Stress tests — no detectable redomestication effect (power-limited null)

Read this first

What this event study can and cannot prove.

An honest scope statement, set in advance — the single most important guard on this page’s fact-based, no-advocacy posture.

It can

Test whether the redomestication disclosure coincided with an abnormal market reaction under a set of pre-specified counterfactuals (six benchmark models × two event-date anchors × three windows).
Report a minimum detectable effect ( at the clean day) so readers can see what size of effect the design could have found.
Show, by cross-section, that the apparent “significance” under one clock is mechanically explained by AI-server exposure, not by anything Dell-specific.

It cannot

Prove a zero effect. The design is power-limited; a plausible 1–3% governance re-pricing is far below detectability.
Estimate an average effect for all reincorporations. This is one controlled-company case study; the cohort evidence lives in the Reincorporation Index.
Adjudicate welfare or intent, or show the vote was uncertain. A null is equally consistent with a governance-neutral move efficiently priced and with a foregone-conclusion vote the market saw coming.

Eight tests at a glance

Each test attacks a different way the null could have been Dell-specific.

If the clean-day null were hiding a real, Dell-specific redomestication signal — or if any apparent significance under an alternative clock were a genuine charter effect rather than the AI-server cycle — at least one of the eight tests below should isolate Dell. None do.

Both anchors

Event-date sensitivity

EDGAR acceptances were post-close (PRE 14A , DEFA14A ET on ), so May 4 and May 5 are shown co-equal until the Business Wire wire-minute is pinned. May 4 [0,0] fully-adjusted = ; the May 5 spike appears only with the AI days inside the window.

Plain EnglishWe don’t yet know the exact minute the news hit the wire, so we show both candidate event days side by side instead of picking the one that flatters the result.

For instanceOn the clean May 4 day the fully-adjusted return is ; the headline-grabbing spike materializes only once T0 is moved to May 5 and the AI-rally days fall inside the window.

AcademicEDGAR acceptances are post-close (PRE 14A , DEFA14A ET), so May 4 and May 5 are reported co-equal pending the Business Wire wire-minute; no anchor is privileged.

Confound-flagged

Window sensitivity

, , are primary; and overlap the AI rally and late-May fiscal‑Q1 earnings and are confound-flagged. A wide window is never headlined.

Plain EnglishHow many days you count around the event changes the answer. Narrow windows isolate the disclosure; wide ones sweep in unrelated news.

For instanceThe and windows pull in Dell’s May 6 and May 8 AI-rally days and its late-May earnings, so any “effect” they show is contaminated — they are confound-flagged, never headlined.

AcademicPrimary windows are , , ; wider windows overlap identified confounders and are excluded from headline inference.

Stable

Donor leave-one-out

Full LOO over all donors, both anchors. The swing donor is window-specific: ANET at May‑5 (; →), but at May‑4 (); NVDA only . No verdict flips.

Plain EnglishWe rebuild the control basket leaving out one peer firm at a time to check no single firm is secretly driving the whole result. Which firm matters most depends on the window.

For instanceDropping Arista shifts the May-5 CAR from to — a swing — yet the verdict stays non-significant; dropping NVDA moves it only .

AcademicFull leave-one-out over all donors, both anchors. The largest May-4 swing is — at the window (not ANET). No sign or significance change on either clock.

Null

Placebo-in-time

exhaustive pseudo-event dates (deterministic). Actual-day empirical p = – on May 4. May‑5 uncontrolled p = but AI-controlled p = .

Plain EnglishWe re-run the whole study on hundreds of fake event dates to see how unusual the real day actually was.

For instanceThe actual event-day gap is more ordinary than – (i.e. 44–90%) of random pseudo-dates; the May-5 result only looks rare (p = ) until the AI control is added, after which p = .

Academic exhaustive deterministic pseudo-event dates; empirical p computed as the share of placebo gaps at least as extreme as the actual.

Honest limit

Placebo-in-space

Reported both ways on May 5: with ANET in the pool Dell ranks of (the firm ahead is Arista, an earnings-confounded unit); screened (drop ANET) Dell ranks of — the most extreme clean unit. On May 4 Dell is of (least unusual). With donors the minimum attainable permutation p is — it characterizes, it cannot reject at 5%.

Plain EnglishWe ask how extreme Dell looks next to untreated peer firms on the same day. If the charter mattered, Dell should be the standout.

For instanceDell ranks of on May 4 — the least unusual stock in its own pool that day; on May 5 it is of , but the firm ahead of it is Arista (an earnings confound). Screen Arista out and Dell is the most extreme clean unit ( of ).

