Douglas Breeden and Robert Lucas, a Nobel laureate in economics, provided the foundation of the consumption capital asset pricing model (CCAPM) in 1979 and 1978 respectively. Their model is an extension of the traditional capital asset pricing model (CAPM). It’s best used as a theoretical model, but it can help to make sense of variation in financial asset returns over time, and in some cases, its results can be more relevant than those achieved through the CAPM model. Read on to discover how this model works and what it can tell you.

What’s CCAPM?

While the CAPM relies on the market portfolio’s return in order to understand and predict future asset prices, the CCAPM relies on the aggregate consumption. In the CAPM, risky assets create uncertainty in an investor’s wealth, which is determined by the market portfolio (e.g. S&P500). In the CCAPM, on the other hand, risky assets create uncertainty in consumption — what an investor will spend becomes uncertain because his or her wealth, (ie. income and property) is uncertain as a result of a decision to invest in risky assets. (For related reading, see Determining Risk And The Risk Pyramid and The Capital Asset Pricing Model: An Overview .)

In the CAPM, the risk premium on the market portfolio measures the price of risk, while the beta states the quantity of risk. In the CCAPM, on the other hand, the quantity of market risk is measured by the movements of the risk premium with consumption growth. Thus, the CCAPM explains how much the entire stock market changes relative to the consumption growth.

While the CCAPM rarely is used empirically, it is highly relevant in theoretical terms. Indeed, the CCAPM is not used as was the standard CAPM in the real world. Therefore, a firm evaluating a project or the cost of capital is more likely to use the CAPM than the CCAPM. The major reason for this is that the CCAPM tends to perform poorly on empirical grounds. This may be because a proportion of consumers do not actively take part in the stock market and, therefore, the basic link between consumption and stock returns assumed by the CCAPM cannot hold. For this reason, the CCAPM may perform better than the CAPM for people who hold stocks.

From an academic point of view, the CCAPM is more widely used than the CAPM. This is because it 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 CCAPM also provides a fundamental understanding of the relation between wealth and consumption and an investor’s risk aversion.

Calculating CCAPM

A simplified version of the CCAPM can take a linear representation between a risky asset (for example stock) and the market risk premium. However, the difference is the definition of the so-called implied risk-free rate. implied market return and the consumption beta. Therefore, the formula for CCAPM is as follows:

Where:

= Implied Risk-free rate (e.g. Three-month Treasury-bill)

= Expected returns on risky asset (e.g. a stock)

= Implied expected market return

= Implied market risk premium

= Consumption beta of the asset

The implied returns and risk premium are determined by the investors’ consumption growth and risk aversion. Moreover, the risk premium defines the compensation that investors require for buying a risky asset. As in the standard CAPM, the model links the returns of a risky asset to its systematic risk (market risk). The systematic risk is provided by the consumption beta.

Consumption Beta

The consumption beta is defined as: