Daniel and Titman (1997) challenge the Fama-French interpretation that size and value premia are compensation for systematic risk. They find that it is firm characteristics (book-to-market, market cap), not factor loadings (covariances with HML and SMB), that explain the cross-section of returns.
The debate
Fama and French (1993) argue that high book-to-market and small size proxy for undiversifiable factor risk. If true, returns should be explained by loadings on the HML and SMB factors (covariance structure), not by the characteristics themselves. Stocks with the same factor loadings but different characteristics should earn similar returns.
Daniel and Titman test this by constructing portfolios that match on factor loadings but differ on characteristics (and vice versa). Their results:
- Stocks with similar characteristics but different factor loadings earn similar returns
- Stocks with similar factor loadings but different characteristics earn different returns
- The return premia on small-cap and high B/M stocks do not arise from their comovements with pervasive factors
Methodology
They form 25 size/B/M portfolios (following Fama-French), then within each cell, sort on HML loading. If the risk story is correct, high-HML-loading stocks should earn more than low-HML-loading stocks within the same characteristic cell. They find no such effect: the cross-sectional variation is driven by characteristics, not loadings.
Implications
- For the value premium: the return to value may reflect mispricing (per Lakonishok, Shleifer, and Vishny 1994) rather than compensation for a “distress factor”
- For factor models: factor mimicking portfolios (HML, SMB) may work empirically not because they capture risk, but because they mechanically sort on the same characteristics that drive returns
- For risk models: the distinction between characteristics-based and covariance-based approaches maps onto the return-based vs. holdings-based model debate. Holdings-based models like MAC3 directly use characteristics.
Subsequent debate
Davis, Fama, and French (2000) extended the sample to 1929-1997 and found that the covariance structure does explain returns in the longer sample, particularly in the pre-1963 period. The Daniel-Titman result may be sample-specific or limited by statistical power. The debate remains unresolved and is one of the central questions in empirical asset pricing.