19-Factor Risk Model Methodology

A Barra USE4-style factor model for decomposing portfolio risk and return into systematic and idiosyncratic components.

Overview

Factor models explain security returns as a linear combination of common factor returns plus an idiosyncratic component. The general form is:

\displaystyle R_i = \alpha_i + \sum_{k=1}^{K} \beta_{i,k} f_k + \epsilon_i

Where:

$R_i$ is the return of security $i$
$\alpha_i$ is the security-specific alpha (skill)
$\beta_{i,k}$ is the exposure of security $i$ to factor $k$
$f_k$ is the return of factor $k$
$\epsilon_i$ is the idiosyncratic (stock-specific) return

Validation Status

Quantitative factor-model claims are pulled from the claims registry so users can distinguish code-backed model dimensions from validation targets that are still waiting on the Track A harnesses.

Backed claim

19 count

Count of factors defined in FactorExposures interface. Verified: 19 factors in src/services/factors.ts

Evidence provenance

factor-model-19

Test evidence: tests/services/factors.test.ts

Planned validation

0.6 correlation

Redefined for a risk model (bd-2lg9oy.10): the IC is the per-window Spearman correlation of factor-model predicted σ against realized σ across portfolios. The earlier return-prediction IC (docs/claims/factor-ic-latest.json) measured 0.0019 and is the wrong statistic for a risk model. Measured 2026-11-02 on a local mirror of production's v1.2.0 factor returns, covariances and batch_job exposures (per-year return and covariance hashes equal production's), 2012-01 to 2026-08: mean 0.423 (SE 0.012) over 161 disjoint 21-session windows and 7,949 forecasts (docs/claims/risk-forecast-eval-latest.json). Was 0.348 over 173 windows on 2026-10-12, before production's 2021-2026 re-estimation (2026-10-22 to 10-26) and before the evaluator read only batch_job exposures (lo6pp6.2), which drops 2020 (gap-fill rows only); the two changes are not decomposed. Below the >= 0.60 goal: NOT MET. Re-dated 2026-11-01 to 2026-12-31 while v1.3.0 regression and universe calibration (bd-mic05q, bd-barra-cert-epic-vma96) remain in progress.

Evidence provenance

ic-0.62

Computed 2026-11-02; evidence tests/research/risk_forecast_eval.test.ts; docs/claims/risk-forecast-eval-latest.json; target 2026-12-31

Planned validation

0.98-1.02 ratio

Now scored against FACTOR-MODEL sigma (sqrt(x'Σ_F x + Σ w²σ²_ε) as of each forecast date), not trailing realized volatility (bd-2lg9oy.10). Measured 2026-11-02 on a local mirror of production's v1.2.0 artifacts and batch_job exposures, 2012-01 to 2026-08, 161 disjoint 21-session windows, 7,949 forecasts: bias 1.048, 95% CI [0.998, 1.106] (2026-10-12: 1.064, CI [0.962, 1.205] over 173 windows, before production's 2021-2026 re-estimation and the batch_job-only exposure read that drops 2020). The point estimate lies outside [0.98, 1.02] and the interval is too wide to confirm or refute the target: NOT DEMONSTRATED. The point-in-time top-120 book alone (66 windows from 2021) measures 1.080, CI [0.94, 1.30]. The earlier 1.07 figure scored the trailing-volatility baseline. Re-dated 2026-11-01 to 2026-12-31 while v1.3.0 calibration (bd-mic05q, bd-barra-cert-epic-vma96) remains in progress.

Evidence provenance

bias-ratio-0.98-1.02

Computed 2026-11-02; evidence tests/research/risk_forecast_eval.test.ts; docs/claims/risk-forecast-eval-latest.json; target 2026-12-31

Planned validation

94 percent

Scored against the factor model's own 95% VaR (1.6449·σ_pred) on a local mirror of production's v1.2.0 artifacts and batch_job exposures, measured 2026-11-02 over 2012-01 to 2026-08 (bd-2lg9oy.10): pooled coverage 96.1% over 166,929 portfolio-days, meeting the >= 94% goal (2026-10-12: 96.6% over 179,298, before production's 2021-2026 re-estimation and the batch_job-only exposure read that drops 2020). Calibration errs conservative: on the point-in-time top-120 series coverage is 96.25% over 1,386 days, so Kupiec rejects exact 95% (p=0.026, too few violations), while Christoffersen finds no clustering (p=0.18). The prior 93.79% (docs/claims/var-coverage-latest.json) scored a trailing-volatility VaR. Re-dated 2026-11-01 to 2026-12-31 while Kupiec exact-95% calibration on the point-in-time book remains open under v1.3.0.

Evidence provenance

var-coverage-94.2

Computed 2026-11-02; evidence tests/research/risk_forecast_eval.test.ts; docs/claims/risk-forecast-eval-latest.json; target 2026-12-31

Source: docs/claims.json, generated 2026-09-07.

