Consumption based asset pricing

What Is Consumption Based Asset Pricing?

Consumption based asset pricing is a fundamental approach within asset pricing theory that seeks to explain how the prices of financial assets are determined by an investor's consumption and saving decisions. It falls under the broader category of asset pricing models within financial economics. The core idea is that the value of an asset is directly linked to the utility investors derive from consuming goods and services, and how that utility changes over time and across different states of the world. In this framework, investors are assumed to make investment decisions to smooth their consumption over time, leading them to value assets that provide payoffs when their consumption is low (and thus, the marginal utility of consumption is high).

History and Origin

The foundation of modern consumption based asset pricing was laid by economist Robert Lucas Jr. with his seminal 1978 paper, "Asset Prices in an Exchange Economy."⁵ This work established a general equilibrium model where asset prices are determined endogenously by individuals maximizing their utility from consumption in an economy with stochastic production. Subsequent work, particularly by Douglas Breeden (1979) and later by Lars Peter Hansen and Kenneth Singleton (1982), formalized the Consumption Capital Asset Pricing Model (C-CAPM), explicitly linking asset returns to the covariance with aggregate consumption growth. This paradigm provided a rigorous framework for understanding how risk and time preference influence asset valuations by modeling a representative agent's utility function over consumption.

Key Takeaways

Consumption based asset pricing links asset values to investors' consumption patterns and their marginal utility of consumption.
It assumes investors aim to smooth consumption over time, valuing assets that pay off during periods of low consumption.
The framework uses a stochastic discount factor (SDF) to discount future payoffs, with the SDF being inversely related to consumption growth.
While theoretically elegant, empirical applications of early consumption based asset pricing models faced challenges, notably the equity premium puzzle.
It provides a coherent theoretical basis for understanding risk premia in financial markets.

Formula and Calculation

The fundamental pricing equation in consumption based asset pricing, derived from the investor's intertemporal optimization problem, states that the price of an asset today is the expected discounted value of its future payoffs, where the discount factor is related to the marginal utility of consumption. This is often expressed using a stochastic discount factor ($M_{t+1}$), also known as the pricing kernel:

P_t = E_t \left[ M_{t+1} (P_{t+1} + D_{t+1}) \right]

Alternatively, in terms of expected returns, the formula for the Consumption Capital Asset Pricing Model (C-CAPM) is often presented as:

E_t[R_{i,t+1}] - R_{f,t+1} = - \frac{Cov_t(R_{i,t+1}, M_{t+1})}{E_t[M_{t+1}]}

Where:

(P_t) = The price of the asset at time (t)
(E_t[\cdot]) = Expectation conditional on information available at time (t)
(M_{t+1}) = The stochastic discount factor (intertemporal marginal rate of substitution) between time (t) and (t+1)
(P_{t+1}) = The price of the asset at time (t+1)
(D_{t+1}) = The dividend or payoff from the asset at time (t+1)
(R_{i,t+1}) = The return on asset (i) from time (t) to (t+1)
(R_{f,t+1}) = The risk-free rate from time (t) to (t+1)
(Cov_t(\cdot)) = Conditional covariance

For a representative agent with power utility function, (U(C) = \frac{C^{1-\gamma}}{1-\gamma}), the stochastic discount factor (M_{t+1}) is given by:

M_{t+1} = \beta \left( \frac{C_{t+1}}{C_t} \right)^{-\gamma}

Where:

(\beta) = The subjective discount rate (reflecting impatience)
(C_t) = Aggregate consumption at time (t)
(\gamma) = The coefficient of risk aversion (reflecting the curvature of the utility function)

Interpreting Consumption based asset pricing

Interpreting consumption based asset pricing involves understanding that investors value assets based on how those assets help them smooth their consumption over time. An asset is considered riskier, and thus commands a higher expected return, if its payoffs are negatively correlated with aggregate consumption growth. When aggregate consumption is low, the marginal utility of an additional unit of consumption is high. Therefore, assets that pay out more in states of the world where aggregate consumption is low are highly valued by investors, as they provide insurance against poor consumption outcomes. Conversely, assets that pay out when aggregate consumption is already high provide less utility and thus must offer a higher expected return to compensate investors for this undesirable consumption pattern. This framework highlights the importance of macro-level consumption dynamics in determining individual asset values and overall market efficiency.

Hypothetical Example

Consider two hypothetical assets, Asset A and Asset B, in an economy with fluctuating economic growth and consumption.

Scenario 1: Strong Economic Growth

Aggregate Consumption Growth: High
Asset A Payoff: $10
Asset B Payoff: $10

Scenario 2: Weak Economic Growth (Recession)

Aggregate Consumption Growth: Low
Asset A Payoff: $5
Asset B Payoff: $15

Under consumption based asset pricing, investors would prefer Asset B over Asset A, assuming both have the same expected payoff over time. Why? Because Asset B provides a higher payoff (($15)) precisely when aggregate consumption is low (($5)), meaning the extra income is more valuable in that state (due to high marginal utility of consumption). Asset A, on the other hand, provides a lower payoff in the recession scenario, exacerbating the negative impact of low consumption. To hold Asset A, investors would demand a higher expected return to compensate for its undesirable correlation with their consumption patterns. This illustrates how the covariance between an asset's returns and aggregate consumption is a key determinant of its price and expected return.

