The consumption-based capital asset pricing model (CCAPM) is a model of the determination of expected (i.e. required) return on an investment. The foundations of this concept were laid by the research of Robert Lucas (1978) and Douglas Breeden (1979).
The model is a generalization of the

capital asset pricing model
In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.
The model takes into accou ...

(CAPM). While the CAPM is derived in a static, one-period setting, the CCAPM uses a more realistic, multiple-period setup. The central implication of the CCAPM is that the expected return on an asset is related to "consumption risk", that is, how much uncertainty in consumption would come from holding the asset. 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.
Formally, the CCAPM states that the expected risk premium
A risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. It is used widely in finance and economics, the general definition being the expected risky return less ...

on a risky asset, defined as the expected return on a risky asset less the risk free return, is proportional to the covariance
In probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the les ...

of its return and consumption in the period of the return. The consumption beta
Beta (, ; uppercase , lowercase , or cursive ; grc, βῆτα, bē̂ta or ell, βήτα, víta) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Modern Greek, it represents the voiced labi ...

is included, and the expected return is calculated as follows:Romer, David. Advanced Macroeconomics, ch. 7.
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