MAC3 (Multi-Asset-Class, 3rd generation) is Bloomberg’s commercial equity risk model, launched in 2020 as the successor to MAC2 (2016). Unlike academic factor models that aim to explain expected returns, MAC3 is designed to forecast portfolio volatility and provide a well-conditioned covariance matrix for mean-variance optimization.
Alpha factors vs. risk factors
MAC3 distinguishes between two roles a style factor can play:
- Alpha factors are related to expected returns (the “pricing anomalies” that violate the CAPM). They can be identified by sorting stocks into quintiles on a characteristic: if the long-short quintile portfolio has positive drift, the factor explains alpha.
- Risk factors identify sources of portfolio volatility or systematic comovement. A sort on market-beta produces a long-short portfolio with much higher volatility than a random selection, even if the factor has no return premium.
Some factors serve both roles (e.g., momentum). A risk model needs far more factors than would be “priced” in academic terms, because the goal is predicting volatility, not explaining expected returns.
Style factor construction
All style factors are standardized to cap-weighted mean zero and equal-weighted unit standard deviation within each country. Composite factors (built from multiple descriptors) are formed by weighting descriptors, then re-standardizing. Outliers are trimmed via a two-pass algorithm: first using the robust standard deviation (median absolute deviation x 1.4826), then conventional SD.
Missing fundamental data is filled with the equal-weighted industry mean of the raw descriptor.
1. Market Beta
Regression of local excess stock returns against the cap-weighted ESTU return, estimated by weighted least-squares with exponentially decaying weights. Uses L-day rolling windows to handle trading asynchronicity and serial correlation. IPO betas are shrunk toward the cap-weighted country mean.
See market-beta.
2. Residual Volatility
EWMA volatility of the residuals from the market beta regression. Captures the low-volatility anomaly: high-residual-volatility stocks tend to underperform low-volatility peers even after controlling for beta, size, and value (Ang et al. 2009 found a 1.31%/month spread across 23 developed markets).
MAC2 combined market beta and residual volatility into a single “volatility” factor; MAC3 splits them because they capture different dimensions of risk.
See residual-volatility.
3. Momentum
Weighted average of trailing log returns over ~252 trading days:
Weighting scheme deviates from the standard academic 12-1 month measure:
- First 10 trading days (2 weeks): zero weight, removing short-term reversal
- Days 11-31: linearly increasing weights (ramp-in)
- Days 32-231: constant weights
- Days 232-252: linearly declining weights (ramp-out)
The linear ramps prevent spurious jumps in exposure when large returns enter or exit the window. IPOs receive the cap-weighted mean momentum of the ESTU (i.e., zero standardized exposure), blending toward their own momentum as history accumulates.
See momentum.
4. Size
Log of market capitalization (CUR_MKT_CAP). Since the distribution is cap-weighted mean zero, large caps have positive exposure (~+1) and small/micro caps have negative exposure (down to ~-4), with the median around -2.
See size.
5. Mid-Cap
Captures non-linear size effects that the log-linear size factor misses:
where is the standardized size exposure and , are empirically determined. After standardization, mid-cap stocks have positive exposure while both large and small caps have negative exposure. Introduced in MAC3 (not present in MAC2).
6. Earnings Yield
Composite of two descriptors:
- Historical E/P (HEP): trailing 12-month net income / market cap
- Forward E/P (FEP): blended Bloomberg consensus EPS forecast / price. Uses a time-weighted average of current and next fiscal year forecasts, with weight proportional to months remaining in the fiscal year.
This factor corresponds to the E/P anomaly documented by Basu (1977). It is separated from the valuation factor in MAC3 (MAC2 combined them) because earnings yield and price multiples capture somewhat different dimensions of value.
7. Valuation
Composite of three price-multiple descriptors:
| Descriptor | Numerator | Denominator |
|---|---|---|
| Book-to-Price (B2P) | TOT_COMMON_EQY | CUR_MKT_CAP |
| Sales-to-Price (S2P) | SALES_REV_TURN | CUR_MKT_CAP |
| Cash-Flow-to-Price (CFP) | CF_CASH_FROM_OPER | CUR_MKT_CAP |
These are the classic value metrics. The academic HML factor uses only book-to-market; MAC3 uses a broader set of multiples for more robust risk capture.
8. Dividend Yield
Bloomberg indicated dividend yield (DIVIDEND_INDICATED_YIELD): the most recently announced annualized dividend divided by the current market price. Related to value but sometimes treated separately because high-dividend stocks have distinct risk characteristics (tax clientele effects, sector concentration in utilities/REITs).
See dividend-yield.
9. Long-Term Reversal
Constructed like momentum but with a different weighting window:
- First 12 months: zero weight (removes momentum signal)
- Month 13: linearly increasing weights (ramp-in)
- Months 14-47: constant weights
- Month 48: linearly declining weights (ramp-out)
Captures the DeBondt and Thaler (1985) effect: stocks that performed poorly over the past 3-5 years tend to outperform subsequently. Introduced in MAC3 (not in MAC2).
See long-term-reversal.
10. Liquidity
Composite of three descriptors:
- Share Turnover (STO): EWMA of daily shares traded / shares outstanding. Higher turnover = higher liquidity.
- Bid-Ask Spread (BAS): EWMA of -(ask - bid) / price. Sign is flipped so positive exposure = higher liquidity. Based on Amihud and Mendelson (1986).
- Modified Amihud (AMH): EWMA of -(|return| / share turnover). Modified from Amihud (2002) to use share turnover instead of dollar volume, avoiding collinearity with the size factor. Sign flipped so positive = more liquid.
