## What Is the Consumption Capital Asset Pricing Model (CCAPM)?

The consumption capital asset pricing model (CCAPM) is an extension of the capital asset pricing model (CAPM) that uses a consumption beta instead of a market beta to explain expected return premiums over the risk-free rate. The beta component of both the CCAPM and CAPM formulas represents a risk that cannot be diversified away.

### Key Takeaways

- The CCAPM predicts that an asset's return premium is proportional to its consumption beta.
- Consumption beta is the coefficient of the regression of an asset's returns and consumption growth, where the CAPM's market beta is the coefficient of the regression of an asset's returns on the market portfolio returns.

## Understanding the Consumption Capital Asset Pricing Model (CCAPM)

The consumption beta is based on the volatility of a given stock or portfolio. The CCAPM predicts that an asset's return premium is proportional to its consumption beta. The model is credited to Douglas Breeden, a finance professor at Fuqua School of Business at Duke University, and Robert Lucas, an economics professor at the University of Chicago who won the Nobel Prize in Economics in 1995.

The CCAPM provides a fundamental understanding of the relationship between wealth and consumption and an investor's risk aversion. The CCAPM works as an asset valuation model to tell you the expected premium investors require in order to buy a given stock, and how that return is affected by the risk that comes from consumption-driven stock price volatility.

The quantity of risk related to the consumption beta is measured by the movements of the risk premium (return on asset and risk-free rate) with consumption growth. The CCAPM is useful in estimating how much stock market returns change relative to consumption growth. A higher consumption beta implies a higher expected return on risky assets. For instance, a consumption beta of 2.0 would imply an increased asset return requirement of 2% if the market increased by 1%.

The CCAPM incorporates many forms of wealth beyond stock market wealth and provides a framework for understanding variation in financial asset returns over many time periods. This provides an extension of the CAPM, which only takes into account one-period asset returns.

The formula for CCAPM is:

$\begin{aligned} &R = R_f + \beta_c ( R_m - R_f ) \\ &\textbf{where:} \\ &R = \text{Expected return on a security} \\ &R_f = \text{Risk-free rate} \\ &\beta_c = \text{Consumption beta} \\ &R_m = \text{Return on the market} \\ \end{aligned}$

## CCAPM vs. CAPM

While the CAPM formula relies on the market portfolio's return to predict future asset prices, the CCAPM relies on aggregate consumption. In the CAPM, the market return is typically represented by the return on the S&P 500. Risky assets create uncertainty in an investor's wealth, which is determined in the CAPM by the market portfolio using the market's beta of 1.0. CAPM assumes that an investor cares about the market return and how their portfolio's return varies from that return benchmark.

In the CCAPM formula, on the other hand, risky assets create uncertainty in *consumption*—how much a person will spend becomes uncertain because the level of wealth is uncertain due to investments in risky assets. The CCAPM assumes investors are more concerned about how their portfolio returns vary from a different benchmark than the overall market.