ri , t 1
where i,t is the time series regression coefficient for each sector i from the CAPM estimated
through time t. M i,t is the predicted return for each sector i at time t estimated by the time
varying parameter model (TVPFM) in (5) using factors and parameters through time t. 0,t is the
i n t e r c e p t a n d t , 1 a n d t , 2 a r e s l o p e c o e f f i c i e n t s o n t h e e s t i m a t e d m a r k e t b e t a s a n d t h e p r e d i c t e d
returns of the time varying comparable to that performed
parameter by Ferson
and Harvey (1999) where a predicted return calculated
with lagged macroeconomic factors is included in a cross-sectional test of three factor model. Results of a number of cross-sectional regressions are using the method presented in Fama-MacBeth (1973).
the Fama and French presented in Table 6
(Insert Table 6 here)
In Panel A, estimates for the CAPM betas and predicted returns from OLS regressions on lagged macro factors are generated using expanding samples from the first week in January 1990 through time t. Cross-sectional regressions are performed for each time t, from the week ending
October 14, 1994 to the week ending January 10, 2003, for a total of 429 regressions. These expanding sample estimates represent the full unconditional estimates for the CAPM betas and factor model predicted returns through time t. In the regression including only market betas, there is little evidence supporting the proposition that the CAPM significantly explains the cross- section of returns for the selected sector portfolios. In the second regression in Panel A, the predicted returns from the expanding sample OLS factor model do little better describing the cross-section of returns, with an insignificant coefficient of similar magnitude to that on the market portfolio.
Given the strong evidence presented here for time varying risk sensitivities in the TVPFM, it is also of interest to test if the sector CAPM can be improved by allowing for time variation in the market beta. A number of studies of late have attempted to prop up the CAPM in the face of relentless attack by models that incorporate portfolio attributes as well as the market portfolio.