Using Equations (4) and (5), the difference of abnormal presidential premiums between the unconditional CAPM (used in the literature) and conditional TFPM regressions can be written as
Therefore, three situations may explain why the conditional TFPM is able to capture the presidential premium.
We also estimated an alternative version of the conditional TFPM in which the [beta]s vary over time as a linear function of the default risk premium (Jagannathan and Wang, 1996, Equation (11)) using generalized method of moments (GMM).
Finally, note the small difference between the CAPM and TFPM plots, suggesting that the size and value effects are less of a concern for the presidential premium among big stocks.
However, as noted in Panel F, the presidential premiums among small firms decrease substantially when the TFPM is used.
The residual autocorrelations decrease even further when the conditional CAPM and TFPM are used and, in a few instances, are significantly negative.
This paper examines whether risk helps explain this return differential, using conditional versions of the CAPM and TFPM in which systematic risk is allowed to vary across presidential cycles.
Stangl and Jacobsen (2007) focus their investigation on the presidential puzzle in industry index returns and find no evidence of political effects whether they use the CAPM or TFPM.