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Some extensions of the conditional CAPM

Vendrame, Vasco

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Vasco Vendrame
Associate Director - Academic Enhancement - UG


The objective of this thesis is to consider some extensions of the CAPM and to investigate whether such extensions can offer a better explanation for the US average equity returns. This thesis focuses on four main extensions: (i) time-varying factor loadings; (ii) higher moments (coskewness and cokurtosis); (iii) time-varying risk premia,; and (iv) conditional versions of the CAPM using individual assets.
Time-series and cross-sectional tests, conducted on portfolios sorted on market capitalization and/or the book-to-market ratio, show no evidence in support of CAPM. While the standard CAPM predicts that the risk premium should be positive and the intercept from a regression of expected returns on beta should be insignificant, the empirical evidence from the relatively simple models goes contrary to expectation. The use of time-varying betas with dynamic conditional correlations improves the performance of the CAPM, but does not confirm its validity. The introduction coskewness and cokurtosis does not rescue the CAPM. In particular, the unconditional four-moment CAPM is rejected as coskewness and cokurtosis are not found to have additional explanatory power for the cross-section of returns of portfolios of stocks sorted on market capitalization and book-to-market. The conditional four-moment CAPM where coskewness and cokurtosis are obtained as counterparts of the covariance using dynamic conditional correlation is also rejected.
Time-varying risk premia, based on simple bull and bear regimes, combined with the conditional CAPM and the conditional four-moment CAPM, lead to interesting results. In particular, the hypothesis of time-varying risk premia is never rejected, and the conditional CAPM produces a positive beta premium.
The conditional CAPM and conditional four-moment CAPM are tested on individual assets. The results support the CAPM for individual stocks over the last 30 years. The four-moment CAPM seems to work especially well when the SMB factor is added to the model. All of the factors have the expected sign: beta demands a positive premium, coskewness a negative premium and cokurtosis a positive premium. Interestingly, SMB retains significance and has a positive risk premium. Small stocks tend to earn higher returns even after accounting for the comoments.


Vendrame, V. Some extensions of the conditional CAPM. (Thesis). University of the West of England. Retrieved from

Thesis Type Thesis
Publicly Available Date Jun 6, 2019
Keywords higher-moment CAPM, kurtosis, skewness, cross sections, individual assets, dynamic conditional correlation, GARCH, switching regimes
Public URL
Award Date Aug 6, 2014


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