Portfolio Factor Exposures

Portfolio-level factor exposure is the weighted sum of security-level exposures:

\displaystyle \beta_{P,k} = \sum_{i=1}^{N} w_i \cdot \beta_{i,k}

Where $w_i$ is the portfolio weight of security $i$ (position value divided by total portfolio value).

Factor Orthogonalization & Sector Standardization

To ensure factors capture independent incremental information and to reduce collinearity in cross-sectional regressions, intermediate factor loadings are orthogonalized using a weighted Gram-Schmidt process. Each factor is projected against preceding factors and the residual becomes the orthogonalized factor.

For a target factor $X$ being orthogonalized against a base factor $Y$ :

\displaystyle X^{\perp} = X - \frac{\sum_i w_i X_i Y_i}{\sum_i w_i Y_i^2} \cdot Y

In v1.2.0 the weights $w_i$ are market capitalizations, so larger companies have proportionally more influence on each projection.

Post-Orthogonalization Sector Standardization: Following the Gram-Schmidt projection, exposures undergo a second standardization pass within GICS sectors, followed by coverage masking. Because within-sector re-centering is piecewise-affine by group, the persisted exposures matrix in security_factor_exposures is non-orthogonal by design. This preserves sector-neutral style z-scores across diverse industry distributions while maintaining bounded cross-factor correlations.

Exposure units: In v1.2.0 each raw style value is clipped at the cap-weighted mean ± 3 cap-weighted standard deviations, z-scored within its GICS sector using that sector's cap-weighted mean and standard deviation (a sector with fewer than 5 names uses the whole cross-section), re-centered to a cap-weighted mean of 0 and rescaled to an equal-weighted standard deviation of 1, with no clip after the rescale. This runs twice, around a cap-weighted Gram-Schmidt pass that removes from each style factor its projection on the style factors listed before it. A name without the raw inputs is stored as NULL, not 0. That chain wrote every v1.2.0 row dated from 2026-07-01; rows dated 2005 through 2026-06-30 were written in June 2026 by an earlier chain that ran the Gram-Schmidt pass on raw, uncentred values, so the two vintages share the v1.2.0 label but not one method.

Orthogonalization Order: The order matters. We follow the Barra convention: SIZE, SIZENL, BTOP, EARNYILD, DIVYILD, GROWTH, LEVERAGE, BETA, BETANL, RESVOL, LIQUIDITY, MOM3WKZS, MOM11MNZS, RET5DZS, SHORTINTEREST, HFOWN, PASSOWN, SHIMCAPZS. MARKETBETA, the constant intercept, is not orthogonalized or standardized.

Factor Return Computation

Daily factor returns are estimated using weighted cross-sectional regression:

\displaystyle \hat{f} = (X^T W X)^{-1} X^T W R

Where $X$ is the matrix of factor exposures, $W$ is a diagonal weight matrix of market capitalizations, and $R$ is the vector of security returns.

Estimation convention: In v1.2.0 the factor returns for date t regress each stock's return on day t on its exposures as of the same day t (same-day pairing: SIZE uses that day's market cap and the BETA and RESVOL windows end on t). The fit is weighted least squares in which each stock's squared residual is weighted by its market cap (the row multiplier is the square root of market cap); the 19 factors are the only columns, with MARKETBETA as the intercept.

Factor Covariance Matrix

We estimate the factor covariance matrix using an Exponentially Weighted Moving Average (EWMA) with dual half-lives for robustness:

\displaystyle \Sigma = \lambda \cdot \Sigma_{\text{short}} + (1-\lambda) \cdot \Sigma_{\text{long}}

Short half-life: 32 days (responsive to recent volatility)
Long half-life: 128 days (stable, long-term structure)
Blend weight: $\lambda = 0.5$ (equal weight by default)

The EWMA weight for observation $t$ days ago is:

\displaystyle w_t = \left(\frac{1}{2}\right)^{t / \tau}

Where $\tau$ is the half-life in days.

The 19 Factors

Our model includes the broad-market intercept plus 18 style factors. Each style factor captures a systematic source of return that has been documented in academic literature and used in practice by institutional investors.

Broad market (MARKETBETA)

The stock model's common market component, with a base loading of 1 for each stock: the market intercept, exactly 1.0 for every security on every date, so its factor return is the move all stocks share that day. Portfolio loadings also reflect position direction and any supported leverage adjustment. It does not vary across stocks; how strongly each stock has moved with the market is the separate Historical Beta (BETA) factor.

\displaystyle \text{MARKETBETA}_i = 1

Units: Constant 1.0 for every security; not standardized.

Interpretation: A positive exposure has more long than short exposure to the common market component; a negative exposure has more short than long exposure to the common market component.

Size (Market Cap) (SIZE)

Company size measured by log market capitalization (the natural log of market cap on the model date), scored against the cap-weighted average company of the stock's own GICS sector. Positive values are larger than that sector average and negative values smaller, so a mega-cap in a sector of mega-caps scores near 0, below a smaller company that is large for its own sector.

\displaystyle \text{SIZE}_i = \allowbreak\ln(\text{MarketCap}_i)