anomaly-atlas
Honesty doctrine. Every candidate anomaly is an artifact until proven otherwise; in-sample results are never findings; past statistical regularity does not imply future returns. This is research on statistical properties of market data — not investment advice, not a trading system.

Research / research/notes/mean_reversion_leadlag.md

Phase 1 notes — short horizon mean reversion & lead lag

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Phase 1 notes — short-horizon mean-reversion & lead-lag · created Tue Aug 11 2026 20:00:00 GMT-0400 (heure avancée de l’Est) · Simon-Pierre Boucher

Short-horizon mean-reversion & lead-lag (Q1, Q2)#

Phase 1 literature notes. All citations verified via OpenAlex, accessed 2026-08-12. Epistemic status flags: robust / decayed / disputed / likely-artifact.

1. The founding results#

  • Lo, A. W. & MacKinlay, A. C. (1988). Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test. Review of Financial Studies 1(1), 41–66. https://doi.org/10.1093/rfs/1.1.41 — The variance-ratio test rejects the random walk for weekly index returns 1962–1985 (VR > 1: momentum at the index level), explicitly not fully explained by infrequent trading. Status: robust as a historical fact; the effect itself decayed.
  • Lehmann, B. N. (1990). Fads, Martingales, and Market Efficiency. Quarterly Journal of Economics 105(1), 1–28. https://doi.org/10.2307/2937816 — Weekly winner/loser reversals in individual stocks survive his spread corrections. Status: disputed — later work attributes much of it to bid-ask bounce and liquidity provision compensation.
  • Jegadeesh, N. (1990). Evidence of Predictable Behavior of Security Returns. Journal of Finance 45(3), 881–898. https://doi.org/10.1111/j.1540-6261.1990.tb05110.x — Strong negative first-order monthly serial correlation in individual stocks. Status: decayed post-publication (see McLean–Pontiff below).

Key structural insight for Q1: at the index/portfolio level early evidence showed VR > 1 (positive autocorrelation), while individual stocks showed reversal. The difference is exactly the cross-autocorrelation structure — which is where the artifacts live.

2. Lead-lag: the anomaly and its artifact twin#

  • Lo, A. W. & MacKinlay, A. C. (1990). When Are Contrarian Profits Due to Stock Market Overreaction? Review of Financial Studies 3(2), 175–205. https://doi.org/10.1093/rfs/3.2.175 — Contrarian profits come largely from lead-lag cross-autocorrelations (large leads small), not overreaction. The canonical Q2 result.
  • Scholes, M. & Williams, J. (1977). Estimating betas from nonsynchronous data. Journal of Financial Economics 5(3), 309–327. https://doi.org/10.1016/0304-405X(77)90041-1 — Non-synchronous observation biases correlations/betas and manufactures spurious lead-lag. The artifact null for all of Q2 — our expB measured exactly this on hfmarketdata.io (SPY "leads" stale tickers +0.047 at 1min; SPX lags SPY +0.065).
  • Epps, T. W. (1979). Comovements in Stock Prices in the Very Short Run. Journal of the American Statistical Association 74(366a), 291–298. https://doi.org/10.1080/01621459.1979.10482508 — Cross-correlations shrink as sampling gets finer (the Epps effect). At our 1min floor, contemporaneous correlations are mechanically attenuated and the "missing" correlation shows up at leads/lags. Any 1min lead-lag claim must model this.
  • Chordia, T., Roll, R. & Subrahmanyam, A. (2005). Evidence on the speed of convergence to market efficiency. Journal of Financial Economics 76(2), 271–292. https://doi.org/10.1016/j.jfineco.2004.06.004 — Predictability from order flow is arbitraged away within 5–60 minutes (already by 2005). Sets the prior: minute-scale inefficiencies in liquid names should be tiny-to-absent in our 2020s data.

3. What decayed#

  • McLean, R. D. & Pontiff, J. (2016). Does Academic Research Destroy Stock Return Predictability? Journal of Finance 71(1), 5–32. https://doi.org/10.1111/jofi.12365 — Across 97 published predictors: −26 % out-of-sample, −58 % post-publication. The base rate for our whole project.
  • Chordia, T., Subrahmanyam, A. & Tong, Q. (2014). Have capital market anomalies attenuated in the recent era of high liquidity and trading activity? Journal of Accounting and Economics 58(1), 41–58. https://doi.org/10.1016/j.jacceco.2014.06.001 — Anomaly profits attenuate sharply post-decimalization as liquidity/arbitrage grows. Directly relevant: our data (2000→2026) spans this attenuation; sub-period stability checks (expH) are mandatory.
  • Jacobs, H. & Müller, S. (2020). Anomalies across the globe: Once public, no longer existent? Journal of Financial Economics 135(1), 213–230. https://doi.org/10.1016/j.jfineco.2019.06.004 — Decay is largely a U.S. phenomenon. Our data is U.S.-centric: expect the fastest decay regime.

4. Implications for our experiments (expC, expD)#

  1. Reversion at 1min in liquid names should be ≈ 0 (bounce-free mega-caps showed AC1 CI covering 0 in expB) — a negative finding here is the expected, publishable outcome.
  2. Any reversion in mid/low liquidity must beat the measured bounce null (expB: AC1 −0.05 to −0.23 with zero economics).
  3. Any lead-lag must beat the staleness-predicted cross-correlation AND survive on both-fresh subsamples (Scholes–Williams; Epps).
  4. Test sub-periods: pre/post 2010 and pre/post publication of the classic papers; expect attenuation à la Chordia et al.
  5. Horizon matters: 1min → daily aggregation sweeps let us find where (if anywhere) reversion exceeds its artifact floor.