The specification in (5) allows for time variation in factor sensitivities and return variances consistent with the sector parameter stability diagnostics discussed in the previous section. To further investigate the appropriateness of the specification in (5) to capture these return dynamics, we also consider three alternative specifications to independently evaluate the importance of time variation in the factor sensitivities and return variances. The capability of each model to describe the data is evaluated by calculating marginal likelihood values for each model and computing Bayes factors. The methodology for calculating Bayes factors employed here follows that in Chib (1995) and is discussed in further detail below.

The first of the alternative model specifications is a simple factor model with fixed unconditional factor sensitivities and fixed unconditional variance. The first alternative specification is r_{i,t1 } _{0 } _{1}divyield_{t } _{2 }spread_{t } _{3}oil_{t } _{4 }junk_{t } u_{i,t1 }(5a)

) , 0 ( ~ 2 , i u t i N u .

The model in (5a) is intended to serve as a benchmark case.

The second alternative specification is designed to test the importance of the introduction of time variation in factor sensitivities while holding the variance term constant. The second alternative specification is given by

r_{i,t1 } _{0,t1 } _{1,t1 }

divyield

_{t } _{2,t1 }

spread

_{t } _{3,t1 }

oil

_{t } _{4,t1 }

junk

_{t } u_{i,t1 }

(5b)

) , 0 ( ~ 2 , i u t i N u .

Finally, the third alternative heteroskadacticity into the specification is

specification is intended model, holding factor

to evaluate the importance of incorporating

sensitivities

fixed.

The

third

alternative

r_{i,t1 } _{0 } _{1}divyield_{t } _{2 }spread _{t } _{3}oil_{t } _{4 }junk_{t } u_{i,t1 }

(5c)

) , 0 ( ~ 2 , , t S i u t i N u .

11