observable directly with positioning data. The fragility proxy is price-only and the cross-sectional saturation axis exists only from 2026; the bridge between convergence and propagation is therefore open. Rolling-peak episodes reset the reference during long bear markets. Every number on this page is a statistical observation published by a financial publisher — not a forecast, not advice.

10References

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