Value is the tendency for stocks with low prices relative to fundamentals (high book-to-market, high earnings yield, etc.) to earn higher average returns than expensive growth stocks.
Construction
The standard academic measure is book-to-market equity (BE/ME): the ratio of a firm’s book value of common equity to its market capitalization. The value factor HML (High Minus Low) is constructed by going long stocks in the top 30% of BE/ME and short stocks in the bottom 30%, controlling for size.
In Asness, Moskowitz, and Pedersen (2013), value is extended beyond equities using asset-class-appropriate measures: B/M for stocks, yield spreads for bonds, 5-year reversal for currencies and commodities, and relative-to-trend measures for country equity indices.
Key empirical evidence
Fama and French (1992) established that BE/ME is the strongest cross-sectional predictor of returns, with a spread of 1.53%/month between the highest and lowest BE/ME deciles. In Fama-MacBeth regressions, the BE/ME slope is 0.50%/month (t=5.71), far exceeding size or beta.
Fama and French (1993) formalized this into HML, averaging 0.40%/month (t=2.91) in the 1963-1991 sample. HML averages 0.37%/month in the extended 1963-2013 sample used in the five-factor model.
Relationship with other factors
Value has a strong negative correlation with momentum (approximately -0.6 within equity markets, -0.54 across asset classes). This makes the two strategies excellent complements: a 50/50 combination produces a Sharpe ratio of 1.42 across all asset classes.
Value is also negatively correlated with profitability and quality. Profitable firms tend to be growth stocks (low BE/ME). Controlling for gross profitability dramatically improves the value spread: from 0.41% to 0.68%/month in double sorts (Novy-Marx 2013).
HML redundancy in the five-factor model
A striking finding from Fama and French (2015): when RMW and CMA are added to the model, HML’s intercept drops to essentially zero. Its average return is fully absorbed by its loadings on the other factors. A four-factor model dropping HML performs identically to the five-factor model. The authors caution this may be sample-specific.
Theoretical rationale
Two competing explanations:
- Risk-based: High BE/ME firms are financially distressed, with poor earnings prospects. Investors demand higher returns to compensate for this distress risk (Chan and Chen 1991, Fama and French 1993).
- Behavioral: Investors systematically extrapolate past growth too far into the future, overpricing “glamour” stocks and underpricing “value” stocks. Lakonishok, Shleifer, and Vishny (1994) showed that two-dimensional sorts (combining C/P with past sales growth) produce 10.7%/yr value-glamour spreads, and that value stocks do not underperform in recessions, challenging the risk explanation.
- Characteristics debate: Daniel and Titman (1997) argued that it is the characteristics (B/M, size) rather than factor loadings (covariances with HML/SMB) that drive returns, undermining the risk-factor interpretation. Davis, Fama, and French (2000) contested this in longer samples.
The gross profitability premium challenges the distress story: profitable firms are less prone to distress yet earn higher returns, and controlling for profitability strengthens the value premium.
Migration mechanism (Fama and French 2007)
Fama and French (2007) decompose the value premium into contributions from stocks that stay in the same portfolio versus those that migrate across value groups. Three of four migration groups contribute to the premium (1927-2006):
- Plus (value stocks that improve): value stocks that earn high returns and migrate to neutral or growth, or are acquired. Plus transitions contribute roughly 3.5 percentage points more per year to value portfolio returns than to growth portfolios.
- Minus (growth stocks that deteriorate): growth stocks that earn low returns and move toward value or are delisted. Minus transitions contribute 5.1 pp/yr to the small-cap value premium and 1.2 pp/yr for large caps.
- Same (non-migrators): value stocks that remain value earn modestly higher returns than growth stocks that remain growth, contributing 1.0 pp/yr (small) and 1.7 pp/yr (large) to the premium.
One offset: small growth stocks migrate to big-cap status more frequently than small value stocks (11.8% vs. 8.5% of market cap), which works against the value premium by 2.9 pp/yr. See migration for the full framework.
Reports of value’s death (Arnott, Harvey et al. 2021)
Arnott, Harvey, Kalesnik, and Linnainmaa (2021) argue that value’s post-2007 underperformance does not signal the death of the value premium. They decompose value-minus-growth returns into three structural components:
- Revaluation: changes in the valuation spread between value and growth. This is the primary driver of value’s recent losses. The spread widened from the 25th percentile in 2007 to an unprecedented 100th percentile by June 2020, meaning value stocks reached their all-time cheapest level relative to growth.
- Migration: value stocks appreciating out of the value portfolio and growth stocks deteriorating into it. This structural component showed no meaningful change pre- vs. post-2007.
- Income yield: growth stocks’ higher profitability and sales growth, which offsets some of migration’s benefit to value. Also structurally stable.
Key findings:
- Over 1963-2020, even including the 13.5-year drawdown, value remained one of the most impressive factors in risk-return terms.
- The current drawdown (-54.8%) eclipsed the tech bubble drawdown (-40.6%) and at 13.5 years was by far the longest.
- The extreme widening of value spreads is inconsistent with “crowding” narratives and instead suggests larger future returns.
- The structural premium (migration + income yield, purged of revaluation) remained positive throughout.
- Unless the valuation spread continues to widen indefinitely, value is highly likely to outperform growth going forward.
Value is not an interest rate bet (AQR 2022)
Asness (2022) challenges the widespread assumption that value is essentially a bet on interest rates. The argument that growth stocks have “longer duration” cash flows and should therefore be more sensitive to rate changes is superficially appealing but empirically and mathematically wrong:
- Empirical: the rolling 5-year correlation of HML-Devil with changes in the 10-year Treasury yield averages only about 0.10 over 1950-2022. The correlation spiked in the most recent 5 years but this is an outlier relative to the full history.
- Duration math: diversified growth portfolios outgrow value portfolios by only about 4% per year for the first 5 years, with no excess growth thereafter. This near-term growth advantage produces a duration difference of only 0.4 years between value and growth, far too small to generate meaningful interest rate sensitivity. Only a “unicorn” assumption of 10% perpetual growth (which has no empirical support) would produce a substantial duration gap (~10 years).
- Bubble explanation: the recent elevated correlation likely reflects bubble dynamics. If investors price growth stocks as if they were unicorns, the implied duration gap widens and value will trade correlated with rates. The correlation and the wide value spreads may be the same bubble manifesting differently.
Global evidence
Value premia are found in every asset class and market studied. Asness et al. (2013) document significant value returns in U.S., U.K., European, and Japanese equities, as well as country equity indices, currencies, government bonds, and commodities.
Sources
- The Cross-Section of Expected Stock Returns (File, DOI)
- Common risk factors in the returns on stocks and bonds (File, DOI)
- A five-factor asset pricing model (File, DOI)
- The other side of value: The gross profitability premium (File, DOI)
- Value and Momentum Everywhere (File, DOI)
- Quality minus junk (File, DOI)
- Migration (File, DOI)
- Reports of Value’s Death May Be Greatly Exaggerated (File, DOI)
- Is Value Just an Interest Rate Bet? - AQR (File, URL)
- Contrarian Investment, Extrapolation, and Risk (File, DOI)
- Evidence on the Characteristics of Cross Sectional Variation in Stock Returns (File, DOI)