AcademicWith donors the smallest attainable permutation p is 1/ = ; rejection at 5% is arithmetically impossible until the pool reaches ≥ . Reported as characterizing, both with ANET (Dell /) and screened (Dell /).

The mechanism chart — N=7/8

AI-loading cross-section

Regress each peer’s CAR on its AI-beta. Full N = May‑5 : slope , R² , p = . Screened (drop ANET, N = ): slope , R² , p = , Spearman ρ = — Arista is an earnings confound (screen #2), not the AI cycle; dropping it strengthens the gradient. May‑4 slope is flat both ways (R² ). Preliminary N=7/8 pending the donor export.

Plain EnglishWe line every firm’s return up against how AI-exposed it is. If the charter drove Dell’s move, Dell would sit far off that line.

For instanceDell sits on the line (screened residual ): its CAR is what its AI-exposure predicts, not a Dell-specific signal.

AcademicCross-sectional OLS of CAR on AI-beta. Full N = : May-5 slope , R² , p = (Spearman ρ = , p = ). Screen-justified exclusion of ANET (Q1 FY26 earnings May 5 AC, −13.61% May 6) gives N = : slope , R² , p = ; Spearman ρ = (p = ) — the gradient strengthens. Preliminary pending the ≥19-donor export.

Corroborative

GARCH(1,1)

Day-0 standardized abnormal return is insignificant: market z = (p = ); AI-controlled z = (p = ). A complementary framework that corroborates the OLS-σ null. The Normal fit hit a boundary (α≈0, β≈1); a Student-t refit (z = ) and a 500-day window (z = , boundary relaxed) give the same verdict.

Plain EnglishVolatility clusters, so we re-measure the disclosure-day surprise against time-varying volatility instead of one flat average.

For instanceThe day-0 standardized return is tiny either way — market z = (p = ), AI-controlled z = (p = ) — confirming the headline null.

AcademicGARCH(1,1) standardized abnormal return, a complementary (not independent) framework. The Normal fit hit a boundary (α≈0, β≈1); a Student-t refit (z = , p = ) and a 500-day-window refit (z = , p = , which relaxes the boundary) leave the verdict unchanged. It corroborates the OLS-σ null.

Cause identified

Confounder log & power

May 6 and May 8 are Dell’s own returns (AI-server rally), not “sector tailwinds.” Confounder log also flags ANET — Q1 FY26 earnings May 5 2026 AC; May 6; firm-specific, excluded at the May-5 anchor per screen #2. Benjamini-Hochberg is reported within the -cell primary family, separate from the -cell grid. The MDE is always reported; the admissible claim is strictly “no detectable effect, MDE .”

Plain EnglishWe name the actual cause of the big numbers and state honestly how small an effect the design could have caught.

For instanceWith σ = the smallest effect detectable at 80% power is ; a 1–3pp governance re-pricing is invisible, while May 6 () and May 8 () are Dell’s own AI-server returns.

AcademicBenjamini-Hochberg is reported within the -cell primary family, separate from the -cell grid; the admissible claim is strictly “no detectable effect, MDE ” — the design cannot license a stronger statement.

Figure 1 · Headline scoreboard

On the clean disclosure day, the disclosure-day return is indistinguishable from zero

Six benchmark models applied to the disclosure-day window (, primary anchor T0 = ). Every cell is non-significant (all p_BH = ). The TOST tile does not affirm equivalence — this is a power-limited null, not an equivalence-confirmed one.

Mean-adjusted

p_BH = · null

Market (S&P 500)

p_BH = · null

Market + sector (XLK)

p_BH = · null

Market + sector + AI

p_BH = · fully adjusted null

Donor-weighted control portfolio

p_BH = · null

Donor portfolio (drop NVDA)

p_BH = · null

GARCH(1,1) day-0 (market)

z =

p = · corroborative null

TOST equivalence (±2 pp band)

p ≈

does NOT affirm equivalence — power-limited null

What this shows. On the day Dell’s redomestication crossed EDGAR, the stock moved indistinguishably from zero under every benchmark. The fully-adjusted (market + sector + AI) figure is . GARCH(1,1) corroborates the OLS-σ null. The TOST tile is highlighted because it does not reach equivalence at ±2 pp (p ≈ ); the correct claim is “no detectable effect,” with a minimum detectable effect of .

For instance. Take the fully-adjusted (market + sector + AI) tile: the disclosure-day return is with p_BH = — indistinguishable from zero. A reader looking for a charter-driven re-pricing finds none on the clean day; the only way to surface a large number is to switch clocks (T0 = May 5) and drop the AI control, which is exactly what the eight tests below diagnose as the AI-server rally.