See liquidity.
11. Growth
Composite of four descriptors:
| Descriptor | Method |
|---|---|
| Historical Sales Growth (HSG) | 5-year regression slope of annual sales vs. time, normalized by mean total assets |
| Historical Earnings Growth (HEG) | Same method using NET_INCOME |
| Medium-Term Growth (MTG) | Ratio of Bloomberg FY3 / FY2 EPS forecasts |
| Long-Term Growth (LTG) | Mean analyst-predicted earnings growth over 3-5 years |
Blends backward-looking and forward-looking growth signals. Related to the growth component of QMJ.
12. Variability
Composite of three descriptors, each computed as the standard deviation of the annual fundamental over the trailing 5 years, normalized by mean total assets:
- Variability of Net Income (VNI)
- Variability of Sales (VSA)
- Variability of Cash Flow (VCF)
Considered a quality signal: low variability (stability) is associated with higher quality. Maps to the safety component of QMJ, which includes earnings volatility.
13. Profit
Composite of three descriptors:
| Descriptor | Formula |
|---|---|
| Return on Assets (ROA) | NET_INCOME / BS_TOTAL_ASSETS |
| Return on Equity (ROE) | NET_INCOME / TOT_COMMON_EQY |
| Profit Margin (PRM) | NET_INCOME / SALES_REV_TURN |
Directly related to the academic profitability factor. Note that MAC3 uses net-income-based measures, while Novy-Marx (2013) argues gross profits is cleaner because items lower on the income statement are polluted by expensed investments. The FF5 model’s RMW uses operating profitability.
14. Leverage
Composite of three descriptors, all using the same numerator (long-term debt + short-term debt):
| Descriptor | Denominator |
|---|---|
| Debt-to-Assets (D2A) | BS_TOT_ASSET |
| Debt-to-Book (D2B) | TOT_COMMON_EQY |
| Debt-to-Market (D2M) | CUR_MKT_CAP |
Viewed as an inverse quality signal: highly levered firms are regarded as lower quality. Maps to the leverage sub-component of QMJ’s safety measure.
Industry and country factors
Industry beta factors
Based on the Bloomberg Industry Classification System (BICS): 11 sectors, 20 industry groups, 59 industries, 214 sub-industries. The granularity level is chosen to maximize both explanatory power and statistical significance.
Unlike the traditional binary (0/1) approach, MAC3 estimates industry betas by regressing each stock’s excess return against its industry’s cap-weighted return. Betas are trimmed to [~0.4, ~2.0] and standardized to cap-weighted mean 1. This yields:
- Higher explanatory power without adding factors
- Higher statistical significance of factor returns
- Reduced spurious correlations between factor and specific returns
Country beta factors
Estimated identically to industry betas: regression of stock returns against the cap-weighted country portfolio return. Same trimming and standardization. Used only in multi-country models.
Satellite country factors
Stocks in satellite countries (e.g., Canada in the US model) are exposed to all model factors but excluded from the main ESTU. A dedicated satellite factor captures the country’s unique risk characteristics without contaminating the core factor estimates. Satellite factor returns are estimated from the residuals after removing all other factor contributions.
Factor return estimation
Factor returns are estimated daily via constrained weighted cross-sectional regression:
Constraints: cap-weighted industry factor returns sum to zero; cap-weighted country factor returns sum to zero. This preserves the interpretation of the market factor as the cap-weighted ESTU return.
Regression weights: inverse residual variance (from the residual volatility factor), not the traditional square-root-of-market-cap. This is econometrically optimal (minimizes noise in factor return estimates) and empirically reduces spurious factor-specific correlations.
Return winsorization: stock returns are trimmed conservatively to prevent extreme observations from distorting factor returns, but not so aggressively as to flip the sign on long-term factor drifts (e.g., the small-cap premium).
Covariance estimation and term structure of risk
MAC3 uses daily observations to forecast risk at six horizons: daily, weekly, monthly, quarterly, annual, long-term. The term structure arises from serial correlation in daily factor returns:
- Positive serial correlation: T-period volatility > sqrt(T) x daily volatility
- Negative serial correlation (mean reversion): T-period volatility < sqrt(T) x daily volatility
The factor covariance matrix blends Newey-West (explicit serial correlation) and low-frequency (aggregated) estimates, then applies PCA Shrinkage to produce a well-conditioned matrix reliable for both risk forecasting and portfolio optimization.
Cross-Sectional Volatility (CSV) scaling: uses cross-sectional bias statistics as a feedback loop to detect “instantaneous” regime changes and adjust volatility forecasts. This mitigates underforecasting heading into crises and allows rapid decline after crises subside.
Specific risk
Blends two components:
- Time-series estimate: EWMA volatility of realized specific returns
- Structural model: predicted specific risk based on factor exposures (useful for IPOs with little return history)
A finite-sample adjustment corrects the traditional double-counting of specific risk in factor portfolios. Traditional models inflate factor volatility and deflate specific risk because factor portfolios are estimated from a finite sample of stocks.
Coverage
1 global model, 13 local models (US, Europe, Japan, UK, APAC, Australia, Canada, China A-shares, EMEA, India, Korea, Latin America, South Africa), plus an integrated model aggregating all locals. Covers common stocks, REITs, unit trusts, stapled securities, depositary receipts, and preferred stocks. The ESTU captures ~97% of each country’s market capitalization.
Sources
- MAC3 Global Equity Risk Model (File)