The Bond Risk Premium and the Cross-Section of Equity Returns

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.