# Most well developed are those models incorporating conditional factors, including those presented here, to capture time varying risk. Ferson and Harvey (1991) use conditional information in the estimation of parameters in cross-sectional regression tests of the CAPM and later use conditioning information to calculate parameters in time series regressions in Ferson

and Harvey (1999). Jaganathan & Wang (1996) augment in addition to the market portfolio. A CAPM model with estimated using the Kalman filter can be interpreted as a

the CAPM by including human capital time varying random walk coefficients truly agnostic dynamic model with no

preference as to which exogenous premium on the market portfolio. allows for heterodkedastic errors.

macroeconomic For consistency

variables govern the Bayesian beta

the time varying CAPM proposed

risk also

As presented in Panel B, allowing for Bayesian time variation in the market beta does little to improve the explanatory power of the market portfolio in the cross-section. For both regressions

in Panel B, there is only weak evidence of a positive results when the predicted returns from an expanding

market risk premium.

# As in Panel A,

sample

# OLS

factor

model

are

included

provide little support for the notion that lagged macro factors the variation of sector returns in the cross section either.

describe

a

significant

amount

of

An initial attempt to test the influence of parameter time variation in a predicted returns model in

the cross-section is examined lagged macroeconomic factor previous 50 weeks of data.

in Panel C. Here, time series regressions for the CAPM and the predicted returns are performed using rolling regressions over the In the first cross-sectional regression, again, time variation

introduced by rolling regressions does nothing to describe sector returns. Allowing for time variation increases the apparent risk premium and improves explaining the cross section of portfolio returns.

improve the ability of the CAPM betas to in the predicted return regressions, however, the significance of the predicted returns in

In Panels D and E, cross sectional regressions are performed using the TVPFM predicted returns from (5) as regressors. In each case the size of the apparent risk premium is greater than that observed in the rolling regression example at a similar level of significance. In each case the t-

18