Practical Applications

While the pure form of consumption based asset pricing, particularly the C-CAPM, has faced empirical challenges, its underlying principles are deeply embedded in modern financial theory and have practical implications for various areas:

Risk Premium Estimation: The model provides a theoretical basis for why certain assets command higher risk premia. Assets that perform poorly when investors need cash the most (i.e., when consumption is low) should have higher expected returns.
Macro-Finance Research: Researchers continue to refine consumption-based models by incorporating more realistic assumptions about preferences (e.g., habit formation, Epstein-Zin preferences) or market imperfections. These models are crucial for understanding the links between macroeconomic variables and financial markets.
Quantitative Portfolio Management: While not typically used for direct stock picking, the framework informs sophisticated quantitative strategies that consider aggregate economic conditions and their impact on asset classes. Understanding consumption dynamics, for instance, by analyzing data from sources like the Personal Consumption Expenditures (PCE) from the Federal Reserve Bank of St. Louis, can provide insights into broad market movements and the pricing of systemic risks.⁴
Long-Term Investment Planning: It reinforces the idea that an investor's true goal is to optimize consumption over their lifetime, rather than merely maximizing portfolio value in isolation. This perspective influences discussions on saving rates, retirement planning, and optimal asset allocation.

Limitations and Criticisms

Despite its theoretical elegance, consumption based asset pricing, especially the canonical C-CAPM, has faced significant empirical limitations and criticisms:

The Equity Premium Puzzle: One of the most famous challenges is the equity premium puzzle, first highlighted by Rajnish Mehra and Edward C. Prescott.³ Standard consumption-based models with reasonable levels of risk aversion struggle to explain the historically large difference between the returns on equities and the returns on risk-free assets. To match observed returns, the model requires an implausibly high coefficient of relative risk aversion, suggesting that investors are far more risk-averse than common sense or other economic observations would indicate.
The Risk-Free Rate Puzzle: Closely related is the risk-free rate puzzle, where the model often predicts a much higher risk-free rate than observed in reality, or requires a very low rate of time preference.
Measurement Error in Consumption Data: Critics point to the difficulty in accurately measuring aggregate consumption, especially non-durable goods and services, at a high frequency. These measurement errors can obscure the true relationship between consumption and asset returns. Data frequency (e.g., quarterly vs. monthly) can also impact results.
Simplistic Preferences: Early models often assumed time-separable power utility, which may not fully capture complex investor behaviors such as habit formation (where current utility depends on past consumption levels) or preferences for the timing of resolution of uncertainty.
Hansen-Jagannathan Bounds: While a powerful tool for evaluating asset pricing models, the Hansen-Jagannathan bounds, which provide a lower bound on the volatility of any valid stochastic discount factor, have shown that standard consumption-based models often imply an SDF volatility that falls below this lower bound, indicating their inability to explain observed asset return volatility.¹, ²

These limitations have spurred extensive research into more sophisticated consumption-based models, incorporating richer preference structures or alternative sources of risk.

Consumption based asset pricing vs. Capital Asset Pricing Model (CAPM)

While both consumption based asset pricing (C-CAPM) and the Capital Asset Pricing Model (CAPM) are fundamental asset pricing models, they differ in their definition of risk and the source of that risk. The CAPM posits that an asset's expected return is determined by its covariance with the market portfolio's return, often proxied by a broad stock market index. Risk, in the CAPM, is primarily systematic market risk, measured by beta. Investors are compensated for bearing this non-diversifiable market risk.

In contrast, consumption based asset pricing argues that an asset's expected return is determined by its covariance with aggregate consumption growth. Here, the "true" risk is consumption risk – the risk that an asset's payoff will be low precisely when an investor's consumption opportunities are also low. The C-CAPM is considered a more fundamental model because it derives asset prices directly from individuals' utility maximization over consumption, rather than assuming the existence of a market portfolio that is mean-variance efficient, as the CAPM does. The CAPM can be seen as a special case or approximation of a consumption-based model under certain restrictive assumptions about preferences and consumption. However, the empirical success of the CAPM (or its extensions like multi-factor models) in explaining cross-sectional differences in expected returns has generally been greater than that of the pure C-CAPM.

FAQs

What is the core idea behind consumption based asset pricing?

The core idea is that the value of an asset is determined by how it helps investors smooth their consumption over time. Assets that provide payoffs when an investor's consumption is otherwise low are more valuable, as they provide high marginal utility, and thus command lower expected returns.

How does risk aversion relate to consumption based asset pricing?

Risk aversion is a crucial component. A higher degree of risk aversion means investors are more sensitive to fluctuations in their consumption. This leads them to demand higher compensation (i.e., higher expected returns) for assets whose payoffs are highly correlated with consumption, as these assets exacerbate consumption volatility.

What is the "equity premium puzzle" in the context of this theory?

The equity premium puzzle is the observation that historical equity returns have been significantly higher than risk-free returns, a difference that standard consumption based asset pricing models struggle to explain without assuming an implausibly high level of investor risk aversion.

Is consumption based asset pricing used in practice by investors?

While direct application in day-to-day portfolio management is limited due to empirical challenges and data complexities, the underlying principles of consumption based asset pricing heavily influence modern financial theory and macroeconomic modeling. It provides a foundational understanding of risk and return beyond simpler models.