Full results
Every test, coefficient and confidence interval. Newey-West standard errors throughout; out-of-sample figures use expanding windows refit monthly, or leave-one-year-out where the event sample is too thin.
1. Is conductance a constant with noise?
Under the null that G is constant and volume co-moves with volatility only through
information arrival, log conductance is iid. The null distribution comes from
2,000 iid bootstraps preserving the exact fat-tailed marginal.
| Statistic | Observed | Null mean | Null p99 | p |
|---|---|---|---|---|
| AR(1) | 0.0549 | −0.0003 | 0.0350 | <0.0005 |
| AR(22) | 0.0911 | 0.0004 | 0.0352 | <0.0005 |
| Ljung-Box(22) | 1021.5 | 22.2 | 40.0 | <0.0005 |
| Variance ratio, 5d | 1.34 | 1.00 | 1.10 | <0.0005 |
| Variance ratio, 22d | 3.11 | 1.00 | 1.23 | <0.0005 |
| Variance ratio, 66d | 6.82 | 1.00 | 1.42 | <0.0005 |
| HAR out-of-sample R² | +7.29% | −0.15% | +0.04% | <0.0005 |
Variance ratios rising with horizon indicate genuine low-frequency structure rather than short-lived noise. Conductance is also not volatility relabelled: corr(log G, log realised vol) = 0.262 and corr(log G, log implied vol) = 0.242.
2. Does holder-base Λ beat realised and implied volatility?
| Horizon | Benchmark | Λ t-stat | Incremental R² | ΔOOS R² |
|---|---|---|---|---|
| 1 day | Realised + implied vol | +2.79 | +0.0020 | −0.0046 |
| 1 week | Realised + implied vol | +2.86 | +0.0068 | −0.0098 |
| 1 month | Realised + implied vol | +2.33 | +0.0102 | +0.0067 |
| 1 day | + conductance's own history | +1.15 | +0.0003 | −0.0039 |
| 1 week | + conductance's own history | +1.39 | +0.0014 | −0.0122 |
| 1 month | + conductance's own history | +1.58 | +0.0040 | −0.0041 |
Λ reaches in-sample significance against the benchmark the theory named, but that survives neither out-of-sample evaluation nor the inclusion of conductance's own past. The blunt number: corr(log Λ, log G) = 0.014.
3. Does signed asymmetry produce signed drift?
| Horizon | Coefficient | t | p | R² |
|---|---|---|---|---|
| 1 day | −0.00009 | −0.63 | 0.53 | 0.0001 |
| 1 week | −0.00038 | −0.62 | 0.53 | 0.0005 |
| 1 month | −0.00230 | −1.09 | 0.28 | 0.0047 |
Signs are consistently negative — the direction the theory predicts, since stressed longs should make a market conduct better downward — but nothing approaches significance.
4. Do large moves cluster in high-Λ states?
| Λ quintile | Q1 (low) | Q2 | Q3 | Q4 | Q5 (high) |
|---|---|---|---|---|---|
| P(large move) | 0.320 | 0.206 | 0.238 | 0.238 | 0.219 |
Non-monotone, and the highest-Λ quintile carries fewer large moves than the lowest — a ratio of 0.68, the wrong direction.
5. The FOMC event study
This is the test that separates a transmission operator from ordinary volatility clustering. FOMC decision dates are fixed years ahead, so news arrival carries no information and the size of each policy surprise is close to unpredictable by construction. Under clustered news, pre-event conductance should add nothing to what options already price. Under a genuine operator, it should forecast the response with a coefficient near 1.
| Predictor | Coefficient | t | p | 95% interval |
|---|---|---|---|---|
| Pre-event log conductance | −0.123 | −0.59 | 0.555 | [−0.53, +0.29] |
| Pre-event log realised volatility | −0.096 | −0.36 | 0.718 | — |
| Pre-event log implied volatility (GVZ) | +1.005 | +2.75 | 0.006 | — |
Implied volatility prices scheduled-event risk almost exactly right. Structural conductance adds nothing, with the wrong sign. The HAC standard error is 0.208, so the predicted +1.0 sits 5.4 standard errors outside the interval — an informative null, not an underpowered one. The result is stable across pre-event windows ending 2, 6 and 11 days out.
The detail that settles it
Pre-event conductance does load strongly on ordinary days (t = +7.98) and loses its significance precisely on days when news arrival is known in advance (t = +1.57). That ordering is backwards for a transmission operator, which should not care whether news was on the calendar. It is exactly what volatility clustering predicts.
6. Ten-asset generalisation
The pre-registered bar: if it only works on gold, it is a gold story dressed as a law. It does not only work on gold.
| Ticker | Asset class | α̂ | Ljung-Box(22) | VR(66) | OOS R² |
|---|---|---|---|---|---|
| HYG | High-yield credit | 0.994 | 1632.6 | 7.21 | +10.1% |
| SLV | Silver | 0.797 | 2459.0 | 11.02 | +9.4% |
| SPY | US large-cap equity | 1.357 | 1208.2 | 8.01 | +8.7% |
| QQQ | US tech equity | 1.022 | 1134.6 | 7.68 | +8.1% |
| USO | Crude oil | 0.734 | 964.4 | 6.30 | +7.3% |
| GLD | Gold | 1.032 | 1021.5 | 6.82 | +7.3% |
| EEM | EM equity | 1.257 | 1103.5 | 7.45 | +7.3% |
| GDX | Gold miners | 1.240 | 1173.6 | 7.45 | +7.2% |
| TLT | Long Treasuries | 1.027 | 729.5 | 6.46 | +5.6% |
| FXE | Euro | 0.412 | 777.0 | 6.51 | +5.2% |
Estimated impact exponents span 0.41 for the euro to 1.36 for the S&P 500, so no single assumed exponent — square-root or Amihud — would have been correct anywhere near universally.
Per-variable Commitments of Traders diagnostic
Construction-free: each raw variable added individually to the full control set, so the result does not depend on how Λ was assembled.
| Variable | Role in the theory | t | ΔOOS R² |
|---|---|---|---|
| Trader count (breadth) | Absorption | −3.18 | +0.79 pp |
| Open interest (depth) | Absorption | −2.88 | +0.46 pp |
| Managed Money net / OI | Forced mass | −1.18 | −0.21 pp |
| Managed Money long / OI | Forced mass | −1.17 | −0.09 pp |
| Managed Money short / OI | Forced mass | +0.99 | −0.74 pp |
| Managed Money gross / OI | Forced mass | −0.04 | −0.49 pp |
| Δ Managed Money net, 5d | Forced mass | −0.25 | −0.26 pp |
| Swap dealer short / OI | Forced mass | −0.49 | −1.58 pp |
| Producer short / OI | Forced mass | −0.41 | −1.29 pp |
All twelve variables jointly add +2.0 percentage points of in-sample R² and lose 5.2 points out of sample — the signature of overfitting.
What this settles
Settled, in the theory's favour
The impact operator is a genuine state variable: persistent, forecastable at 7.3% out-of-sample R², distinct from realised and implied volatility, and present in every liquid market tested. A constant-impact reading is decisively rejected.
Settled, against the theory
That the persistence is produced by the discretion distribution of the holder base. The forced-mass side is flat, the only signal is generic depth and breadth, and the effect disappears on scheduled events where it should be strongest.
Still open
The absorption stack the theory specifies — COMEX registered versus eligible stocks, LBMA vault holdings, Bank of England custody, Swiss customs — was never testable, because the primary sources are blocked. But note the bar it now faces: it would have to explain a signature identical in markets with no vaults at all.