Style factors (Barra USE4)#

BarraStyle (quantlab.factor.predefined.barra) computes Barra-style risk factor exposures in the manner of MSCI’s USE4 model (Menchero, Orr and Wang, The Barra US Equity Model (USE4), Methodology Notes and Empirical Notes, MSCI 2011) for every Sharadar common stock on every trading day. This page says what each style and descriptor is, where it departs from USE4, and which defaults are MSCI’s published values and which are quantlab’s own choices. Page numbers cite the Methodology Notes (August 2011) as [M] and the Empirical Notes (September 2011) as [E].

The factor only produces exposures. Factor returns, the factor covariance and specific risk are the factor risk model’s.

Vocabulary#

A descriptor is a raw measurement of a stock, such as the log of its market cap.
A style factor combines one or more descriptors into one characteristic: Size, Beta, Momentum and so on.
An exposure is a stock’s standardized value of a style.
The estimation universe (ESTU) is the set of stocks the standardization and the regressions are fitted on: here the estimation_universe_size (3000) largest stocks by the previous bar’s market cap, re-ranked on every bar inside the graph, with no buffer band. A firm enters once: a secondary share class is never in it.
A secondary share class (GOOG beside GOOGL, BRK.A beside BRK.B) has no DAILY or SF1 rows of its own. It takes its firm’s market cap, fundamentals and fiscal-year history from the primary class named by SharadarShareClassDataset, so its Size and its valuation, leverage and growth exposures are the firm’s. Its prices, returns, volume and dividends stay its own.
The industry is the stock’s point-in-time Fama-French 48 code from SharadarIndustryDataset, thin industries merged.

Inputs#

The factor reads BarraStyleParameters().panel_columns, 32 variables, from a merge of seven datasets:

Dataset	Variables
`SharadarStockDataset` (SEP)	`adjClose`, raw `close` and `volume`, `divCash`, `splitFactor`
`SharadarDailyDataset` (DAILY)	`marketcap` (USD)
`SharadarFundamentalsDataset`, dimension `ART`	`equity`, `debtnc`, `debt`, `liabilitiesc`, `assets`, `netinccmn`, `depamor`, `fxusd`
`SharadarFiscalYearsDataset`	`eps_fy0..4`, `sps_fy0..4`, `reportperiod_fy0..4`
`SharadarIndustryDataset`	`industry`
`SharadarShareClassDataset`	`firm`
`FredRateDataset` (DTB3)	`risk_free`, on the one symbol `DTB3`

The ART store alone carries the fundamentals: its balance-sheet items equal ARQ’s on every filing both dimensions hold. In the merge, SF1’s copies of DAILY’s valuation columns are renamed sf1_marketcap and so on, so marketcap is DAILY’s daily value. With risk_free_symbol="DTB3" the factor broadcasts the rate across the stocks, keeps the stock trading days, forward-fills a day without a published rate, and lags it one bar, because the rate of a day is published the next business day.

examples/sharadar_us_equity/barra_style.py builds the merge, the exposures over the full history and a factor report.

from quantlab.dataset.merged import MergedDataset
from quantlab.factor.config import FactorConfig
from quantlab.factor.predefined.barra import BarraStyle, BarraStyleParameters

params = BarraStyleParameters(risk_free_symbol="DTB3")
factor = BarraStyle(FactorConfig(
    warmup_bars=params.warmup_bars,            # 526
    dataset=MergedDataset([prices, daily, art, history, industry, share_class, dtb3]),
    mode="batch",
    data_columns=params.panel_columns,
    file_path="factors/market/barra_style/barra_style.zarr",
    kwargs={"risk_free_symbol": "DTB3"},
))
factor.build("2000-02-02", "2026-10-08")

Pipeline on each bar#

A secondary share class takes its firm’s market cap, fundamentals and fiscal-year history ([E] p.51: LNCAP is the firm’s total market cap). The ESTU is chosen from the previous bar’s market cap, secondary classes left out. The market return is the ESTU’s return, weighted by the previous bar’s cap.
Every descriptor is computed (next section).
Each descriptor has its outliers treated on its own distribution ([M] §2.2, p.8): with m and s the equally weighted mean and standard deviation of the raw descriptor over the ESTU, a value further than data_error_sigma * s (10) from m is treated as a data error and dropped, and one further than clip_sigma * s (3) is trimmed to that bound. This applies to every stock, inside the ESTU or not.
Each descriptor is then standardized over the ESTU ([M] §2.3, p.9, eq. 2.4): the mean is weighted by the previous bar’s market cap and the standard deviation is equally weighted, so a cap-weighted portfolio of the ESTU has zero exposure. Stocks outside the ESTU are shifted and scaled by the same numbers.
A style is the fixed-weight sum of its descriptors, the weights renormalized over the descriptors a stock has, then standardized again.
Residual Volatility is orthogonalized against Beta only ([E] p.16 and p.52): it is replaced by its residual from a weighted least-squares regression with an intercept, fitted on the ESTU with square-root-of-cap weights ([E] Appendix B, p.56) and applied to every stock, then standardized again.
Non-linear Size follows [E] p.55: the standardized Size exposure is cubed, orthogonalized against Size by the same regression, then has its outliers treated and is standardized (steps 3 and 4). Non-linear Beta is the same with Beta. Because the outlier step comes last, these two are close to, not exactly, uncorrelated with their regressors.
A style still missing for a stock that has a market cap is imputed from a weighted regression of the style on one intercept per industry and a slope on Size (Size itself on industry alone), fitted on the ESTU ([M] p.9).
Every style is standardized once more, imputed values included.
A stock with no price on the bar (price_column NaN) gets NaN in every descriptor and style. Only the outputs are masked, after steps 1 to 9, so the ESTU statistics and every priced stock’s values are unchanged. A delisted stock therefore has no exposures, although a windowed descriptor would stay defined while its window holds enough past returns and the SF1 fundamentals are carried forward. The rule is the one Alpha101Stock, Alpha158Stock and MarketDataset.tradable_bars use, and it reads only the bar itself, so it looks nothing up ahead. A halted stock loses its exposures on its halt days. industry and estu are not masked: the industry code passes through, and a stock without a market cap is never in the ESTU anyway.

