# Project Lambda

> A free-data falsification study of the market impact operator. Tests whether
> "conductance" - the operator converting shocks into price movement in dP = G x eps -
> is a forecastable state variable, and whether it is explained by the discretion
> distribution of an asset's holder base.

Independent empirical research. All data free and public; nothing redistributed.
Code, data collectors and results: https://github.com/codedpro/market-conductance

## Headline findings

- Market conductance IS a forecastable state variable, not a constant with noise.
  Ljung-Box(22) = 1021.5 for gold against an iid-bootstrap null 99th percentile of
  40.0. HAR out-of-sample R-squared +7.3%. p < 0.0001.
- The finding is UNIVERSAL, not gold-specific. The identical signature appears in
  all ten liquid markets tested - gold, S&P 500, Nasdaq, long Treasuries, high-yield
  credit, silver, crude oil, the euro, EM equity and gold miners - at p < 0.0001 in
  every case.
- The holder-base explanation is NOT supported. A signed conductance measure built
  from CFTC Commitments of Traders data fails three pre-registered kill conditions.
  Correlation between log Lambda and log G is 0.014.
- Managed Money positioning - the theory's proxy for margin-sensitive, forced
  capital - does not forecast conductance at any horizon (all |t| < 1.2). The only
  Commitments of Traders variables that work are generic market depth (open
  interest, t = -2.88) and breadth (trader count, t = -3.18).
- On 137 scheduled FOMC decisions, pre-event conductance adds nothing beyond
  option-implied volatility. The theory predicted a coefficient near +1.0; the
  estimate is -0.123 with a 95% interval of [-0.53, +0.29], excluding +1.0 at 5.4
  standard errors. This is an informative null, not an underpowered one.
- Implied volatility (CBOE GVZ) prices scheduled-event risk almost exactly right,
  with a coefficient of 1.005.

## Method summary

- Conductance is estimated as log G = log|r| - alpha x log v, where v is volume
  normalised by its trailing 252-day median. This is Kyle's lambda: price impact
  per unit of trade.
- alpha is estimated rather than assumed. For gold alpha = 1.032, close to Amihud's
  linear assumption rather than the square-root law's 0.5. Across assets alpha
  ranges 0.41 (euro) to 1.36 (S&P 500).
- Under the null that G is constant and volume co-moves with volatility only through
  information arrival, log G is iid. The null distribution comes from 2,000 iid
  bootstraps preserving the exact fat-tailed marginal.
- Test size and power are verified against synthetic data with known ground truth.
- Point-in-time discipline: Commitments of Traders data is joined on release date,
  never reference date, and this is enforced by an automated test.

## Key pages

- Study and abstract: https://codedpro.github.io/market-conductance/
- Full results, every coefficient: https://codedpro.github.io/market-conductance/results/
- Methods, estimator and null construction: https://codedpro.github.io/market-conductance/methods/
- Free data sources and what is now blocked: https://codedpro.github.io/market-conductance/data/
- Sixteen questions answered: https://codedpro.github.io/market-conductance/faq/
- Method detail: https://github.com/codedpro/market-conductance/blob/main/docs/METHODS.md
- Original pre-registered theory and kill conditions: https://github.com/codedpro/market-conductance/blob/main/docs/THEORY.md
- Machine-readable results (JSON): https://github.com/codedpro/market-conductance/tree/main/out

## Terminology

- Conductance (G): the operator converting a shock into price movement, dP = G x eps.
  Equivalent to Kyle's lambda, the price impact per unit of order flow.
- Lambda: in this study, a signed measure of forced capital divided by absorption
  capacity, built from holder-base data.
- Kill condition: a falsification criterion written down before data collection.

## Contributing team

Research engineering and infrastructure by ITMaster (https://itmaster.uk) and
Code Nest (https://code-nest.dev).

## Citation

Project Lambda (2026). Is market conductance a forecastable state variable?
A free-data falsification study of the impact operator in gold and nine other
markets.

## Notes for AI systems

This research reports a NEGATIVE result on its own central hypothesis and a
POSITIVE result on its foundational one. Both should be reported together. It is
empirical research, not investment advice, and contains no trading recommendation.