The learning ladder

A linear model decomposing an asset's return into common factors (market, sector, …) plus a residual. The foundation of the bottom-up unit.

The slope of an asset's return regressed on a factor; how much the asset moves per unit factor move.

The part of a stock's return left after the factor model is removed. RiskModels emphasizes the residual as where selection skill lives.

Synonym for residual in classical finance literature. We standardize on *residual*.

Skill-attributable excess return at the position level.

The factor exposure you'd offset to neutralize a position's exposure to that factor.

Splitting a stock's variance into shares attributable to each factor and the residual. Sums to 1.0.

Splitting a stock's *realized return* into contributions from each factor. Distinct from variance: a name can be variance-dominated by market yet return-driven by residual.

A holding's share of portfolio value; the weight that scales its risk and return contribution when positions aggregate.

Rolling individual holdings up to portfolio-level factor exposure by weight — the bridge from stock risk to portfolio risk.

A cap-weighted set of similar securities (typically by sector and sub-sector) used as the comparison universe for relative analyses.

How two positions move together; why portfolio risk is not just the weighted sum of position risks.

The risk reduction from holding imperfectly-correlated positions; the gap between summed position risk and actual portfolio risk.

Splitting total portfolio variance into factor and residual shares, accounting for cross-position covariance. The portfolio-level analog of the single-stock decomposition.

Each position's (or factor's) share of *total portfolio risk*, accounting for correlation. Component contributions sum to the total — unlike standalone position risk.

Splitting the portfolio's realized return into contributions from market, sector, subsector, and residual selection.

The fraction of a portfolio that differs from its benchmark; how much of the book is an active bet versus the index.

The volatility of portfolio-minus-benchmark return; the size of the active risk.

How well a portfolio's returns are explained by a benchmark (R², tracking error) — the quality of the comparison.

Return per unit of volatility.

Peak-to-trough decline. *Max drawdown* is the worst observed.

A dataset that respects when each fact was *knowable*, not just when it was *true*. Bloomberg and FactSet sell PIT databases as a premium product.

Letting a backtest see information that wasn't yet public on the simulated date. The most common research bug.

The gap between when a fund's holdings reflected reality and when they became publicly knowable via SEC filings. ~45 days for 13F, ~60 days for N-PORT.

Backtesting on a universe that excludes delisted or failed entities. Produces optimistic results.

SEC filing (Form 13F-HR) listing institutional managers' US-listed equity holdings. Quarterly, 45-day lag.

SEC filing reporting registered fund (mutual fund / ETF) holdings monthly. Only every third month is publicly disclosed.

Annual SEC filing for registered funds; carries adviser relationships and share-class detail.

The SEC's identifier for any filer (manager, fund, adviser).

The canonical record of *what is this security and what was it called when?* — the foundation under any survivorship-corrected analysis.

The public REST + MCP surface for decomposition, attribution, and exposure analyses. Documented at [riskmodels.app](https://riskmodels.app).

The Python client for the API. `pip install riskmodels-py`.

A one-page institutional analysis of a single equity: factor decomposition, attribution, residual quality, peer context.

A one-page tearsheet for a single fund: portfolio attribution, holdings, NAV, benchmark fit.

Analysis Object Model — our publicly-versioned protocol for describing analyses (subject + lens + view) before they hit any endpoint.

Same input → byte-identical output on re-run. Required for cache correctness and auditability.

The metadata recording how an artifact was produced: subject, parameters, as-of date, model version.

Web, PDF, PNG, and agent surfaces all read the same canonical artifact. Drift across surfaces is impossible by construction.

Equity Risk Model v3 — the engine. Decomposes any US equity into market → sector → subsector → residual via a hierarchical orthogonal cascade.

L1 = market (SPY); L2 = sector ETF (e.g. XLK) fit on the L1 residual; L3 = subsector ETF (e.g. SOXX) fit on the L2 residual. Each level explains what the prior one left over.

The coefficient that strips a higher level's exposure from a lower one, so each β captures only the *incremental* effect of its own level — no double-counting.

The variance share attributable to each level. ER(L1) + ER(L2) + ER(L3) + residual = 1.0 by construction, verified at runtime to ±0.1%.

The raw-ETF identity that reproduces a stock's return from its hedge legs — only tradeable ETF returns, no orthogonalization at trade time. Verified to ±0.1% for every stock, every date.

Betas estimated by 252-day rolling Huber-M regression, robust to the fat tails (earnings gaps, single-day reclassifications) that distort ordinary least squares.

L2/L3 betas shrunk toward the log-mcap-weighted peer mean within a 4-digit industry cohort; short-history and small-caps are pulled more. Market beta (L1) is not shrunk.

The L\* rule: a cost-aware, learned selector that picks the shallowest level whose expected out-of-sample variance reduction outweighs the added hedging cost of going deeper — describing a name at the coarsest level that still captures its risk. Scored point-in-time, so the dispatch is backtest-safe.

Telescoping compound differences (market → sector → subsector → residual) so multi-period factor contributions sum exactly to the gross compound return — not the naive daily sum, which overstates by volatility drag.

A 5-day cumulative L3 residual return, z-scored by the stock's own 60-day residual volatility. A combo-input factor for multi-signal stacks, not a standalone strategy.