The Bond Risk Premium and the Cross-Section of Equity Returns
Bibliographic record
Abstract
The cross-section of returns of stock portfolios sorted along the book-to-market dimension can be understood with a one-factor model. The factor is the nominal bond risk premium, best measured as the Cochrane-Piazzesi (2005, CP) factor. This paper ties the pricing of stocks in the cross-section to the pricing of bonds of various maturities, two literatures that have been developed largely in isolation. A parsimonious stochastic discount factor model can price both the cross-section of stock and bond returns. The mean average pricing error across 5 bond and 10 book-to-market stock portfolio returns is less than 60 basis points per year. The model also replicates the dynamics of bond yields as well as the time-series predictability of stock and bond returns. Its key feature is a non-zero risk price on the state variable that governs the bond risk premium. Value stocks are riskier because their returns are high when the bond risk premium is high. Empirically, the CP factor peaks at the end of a recession, when good times lie ahead. We trace back this risk to the fundamentals: the properties of dividend growth. An equilibrium asset pricing model ties the properties of cash flows on stocks to stock and bond risk premia. The model generates the observed value spread as well as the observed sensitivities of excess returns and dividend growth to the bond risk premium. It does so because times when CP is high are times of low marginal utility growth when value stocks receive better news about future cash flows than growth stocks.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".