BL-IS-010: Information Decay Map

Status: RELEASED

Classification: PUBLIC

Revision: 1

Date: 2026-09-09

1. What it measures

Information coefficient, Spearman rank correlation, between a causal signal and a forward return, computed for two different targets at once across a grid of prediction horizons.

IC_dir(h)  =  rho( s_t , r_{t,t+h} )         direction: which way price moves
IC_wid(h)  =  rho( s_t , |r_{t,t+h}| )       width: how far it moves

The two targets are kept apart deliberately. A signal can forecast the magnitude of a move without forecasting its sign, and reporting a single coefficient hides which of the two is actually present. wid_over_dir, the ratio of the two coefficients' magnitudes, is reported alongside both for exactly this reason.

2. Why it exists

The motivating question, put directly during the programme's second review: whether this substrate offers valuable information only before a price move occurs, or only after one has already happened, given that the programme does not treat microstructure data as a predictor. It is measurable from the substrate already in hand, and across both programmes the answer had surfaced only in disconnected pieces, in the ledger rows this record calls S3, WC1, IB1, and B1/BR1, without ever being assembled into one map. This instrument assembles it.

Separating direction from width is the more expensive lesson underneath the design. H-P1 was falsified in part because an earlier measurement read what was width information as if it were direction information. Every cell here carries both coefficients, never one alone.

The instrument characterises. It tests no hypothesis, consumes no pre-registration quota, and computes no profit and loss anywhere in its body. Section 7 states why that is not a limitation.

3. Two regimes, kept separate

Signals fall into two families, built causally from trailing state only, with the held-out era sealed by the same guard every research instrument in this programme carries.

Pre-move is state that exists before any move: open interest z-score, funding percentile, turnover z-score, realised volatility percentile, volatility-of-volatility. Post-move is a move that has just happened, normalised by local realised volatility so a large move on a quiet symbol and a small move on a volatile one are comparable, including one variant conditioned on falling open interest, a weak deleveraging proxy carried forward from an earlier five-minute measurement.

Coefficients are computed per symbol and then averaged across symbols, never pooled by concatenating every symbol's observations into one series. Pooling mixes cross-symbol scale differences with the within-symbol relationship being measured, a defect an earlier one-hour proxy version of this instrument carried before correction.

4. Interface

information_decay_map(panel, horizons, signals) -> DecayMapReport
 
  panel      per-symbol hourly panel: close, open interest, turnover, funding
  horizons   grid of forward horizons in bars: 1, 4, 12, 24, 72
  signals    named causal signal functions, pre-move and post-move
 
Returns, per (signal, horizon) cell: n_symbols (contributing at least 2,000
observations each), n_obs (pooled, for context only), ic_dir_mean/median/t,
ic_wid_mean/median/t, and wid_over_dir.
 
Raises when a signal or forward-return series fails the held-out era
assertion. A cell is omitted, not reported, below 500 observations or 10
contributing symbols.

5. Specification

Given a symbol universe with per-symbol trailing signal s_t and forward
log return r_{t,t+h}:
 
  IC_dir(h, sym) = rho( s_t, r_{t,t+h} )              within symbol
  IC_wid(h, sym) = rho( s_t, |r_{t,t+h}| )             within symbol
 
Cross-symbol aggregation, mean and t-statistic on the per-symbol coefficient
itself, not on pooled observations:
 
  ic_dir_mean(h) = mean_sym( IC_dir(h, sym) )
  t_dir(h)       = ic_dir_mean(h) / ( sd_sym(IC_dir(h,.)) / sqrt(n_symbols) )
 
  wid_over_dir(h) = abs(ic_wid_mean(h)) / abs(ic_dir_mean(h))

The t-statistic answers a narrow question: how consistent the coefficient's sign is across symbols, not how large it is. A small, universally consistent coefficient produces a large t; a large but idiosyncratic one does not.

6. Results: the shape, not a price

Measured across 154 symbols, research era 2022-01 to 2025-06 [E-0039]:

The pattern holds across the full 50-row map, not only these six cells. A post-move signal carries its largest direction coefficient at the shortest horizon tested and decays toward insignificance by 72 bars, t = -0.4 on the strongest such signal at that horizon. A pre-move state signal carries comparatively little direction information at any horizon, but a width coefficient that decays far more slowly and stays significant at t > 35 even at 72 bars.

The answer to the motivating question is not before or after. It is that the two regimes answer different questions: post-move state prices where, pre-move state prices how much. A separate artifact conditioning the same coefficients on fragility and funding regime, E-0006, corroborates the same shape, though its producing script is no longer present in the repository and its figures are reported here as corroboration, not as this instrument's own output.

7. Why it computes no returns

This is the instrument behind R-07: an information coefficient may characterise, and it may never be converted into a profit estimate inside a decision path.

The conversion was tried. The analytical shortcut IC * sigma * z, applied to a conditioned reversion hypothesis, predicted 74.4 basis points at the primary cell; realised gross return measured 13.3, a 5.6-fold overstatement. Two further cells checked under the identical conversion overstated by 13.7-fold and 7.3-fold respectively [E-0021, E-0039]. A single correction factor would rescue a biased but consistent ratio. It cannot rescue this one, because the ratio itself is not stable across configurations that share the same signal and the same instrument.

That is the whole reason this instrument stops where it stops. A coefficient describes the shape of information faithfully. It has never once, on this substrate, priced it faithfully, and every recorded attempt erred the same way: optimistic.

8. What it does not do

It does not rank signals by tradeability, and it does not distinguish a signal that is causally informative from one that is a proxy for another already in the panel: pre/turnover_z and pre/realized_vol_pct move together closely enough here that neither is independent evidence of the other's mechanism. A larger ic_dir_mean is not a larger edge; section 7 is the reason a reader cannot make that substitution regardless of how tempting a cell looks.

It does not correct for the size of its own search. The map reports up to fifty cells across five horizons and multiple signals in one run; a single striking cell is a candidate for a separately pre-registered hypothesis, not a discovery in its own right, and the multiple-testing discipline of R-05 applies to whatever hypothesis is built from one.

9. Cross-references

BL-D-009 rule R-07 and its provenance note. BL-SD-039 sections 7 and 9 for the primary over-prediction case. BL-A-002 section 6 for the information-coefficient notation and prohibition. BL-SD-000 section 8 for the joint citation of E-0006 and E-0039. Evidence E-0039, E-0006, E-0021.

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