We develop a conditional version of the consumption capital asset pricing model (CCAPM) using the conditioning variable from the cointegrating relation among macroeconomic variables (dividend yield, term spread, default spread, and short-term interest rate). Our conditioning variable has a strong power to predict market excess returns in the presence of competing predictive variables. In addition, our conditional CCAPM performs about as well as Fama and French’s (1993) three-factor model in explaining the cross-section of the Fama and French 25 size and book-to-market sorted portfolios. Our specification shows that value stocks are riskier than growth stocks in bad times, supporting the risk-based story.
Understanding the time variation and cross-sectional variation in risk premiums has long been a central research question for financial economists. One way to gain an understanding of the nature of risk premiums is to examine the linkage between financial markets and the macroeconomy, because risk premiums should reflect macroeconomic risk. Cochrane's 2007 review article suggests the following in researching the interaction between macroeconomics and finance:
The challenge is to find the right measure of “bad times,” rises in the marginal value of wealth, so that we can understand high average returns or low prices as compensation for assets’ tendency to pay off poorly in “bad times.”
We propose here the “right measure” that captures economic recessions. It is well-known that time variations in expected returns are related to business cycle (see Fama and French, 1989, and references therein). Expected returns are higher in economic recessions, since investors are less willing to hold risky assets, and lower in economic booms. This evidence suggests that time variations in equity premiums should be accounted for by variables related to business cycle. Previous research focuses mainly on financial indicator variables such as the dividend-to-price ratio, earning-to-price ratio, and dividend-to-earning ratio as candidates for predictive variables. Although these financial indicators can predict market return over long horizons, their predictive powers over business cycle frequencies are limited (Lettau and Ludvigson, 2001a).
We study both the variation in risk premium over time and the variation in risk premium across stocks based on the proposed measure which captures business-cycle-related macroeconomic risks. A starting point of this study is to recognize that macroeconomic variables which are used to predict stock returns — dividend yield, term spread, default spread, and short rate — share a common long-term trend, that is, they are cointegrated. We examine the role of trend deviations in the cointegrated macroeconomic variables in predicting future asset returns and explaining the cross-section of average returns. To account for the cross-sectional patterns, we focus on the consumption capital asset pricing model (CCAPM) with the proposed measure. Despite its poor performance as an asset pricing model (Mankiw and Shapiro, 1986; Breeden, Gibbons, and Litzenberger, 1989; Cochrane, 1996), the CCAPM still draws a lot of attention because consumption-based models are very general and intuitively appealing.1 Moreover, Cochrane (2007) emphasizes the importance of consumption-based models this way: “At some level, the consumption-based models must be right if economics is to have any hope of describing stock markets.” Therefore, our challenge is to improve the empirical performance of CCAPM rather than to develop alternative asset pricing models. It is now well documented that predictive variables such as dividend yield, term spread, default spread, and short-rate are very persistent (Torous, Valkanov, and Yan, 2004; Boudoukh, Richardson, and Whitelaw, 2006). There is, however, ongoing debate as to whether these highly persistent variables are indeed non-stationary. For example, Roll (2002) states that predictive variables that are functions of asset prices, such as dividend yield, could be non-stationary under rational expectations. On the other hand, as documented in Cochrane (2005), dividend yield should be stationary because asset price and dividend are cointegrated. In this study, we do not argue whether these variables are integrated or not; rather, we argue that the use of highly persistent time-series variables in predictive regressions as well as cross-sectional analyses causes statistical problems, as documented by Ferson, Sarkissian, and Simin (2003).
