Asset Pricing: Consumption-Based Models

Core Concept

Consumption-based asset pricing models establish a direct link between asset returns and fundamental economic factors, particularly consumption⁵. The central idea is that asset prices and expected returns are related to "consumption risk" - how much uncertainty in consumption would result from holding a particular asset³.

Key Equations

The basic consumption-based pricing equation is:

$$p_t = E_t \left[ \beta \frac{u'(c_{t+1})}{u'(c_t)} x_{t+1} \right]$$

Where: - $$p_t$$ is the asset price - $$\beta$$ is the time discount factor - $$u'(c)$$ is the marginal utility of consumption - $$x_{t+1}$$ is the asset payoff¹

The expected return formula is:

$$E[r_i] - r_f = \beta_c (r_m - r_f)$$

Where $$\beta_c$$ is the consumption beta²³.

Key Features

Uses a multi-period setting, unlike the single-period CAPM³.
Predicts that assets with higher consumption risk offer higher expected returns³.
Relies on aggregate consumption data rather than market portfolio returns².
Provides a framework for understanding variations in asset returns over multiple time periods².

Advantages

Incorporates many forms of wealth beyond just stock market wealth².
Consumption is more readily measured compared to total wealth, avoiding issues like valuing human capital⁴.

Challenges

Depends on assumptions about utility functions, typically using intertemporally separable utility⁴.
Empirical issues arise when trying to match observed asset prices and returns with consumption data⁵.
Standard models struggle to explain the high observed equity premium and stock return volatility relative to consumption volatility⁵.

Extensions

Researchers have proposed modifications to address empirical challenges, such as:

Campbell and Cochrane's (1999) habit formation model, which introduces slow-moving habit to better explain time-varying expected returns⁵.
Long-run risk models like Bansal and Yaron (2004), which incorporate more complex consumption dynamics⁵.

These extensions aim to better align theoretical predictions with observed asset pricing phenomena while maintaining the fundamental link between consumption and asset prices.