Descriptors and styles#

r is the daily return from adjClose, r_f the risk-free rate of the bar before, excess = r - r_f and log_excess = log(1 + r) - log(1 + r_f). Exponential weights are 0.5 ** (age / half_life) over the trailing window, age 0 for the current bar.

Style (weights)	Descriptor	Definition	Window, half-life
Size	LNCAP	`log(marketcap)`
Beta	BETA	slope of the exponentially weighted least-squares fit of `excess` on the market’s excess return	252, 63
Momentum	RSTR	exponentially weighted sum of `log_excess` over a window ending 21 bars ago, weights not normalized ([E] eq. A2, p.52); a bar without a return adds nothing	504, 126, lag 21
Residual Volatility (0.75, 0.15, 0.10)	DASTD	exponentially weighted standard deviation of `excess`	252, 42
	CMRA	`log(1 + max Z) - log(1 + min Z)`, `Z(T)` the sum of `log_excess` over the last `T` months of 21 bars, `T = 1..12`; NaN when `min Z <= -1`	252
	HSIGMA	weighted standard deviation of the BETA fit’s residual	252, 63
Non-linear Size	NLSIZE	the Size exposure cubed, orthogonalized against Size, outlier-treated and standardized ([E] p.55)
Non-linear Beta	NLBETA	the Beta exposure cubed, orthogonalized against Beta, outlier-treated and standardized ([E] p.55)
Liquidity (0.35, 0.35, 0.30)	STOM, STOQ, STOA	`log(21 * mean daily turnover)` over 1, 3 and 12 months; turnover is `volume * close / marketcap`	21, 63, 252
Dividend Yield	YILD	cash dividends of the last 252 bars, each in today’s share basis, over today’s raw close	252
Book-to-Price	BTOP	book equity over market cap
Earnings Yield (0.15, 0.10)	CETOP	trailing net income to common plus depreciation and amortization, over market cap
	ETOP	trailing net income to common over market cap
Leverage (0.75, 0.15, 0.10)	MLEV	`1 + LD / market cap`
	DTOA	`(LD + current liabilities) / assets`
	BLEV	`1 + LD / book equity`; NaN at book equity <= 0
Growth (0.20, 0.10)	EGRO	slope of a least-squares fit of the last five fiscal years’ EPS on their fiscal year ends, over the mean absolute EPS (see Deviations)	5 fiscal years
	SGRO	the same with sales per share	5 fiscal years

A day’s turnover is its dollar volume over the firm’s market cap. Sharadar gives no per-class share count, so for a firm with several traded classes each class’s turnover, the primary’s included, is its own trading as a share of the whole firm, lower than the class’s own share turnover.

LD is long-term debt (debtnc), or total debt where the balance sheet does not split current from non-current, as for a bank. An SF1 amount meets the USD market cap divided by fxusd.

Deviations from USE4#

Sharadar sells no analyst forecasts and has no preferred-equity field, so:

Earnings Yield has no EPFWD (forward earnings over price, weight 0.75 in USE4): it is CETOP and ETOP only, their weights renormalized.
Growth has no EGRLF (analyst long-term growth, weight 0.70): it is EGRO and SGRO only, their weights renormalized.
CETOP’s cash earnings, which MSCI does not define, are trailing net income to common plus depreciation and amortization.
Preferred equity is taken as 0 in MLEV and BLEV.

One deviation is a choice, not a data gap:

EGRO and SGRO divide the slope by the mean absolute annual value, not by the signed “average annual earnings per share” of [E] p.53: a negative average would flip the growth sign of a loss-making company.

And the universe and the industries approximate MSCI’s:

The ESTU approximates the MSCI USA IMI by the largest 3000 stocks; the industry is a single Fama-French 48 code from SIC, not GICS with multiple-industry weights.

Defaults#

Every window, half-life, lag, weight and threshold is a field of BarraStyleParameters, set through FactorConfig.kwargs.

