Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia are Time-Varying

Abstract

This paper explores the ability of theoretically-based asset pricing models such as the CAPM and the consumption CAPM referred to jointly as the (C)CAPM to explain the cross-section of average stock returns. Unlike many previous empirical tests of the (C)CAPM, we specify the pricing kernel as a conditional linear factor model, as would be expected if risk premia vary over time. Central to our approach is the use of a conditioning variable which proxies for fluctuations in the log consumption-aggregate wealth ratio and is likely to be important for summarizing conditional expectations of excess returns. We demonstrate that such conditional factor models are able to explain a substantial fraction of the cross-sectional variation in portfolio returns. These models perform much better than unconditional (C)CAPM specifications, and about as well as the three-factor Fama-French model on portfolios sorted by size and book-to-market ratios. This specification of the linear conditional consumption CAPM, using aggregate consumption data, is able to account for the difference in returns between low book-to-market and high book-to-market firms and exhibits little evidence of residual size or book-to-market effects. (JEL G10, E21) 9 This debate is borne out in several recent papers; for example, see Daniel and Titman (1997, 1998) and Davis, Fama and French (forthcoming). 10 See Harrison and Kreps (1979).

Empirical proxies for the consumption–wealth ratio

“…Lettau and Ludvigson present empirical evidence against the hypothesis of no cointegration and in favor of the existence of a single cointegrating relationship. In addition, Lettau and Ludvigson (2001a) show that the residual associated with this relationship has predictive power for excess stock returns-a result that they suggest is consistent with the proposition that this residual does indeed summarize information about expected future asset returns-while Lettau and Ludvigson (2001b) and (2002a) use this residual as a direct proxy for expected asset returns in order to construct models of cross-sectional asset prices and capital investment.…”

Conditional risk–return relationship in a time-varying beta model

“…Studies such as Harvey (1989) and Harvey (1991, 1993) suggest that a constant beta estimated by OLS may not capture the dynamics of beta. Jagannathan and Wang (1996) and Lettau and Ludvigson (2001) show that conditional CAPM with a time-varying beta outperforms the unconditional CAPM with a constant beta. Franzoni (2004, 2005) also argue that an econometric model that fails to mimic the investors' learning process of time-evolving beta may lead to inaccurate estimates of beta.…”

Forecasting Returns with Fundamentals-Removed Investor Sentiment

“…Primarily, Lemmon and Portniaguina [7] use quarterly data and this paper uses monthly data. Lemmon and Portniaguina [7] use the following nine fundamentals: default spread (DEF), as measured by the difference between the yields to maturity on Moody's Baa-rated bonds and Aaa-rated bonds; yield on 3-month Treasury bills (RF); dividend yield (DIV), following Fama and French [21]; real GDP growth (GDP); growth in personal consumption expenditures (CONS); labor income growth (LABOR), as measured by the per capita growth in total personal income minus dividend income, deflated by the PCE deflator; the Bureau of Labor Statistics unemployment rate (URATE), seasonally adjusted; inflation rate (INF), measured by the change in the consumer price index; and the consumption-to-wealth ratio (CAY) from Lettau and Ludvigson [22]. The dividend yield measure can be obtained from the difference between CRSP's value-weighted return index and its value-weighted return index excluding dividends.…”