[1] The foundations of this concept were laid by the research of Robert Lucas (1978) and Douglas Breeden (1979).
While the CAPM is derived in a static, one-period setting, the CCAPM uses a more realistic, multiple-period setup.
Assets that lead to a large amount of uncertainty offer large expected returns, as investors want to be compensated for bearing consumption risk.
The CAPM can be derived from the following special cases of the CCAPM: (1) a two-period model with quadratic utility, (2) two-periods, exponential utility, and normally-distributed returns, (3) infinite-periods, quadratic utility, and stochastic independence across time, (4) infinite periods and log utility, and (5) a first-order approximation of a general model with normal distributions.
The consumption beta is included, and the expected return is calculated as follows:[4]