Field	Default	Source
`beta_window`, `beta_half_life`	252, 63	USE4
`momentum_window`, `momentum_half_life`, `momentum_lag`	504, 126, 21	USE4
`dastd_window`, `dastd_half_life`	252, 42	USE4
`cmra_months`, `cmra_month_length`	12, 21	USE4
`liquidity_month_length`, `stoq_months`, `stoa_months`	21, 3, 12	USE4
`dividend_window`	252	USE4
`growth_years`	5	USE4
descriptor weights	as in the table above	USE4, renormalized where a descriptor is absent
`clip_sigma`	3	USE4 ([M] §2.2, p.8)
`estimation_universe_size`	3000	ours (USE4 uses the MSCI USA IMI)
`data_error_sigma`	10	ours (USE4 does not publish it)
`orthogonalization_weighting`	`"sqrt_cap"`	USE4 (“regression-weighted”, [E] p.55; the regression weight, Appendix B, p.56)
`imputation_regressors`, `imputation_weighting`	industry and Size, `"sqrt_cap"`	ours
`beta_min_observations`	63	ours
`momentum_min_observations`	252	ours
`volatility_min_observations`	63	ours
`liquidity_min_fraction`	0.5	ours
`dividend_min_observations`	126	ours
`min_growth_years`	3	ours
EGRO and SGRO over the mean absolute annual value		ours (see Deviations)
a missing regressor taken at its weighted mean in an orthogonalization		ours
turnover over the firm’s market cap for every share class		ours (no per-class share count in Sharadar)

On real data#

examples/sharadar_us_equity/barra_style.py on the training server, on the 2026-10-05 Sharadar pull and FRED’s DTB3:

Size and cost. The store covers 6,476 trading days (2001-01-02 to 2026-10-02) of 17,090 permatickers and is 7.1 GB. Building it takes 5.1 minutes: reading and merging the seven inputs about 4 minutes, the compiled graph 27 seconds, writing the store 29 seconds; the whole script, the coverage count and the factor report included, takes 9.3 minutes with a 280 GB peak of memory on a 128-core machine.
Coverage. Over the estimation universe (3,000 stocks every day), each of the 12 styles has a value in at least 99.90% of the cells in every year, and the industry code in 99.87%.
Size correlates with the log of DAILY’s market cap at 0.999, 1.000 and 0.999 (2005-06-30, 2015-06-30 and 2024-06-28) across the estimation universe. The outlier step clips the largest companies, not the smallest: 29, 22 and 13 of the 3,000 are trimmed to 3 equally weighted standard deviations above the equally weighted mean of LNCAP on those days (1.0%, 0.7% and 0.4%), and none at the lower bound.
Share classes. On 2024-06-28, 189 secondary share classes trade (an SEP price that day). 188 have a firm; LGF.A has no CIK in TICKERS. 187 of them get Size and every fundamentals-based style; LLYVK’s firm has no DAILY market cap that day. GOOG, BRK.A and FOX have exactly the Size and Book-to-Price of GOOGL, BRK.B and FOXA. The estimation universe is the same on every bar as without the share classes.
Beta. A raw BETA recomputed independently in numpy has a cap-weighted mean of 1.005, 1.005 and 1.033 over the estimation universe on those days, and style_beta correlates with it at 0.991, 0.998 and 0.973.

Factor report against the 21-bar forward open-to-open return, every stock, 2005-2025 (mean daily rank IC and its Newey-West t-statistic):

Style	IC	t	Lag-1 rank autocorrelation
Size	0.079	15.2	1.000
Beta	-0.000	-0.0	0.996
Momentum	0.055	9.1	0.990
Residual Volatility	-0.097	-14.9	0.997
Non-linear Size	0.040	10.5	0.995
Non-linear Beta	0.003	0.9	0.985
Liquidity	-0.014	-2.0	0.999
Dividend Yield	0.050	9.1	0.999
Book-to-Price	0.003	0.6	0.998
Earnings Yield	0.070	12.5	0.997
Leverage	0.004	0.7	0.999
Growth	0.016	5.7	0.998

Over all common stocks, micro caps included, the small, volatile and unprofitable stocks did worst, so Size, Earnings Yield and Dividend Yield have positive ICs and Residual Volatility a negative one; Momentum is positive and Beta flat.

Operators#

The factor is one KunQuant graph in double precision, built from operators in quantlab.factor.kunquant_ts (the time-series ones) and quantlab.factor.kunquant_cs (the cross-sectional and elementwise ones), each tested alone against a float64 numpy reference: EWSum, EWVar, EWBeta, EWResidualStd, CMRA, CrossSectionalTopN, CrossSectionalWeightedMean, CrossSectionalSigmaClip, CapWeightedStandardize, RenormalizedCombine, CrossSectionalWLSResidual and CrossSectionalIndustrySizeFill. The split basis of the dividends and the risk-free broadcast are prepared in numpy before the graph runs. KunQuant’s Log is accurate to about 4e-10 absolute in double, so outputs built on log returns carry that error.

The factor is batch only: mode="stream" is refused.