Quality is defined as characteristics that investors should be willing to pay a higher price for, holding all else equal. The QMJ (Quality Minus Junk) factor goes long high-quality stocks and short low-quality “junk” stocks.
Definition
Asness, Frazzini, and Pedersen (2019) decompose quality into three components, motivated by a dynamic valuation model derived from Gordon’s growth formula:
- Profitability: composite z-score of gross profits/assets, ROE, ROA, cash flow/assets, gross margin, and low accruals
- Growth: 5-year growth in each profitability measure
- Safety: composite of low market beta, low leverage, low bankruptcy risk (O-score, Z-score), and low earnings volatility
The overall quality score is the z-score of the average of these three components.
Factor construction
Following Fama-French (1993) methodology: independent 2x3 sorts on size and quality (top 30%, middle, bottom 30%). QMJ is the average return on the two high-quality portfolios minus the two junk portfolios, value-weighted and rebalanced monthly.
Key empirical results
U.S. (1957-2016):
- QMJ four-factor alpha: 60 bps/month (t=9.95)
- Sharpe ratio: 0.47
- Information ratio: 1.40
Global (1989-2016, 24 countries):
- QMJ four-factor alpha: 61 bps/month (t=8.07)
- Sharpe ratio: 0.64
- Positive returns in 23 of 24 countries
The price-of-quality puzzle
Quality stocks do command higher prices on average, but the relationship is puzzlingly weak (cross-sectional R-squared of only ~10%). This limited pricing of quality means high-quality stocks earn significant risk-adjusted returns while junk stocks earn negative risk-adjusted returns. QMJ loads negatively on market beta, size, and value, meaning quality stocks appear safer, not riskier, than junk.
Time variation
The price of quality varies over time, reaching its lowest point in February 2000 (internet bubble peak) and also declining before the 1987 crash and 2007-2009 financial crisis. A low price of quality significantly predicts high future QMJ returns.
Relationship with other factors
QMJ is negatively correlated with HML, making the two strategies complementary. The combination is sometimes called “QARP” (Quality At a Reasonable Price). During market stress, QMJ benefits from “flight to quality” rather than suffering crash risk.
Analyst errors
Analysts systematically expect junk stocks to outperform quality stocks, contrary to realized returns. This suggests the quality premium may partly reflect mispricing driven by systematically biased expectations.