Method — Hegemonic Growth

01 / Breadth

Skill is worth little without independent bets to apply it to.

The fundamental law of active management states it exactly: realised information ratio scales with forecasting skill and with the root of the number of genuinely independent decisions, degraded by how much of the forecast survives implementation.

IR ≈ IC · TC · √BR

IR: information ratio — active return per unit of active risk
IC: information coefficient — correlation of forecast with outcome
TC: transfer coefficient — the fraction of the forecast that reaches the book
BR: breadth — genuinely independent bets per period

Independence is the term that gets overstated. Two hundred positions driven by one factor is breadth of one. In public equities the same signals are applied by many participants to the same names, so breadth is shared and TC is compressed by crowding. Ownership and capital-formation events are observed by very few and are close to independent of one another, which is where the root-breadth term is actually recoverable.

02 / Decay

Every signal is a decaying asset.

Predictive content dissipates as information diffuses. We model it as exponential decay in the information coefficient and report a half-life with every effect, because what a signal is worth is the integral of its edge over the time it survives, not the height of its backtest.

IC(τ) = IC₀ · e^−τ/λ , t_½ = λ ln 2

τ: time since the observable event
λ: decay constant, estimated per signal family
t½: half-life — the horizon over which half the edge is gone

Where λ is short the binding constraint is operational rather than analytical: the edge is real but disperses before it can be implemented. A signal whose half-life cannot be estimated is usually one nobody has instrumented.

03 / Evidence

A point estimate on thin data is not evidence.

Rates measured on small samples are reported as intervals. We use the Wilson score lower bound, which stays well behaved near zero where the normal approximation does not — and near zero is exactly where a new signal lives.

p̂_lo = [ p̂ + z²/2n − z√( p̂(1−p̂)/n + z²/4n² ) ] / (1 + z²/n)

p̂: observed rate
n: sample size
z: 1.96 at the 95% level

Two hits in forty is consistent with a true rate anywhere from roughly one to seventeen percent. Reporting five percent as the answer is how a programme persuades itself of an edge it has not measured.

04 / Multiplicity

Test enough hypotheses and significance arrives by construction.

Families of tests are declared before they are run and controlled by false-discovery rate rather than reported one at a time. On a corpus of this size an uncorrected search will always find something.

reject H_(i) for i ≤ max{ i : p_(i) ≤ i q/m }

p(i): ordered p-values across the declared family
m: hypotheses in the family, fixed in advance
q: tolerated false-discovery rate

Benjamini–Hochberg, applied to the family rather than to each test alone. The discipline is fixing m before the search; a family defined once the results are known controls nothing.

05 / Sizing

An edge sized wrongly is an edge given back.

Position size follows from the estimate and its uncertainty, not from conviction. We size on a fraction of Kelly, because full Kelly assumes the estimated edge is the true edge — and the whole point of the previous section is that it is not.

f* = μ / σ² , f = k f*, k < 1

f*: full-Kelly fraction under the estimated edge
μ, σ²: expected excess return and its variance
k: the discount applied for estimation error

Estimation error in μ is the dominant risk, and it enters the sizing quadratically. Half-Kelly gives up roughly a quarter of the growth rate for a large reduction in drawdown — a trade any allocator with a redemption window should want made.

Construction

Standards a result clears before it leaves the building.

Point-in-time

Universes are rebuilt from the record as it stood on the decision date, including entities that later ceased to exist. Assembling a universe from survivors embeds an upward bias no modelling removes.

Entity resolution

Identifiers are reconciled across registers before any estimate is computed. One entity appearing under several identifiers inflates apparent breadth and corrupts the root-breadth term directly.

Look-ahead

Fields are checked for availability at the decision date, not at the date they were populated. This is the commonest and least visible cause of a beautiful backtest.

Capacity

Every effect carries its capacity assumption: turnover, participation, and the liquidity of the names it selects. An edge that disappears at size is an artefact of the universe filter.

Provenance

Every figure resolves to a document, an issuer and a date. Derived fields carry their derivation. Where the record cannot answer, that is the answer given rather than the nearest available number.

Published work

Peer-reviewed research by the team.

The transferable problem is recovering structure from a channel that is mostly noise, and stating precisely how much confidence the data supports.

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