Academic reading. Estimation window ( trading days); estimation-period daily σ = . MDE at 80% power (α = 0.05, two-sided): at , at , at . A governance re-pricing of 1–3% lies well inside the non-detectable region.

Figure 2 · The mechanism chart — AI-loading cross-section

Each peer’s May-5 CAR tracks its AI-server exposure — Dell sits on the line

If the apparent May-5 significance were a Dell-specific redomestication signal, Dell would sit far off the line. Instead, regressing each firm’s CAR on its AI-beta (loading on an SMCI/HPE AI factor) places Dell where its exposure predicts. Screen-justified exclusion of Arista — an earnings confound (Q1 FY26 release May 5 after close; screen #2) — gives R² = , p = at N = ; preliminary pending the ≥19-donor export. Arista was masking the gradient, not creating it: dropping it strengthens the fit (full N=8 slope , R² , p → screened slope , R² ; Spearman ρ →).

What this shows. Across the peer panel, May-5 abnormal returns line up with AI-server exposure, not with redomestication status. On the clean, screened pool Dell’s residual is — on the line — meaning its CAR is what its AI-beta predicts, mechanical rather than Dell-specific. On the clean May-4 day there is no AI pattern at all (slope flat, R² , both ways). A flat clean day plus a steep gradient on the AI-rally days, with Dell where its exposure predicts, is the mechanical-repricing signature.

For instance. On the screened (N = ) fit Dell sits on the line with a residual of : its May-5 CAR is what its AI-exposure predicts, not a Dell-specific signal. If the redomestication had moved the stock, Dell would float well above the fitted line. Arista — an earnings confound (Q1 FY26 release May 5 after close, −13.61% May 6) — is excluded under admission screen #2; it was masking the gradient, so dropping it strengthens the line rather than weakening it.

Academic reading. Cross-sectional OLS of CAR on AI-beta. Full N = May-5 : slope , R² , p = (Spearman ρ = , p = ). Screen #2 excludes Arista (firm-specific Q1 FY26 earnings inside the May-5 window), giving the admissible fit at N = : slope , R² , p = ; Spearman ρ = (p = ). The gradient strengthens on the clean pool — Arista was masking it, not driving it. Preliminary, N=7/8 pending the ≥19-donor export. Untreated firms (e.g. NVDA) populate the same line, which is the point: the gradient is AI exposure, not the charter.

Figure 3 · Placebo-in-space

Dell is not the most unusual firm in the panel on the clean day

Each donor and Dell ranked by standardized May-5 gap, reported both ways. With Arista in the pool Dell ranks of on May 5 (the firm ahead is Arista, an earnings confound, screen #2); screened (drop ANET) Dell ranks of — the most extreme clean unit. On May 4 it is of — least unusual. Honest limit: with only donors the minimum attainable permutation p is ; the test characterizes Dell’s position but cannot reject at 5% until the pool reaches ≥ .

What this shows. Permutation inference asks: among the firms in the panel, how extreme is the treated firm? On May 4 Dell is the least unusual firm of . On May 5 it is with Arista in the pool — but Arista is an earnings confound (screen #2), so on the clean screened pool Dell is the most extreme unit ( of ). Both ways the position is consistent with the AI-rally days, not a clean-day Dell-specific charter signal.

For instance. On the clean disclosure day Dell ranks of — the least unusual stock in its own pool that day. A genuine charter shock would push the treated firm toward rank 1; being dead last is the opposite of a Dell-specific signal. On May 5 it rises to with Arista included and to once Arista (an earnings confound) is screened out — the AI-rally signature, not the charter.

Academic reading. A permutation test over firms can attain at best p = 1/ = ; rejection at the 5% level is arithmetically impossible until the donor pool reaches ≥ (the ICE export is pending). This test is reported as characterizing, not confirmatory.

Figure 4 · Donor leave-one-out

No single donor drives the donor-weighted control portfolio

Baseline May-5 CAR versus the CAR when each donor is dropped in turn. The swing donor is window-specific: at May-5 it is Arista (ANET) at , but at May-4 the largest single-donor shift is at the window (); NVDA moves the May-5 CAR only . No verdict flips on either anchor.

What this shows. If the donor-weighted control portfolio were a NVIDIA artifact, dropping NVDA would collapse the result. It does not — NVDA moves the May-5 CAR only . The largest May-5 swing comes from Arista (); at the May-4 anchor the largest is at the window (). Either way no verdict flips and the May-4 clean-day null is untouched.

For instance. Dropping Arista (ANET) moves the May-5 CAR from to — a swing, the largest of any single donor — yet the verdict stays non-significant. Dropping NVDA moves it only , so the result is not a NVIDIA artifact.

