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Information horizon

Every alpha is perishable: its forecasting power (IC) decays over time at a rate that is an intrinsic property of the signal. src/alphas/horizon.py measures that decay and turns it into two free wins — a principled rebalance cadence and a lagged blend that raises the information ratio.

Research clock only

A diagnostic over an existing alpha's decay structure; it places no orders.

Decay and half-life​

IC measured at increasing lags n (the alpha at t vs the residual return realized n periods later) follows:

IC(n) = IC₀ · δ^n            half-life HL = −ln 2 / ln δ

fit_decay fits δ by log-linear regression on the reliable, positive-IC lags and reports the fit R² — a low R² means the decay isn't a clean exponential, so don't over-trust the half-life. Because value added scales with IR², the value-added half-life is half the IC half-life — stale alphas are more damaging than they look.

Cadence and the breadth↔frequency tradeoff​

IR(Δt) = IC(Δt) · √(1/Δt)

Rebalancing faster raises √BR but acts on less-confirmed information (lower IC) and costs more. The optimum is interior: recommended_cadence returns the Δt that maximizes this IR proxy, so the cadence is chosen, not assumed. The half-life is also the holding period transaction cost should be amortized over — closing that spec's "what holding period?" gap.

The optimal current/lagged blend​

Given decay γ (= δ) and the signal's autocorrelation ρ, the IR-maximizing weight on the current signal is:

w_now = (1 − γ·ρ) / (1 + γ² − 2·γ·ρ)        w_lag = 1 − w_now
  • δ > ρ → diversify: w_lag > 0 — the lag carries independent information.
  • δ < ρ → hedge: w_lag < 0 — it mostly cancels current noise.
  • δ = ρ → the latest signal alone is sufficient.

Matching signal to return horizon​

A signal of half-life HL predicts returns best at a horizon ≈ 1.26·HL (where the signal-return correlation peaks). Surfaced as peak_return_horizon so a short-horizon signal isn't scored against a long-horizon return — a common way to understate real skill.

Caveats it surfaces​

  • Decay should be measured out-of-sample — fitting it on the selection data overstates persistence.
  • The blend adds turnover — its lagged leg is priced through the cost model and blend_recommended is only true when the blend diversifies and its annual turnover cost is modest; a high-turnover blend that would lose net is flagged.
  • Regime-dependent decay — the half-life isn't constant; re-estimate on a rolling window rather than freezing one number.

Where it runs​

services.compute_horizon measures the IC-vs-lag profile (reusing the information-analysis forward-residual machinery), fits the decay, and recommends the cadence + blend. The CLI (python main.py horizon) and the read-only MCP tool compute_horizon route through it.