The equity premium and the value premium puzzles constitute two of the focal points of the asset pricing literature. As it is well known, the starting point of the first is the inability of standard consumption models to rationalize the observed level of the equity premium, the volatility and predictability of returns, and the low and stable risk free rate. The value premium puzzle is instead concerned with the failure of the CAPM to explain the cross section of average returns of portfolios sorted according to book-to-market. Surprisingly, these two puzzles are, for the most part, studied separately. This is unfortunate because, as we argue here, the two puzzles cannot be tackled independently: Any economic mechanism proposed to address one of them immediately has general equilibrium implications for the other. In this paper, we show that a workhorse of the “equity premium puzzle” literature, the Campbell and Cochrane (1999) external habit persistence model, imposes strong restrictions on the cross-sectional dispersion of individual assets’ cash flow risk in order for this model to explain the value premium as well. Under such restrictions, though, the model not only implies that value stocks have, endogenously, a higher cash flow risk than growth stocks, as recently documented in the empirical literature, but it also offers new insights on the time series variation of risk premia in the cross section. In particular, the model yields what is to our knowledge the first theoretical explanation for the observed time series variation in the value premium.
As mentioned we posit a representative agent economy in which preferences are of the external habit persistence type introduced by Campbell and Cochrane (1999). This model generates plausible quantitative implications for the market portfolio through the time variation of the market price of consumption risk. We follow Menzly, Santos and Veronesi (2004, MSV henceforth), and embed these preferences in a general equilibrium setting with multiple risky assets. These assets have time varying expected dividend growth and differ from each other in their cash-flow risk, that is, in the covariance of their cash-flow growth with the growth rate of the aggregate economy.
The general equilibrium feature of the model is key to learn about the cash-flow characteristics of value sorted portfolios. Indeed, whether an asset is “value” or “growth” depends on whether its price is low or high relative to the fundamental. Thus we need a general equilibrium model that links, endogenously, firms’ prices to firms’ cash-flow characteristics. Our first contribution is to show that the sorting procedure naturally selects as value stocks those that have a high cash-flow risk, a prediction of the model that is consistent with the empirical evidence.
Second, our model delivers strong predictions about the dynamics of the value premium. There is by now substantial empirical evidence that the value premium varies over time, but, to our knowledge, there is no existing theoretical explanation for this fact. We show here that the interaction between fluctuations in the market price of risk and the cross sectional dispersion of cash-flow risk discussed above delivers time series variation in the value premium: Agents demand a relatively higher compensation for holding assets with cash-flows that covary positively with consumption growth when faced with adverse consumption shocks and thus the value premium is higher in “bad times.” Furthermore, quantitatively the cross sectional dispersion in cash-flow risk needed to generate the observed unconditional value premium also generates plausible fluctuations in this value premium.
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Cash-flow Risk, Discount Risk, and the Value Premium