Academic reading. Donor weights (T0 = May 4): ; pre-period RMSE = . NVDA carries weight — not dominant — so the fit is not AI-cycle-driven. The estimator is a donor-weighted control portfolio (constrained, sum-to-one non-negative weights on returns), inferred by permutation, not Abadie pre-level matching. The Doudchenko–Imbens (2016) cite legitimizes the estimator, not the inference: its permutation test sits on the same -donor pool, so it hits the identical small-pool ceiling (minimum attainable p = ) and cannot reject at 5% until the pool reaches ≥ .

Figure 5 · The macro confound

The big returns are the AI-server rally days — not the disclosure day

Dell’s daily returns around the event. The disclosure day () is near zero; the spikes are Dell’s own May 6 () and May 8 () AI-server returns. Both candidate T0 anchors (May 4 and May 5) are marked; only an anchor that pulls those two days inside the window produces an apparent effect.

What this shows. The disclosure day itself is unremarkable. The two outsized green days — on May 6 and on May 8 — are Dell’s own AI-server returns, shared with the whole AI-hardware cohort. A study that anchors at May 5 swallows them; a study that anchors at the clean disclosure day (May 4) does not, and finds nothing.

For instance. The disclosure day () prints — near zero. The two outsized green bars are on May 6 and on May 8, both Dell’s own AI-server returns shared with the whole AI-hardware cohort. An event window that anchors at May 5 swallows those two days into the “effect”; one anchored at the clean May 4 day excludes them and finds nothing.

Academic reading. The estimation window ends trading days before T0, so no AI-rally day leaks into estimation. Wide event windows (, ) additionally overlap Dell’s late-May fiscal-Q1 earnings and are confound-flagged; they are never headlined.

Figure 6 · The arithmetic identity — Dell’s structural defense

A controller on of the equity left nothing to re-price

Voting power versus equity for the dual/triple-class structure. The controller bloc (Class A + B) holds of the vote on of the equity; the public float is of equity and of the vote. The outcome was certain before the proxy crossed EDGAR — this, not the price reaction, carries the thesis.

What this shows. The vote was an arithmetic identity. With of the voting power locked in the controller bloc, approval was certain before any public shareholder saw the proxy. An efficient market has nothing to re-price when the outcome is not in doubt — which is exactly why the absence of a disclosure-day reaction is neutral, not informative about welfare or intent.

For instance. of the vote sits on of the equity — the outcome was decided before the proxy was filed. The public float holds of the equity but only of the vote, so no plausible public turnout could have changed the result. With approval certain in advance, an efficient market has nothing to re-price on disclosure day.

Academic reading. Voting power: Class A / Class B / Class C . Share counts (Dell 10-Q, as of ): Class A / Class B / Class C = shares. Mechanism: DE→TX by conversion under DGCL §266 / TBOC Title 1 ch. 10.

Full data

Peer panel — CAR by AI-server exposure

Dell and the donor firms, each firm’s AI-beta and its May-5 abnormal return. SMCI and HPE define the AI factor and so do not appear as panel rows. Ranked by AI-beta. Preliminary N = — the panel expands with the donor export.

Company	Ticker	Role	AI-beta	May-5 [0,+1] CAR (%)

The AI factor is defined by (constituents, not shown as panel rows). The panel is preliminary at N = ; permutation inference reaches the 5% level only once the donor pool reaches ≥ .

Conclusion

What the price reaction says — and what carries the thesis.

What the event study establishes

On the clean disclosure day (T0 = , ) the fully-adjusted abnormal return is , statistically indistinguishable from zero (all p_BH = ), corroborated by GARCH(1,1) (z = ). This is a power-limited null — a finding of no detectable effect with a minimum detectable effect of — and not an equivalence-confirmed result; the TOST at ±2 pp returns p ≈ and does not affirm equivalence.

What gets disclosed about the “significant” clock

A spike of up to (t ) appears only at T0 = May 5 with the AI days inside the window and with no AI control; the market + sector + AI model dissolves it to (t , non-significant). The eight stress tests above — especially the AI-loading cross-section — document that this is the AI-server cycle, not the redomestication.

What actually carries the thesis

The controller-arithmetic identity: a controller on of the equity made the outcome certain before the proxy crossed EDGAR. A null price reaction is neutral — it cannot adjudicate welfare or intent — and this study is one controlled-company case; the cohort/population evidence is supplied by the Reincorporation Index.

What still needs pinning before final submission

The Business Wire intraday wire-minute (to fix whether May 4 or May 5 is primary); the donor-pool export that lifts placebo-in-space to ≥ firms; the cross-platform R/Stata reconciliation; and the FF3/FF5/Carhart event-window ARs once Ken French daily factors cover May 2026.