Consumption based asset pricing model: Meaning, Criticisms & Real-World Uses

What Is Consumption-Based Asset Pricing Model?

The Consumption-Based Asset Pricing Model (CAPM) is a foundational concept within asset pricing theory that seeks to explain the prices of financial assets based on their covariance with aggregate consumption growth. At its core, the model posits that investors are primarily concerned with smoothing their consumption over time. Therefore, assets that pay off well when consumption is high (and thus marginal utility of consumption is low) are considered riskier and should offer a higher expected return to compensate investors for this undesirable characteristic. Conversely, assets that perform poorly when consumption is low (when marginal utility is high) are desirable for their insurance-like properties and will thus command a lower expected return. This framework is a cornerstone of modern financial markets analysis, providing a theoretical link between macroeconomic variables and asset valuations.

History and Origin

The theoretical underpinnings of the Consumption-Based Asset Pricing Model (CCAPM) trace back to the pioneering work of economist Robert E. Lucas Jr. His seminal 1978 paper, "Asset Prices in an Exchange Economy," laid much of the groundwork by developing an equilibrium model where asset prices are determined by a representative agent's optimal consumption and saving decisions. This early work provided a rigorous framework for understanding how an investor's desire for consumption smoothing across different states of the economy influences asset valuations.¹¹

Building on Lucas's contributions, the CCAPM gained significant attention in the 1980s, particularly with the introduction of the "equity premium puzzle" by Rajnish Mehra and Edward Prescott in 1985.¹⁰ This puzzle highlighted a significant discrepancy between the historically observed high returns on equity compared to seemingly risk-free assets and the much lower equity premium predicted by standard CCAPM calibrations, assuming plausible levels of investor risk aversion.⁹,⁸ This challenge spurred extensive research aimed at refining the consumption-based asset pricing model and exploring alternative preference structures to better align theory with empirical observations.⁷

Key Takeaways

The Consumption-Based Asset Pricing Model (CCAPM) links asset returns directly to investors' consumption patterns.
It suggests that assets performing well during periods of high aggregate consumption are less desirable and should yield higher returns.
The model assumes investors are rational and seek to smooth their consumption over their lifetime.
The "equity premium puzzle" remains a significant empirical challenge for the standard CCAPM, indicating that the model, in its basic form, struggles to explain historical asset returns without invoking implausibly high levels of risk aversion.
The CCAPM is a fundamental part of asset pricing theory, providing a microeconomic foundation for understanding risk and return.

Formula and Calculation

The core of the Consumption-Based Asset Pricing Model can be expressed through the fundamental asset pricing equation, which relates an asset's price today to its expected future payoff, discounted by a stochastic discount factor (SDF) derived from the investor's marginal utility of consumption.

The general formula for the price of an asset (P_t) at time (t) is:

P_t = E_t \left[ M_{t+1} X_{t+1} \right]

Where:

(P_t): The price of the asset at time (t).
(E_t[\cdot]): The expectation operator conditional on information available at time (t).
(M_{t+1}): The stochastic discount factor (SDF) or pricing kernel, representing the marginal rate of substitution between consumption at time (t) and consumption at time (t+1). This factor is inversely related to the marginal utility of consumption.
(X_{t+1}): The payoff of the asset at time (t+1) (e.g., dividend plus future price).

In a common specification with time-separable power utility function, the stochastic discount factor (M_{t+1}) is often given by:

M_{t+1} = \beta \frac{U'(C_{t+1})}{U'(C_t)}

Where:

(\beta): The subjective discount factor, representing the investor's patience (how much they value future consumption relative to current consumption).
(U'(\cdot)): The marginal utility of consumption.
(C_t): Aggregate consumption at time (t).
(C_{t+1}): Aggregate consumption at time (t+1).

For an asset's expected return (R_{t+1}), the equation can be rearranged as:

E_t[R_{t+1}] = \frac{1}{P_t} E_t[M_{t+1} X_{t+1}]

Or, more commonly:

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

Where:

(R_f): The risk-free rate.
(Cov_t(M_{t+1}, R_{t+1})): The covariance between the stochastic discount factor and the asset's return. This term captures the asset's systematic risk from a consumption perspective. Assets that covary negatively with the stochastic discount factor (i.e., covary positively with consumption growth) will have lower expected returns.

Interpreting the Consumption-Based Asset Pricing Model

Interpreting the Consumption-Based Asset Pricing Model (CCAPM) centers on understanding the fundamental economic intuition that investors derive utility from consumption, not directly from wealth or asset returns. The model implies that investors are willing to accept lower average returns on assets that provide payoffs when their consumption is low and the marginal utility of an extra unit of consumption is high. These assets act as a form of insurance, offering valuable income precisely when it's most needed.

Conversely, assets that tend to pay off generously when consumption is already high and the marginal utility of consumption is low are considered undesirable. Investors demand a higher expected return for holding such assets, as they provide wealth when it is least valuable. This perspective highlights the importance of an asset's covariance with aggregate consumption growth, rather than just its volatility, in determining its risk premium. The smoother an investor's lifetime consumption path, the greater their overall utility, which is a core tenet of consumption smoothing theory.⁶ A key insight is that the model's implications extend to the real interest rate, suggesting that expected real returns should reflect both consumption growth and investor preferences.

Hypothetical Example

Imagine an investor named Sarah whose primary goal is to maintain a stable level of consumption throughout her life. She is considering two investments: a bond fund and a stock fund.

Scenario 1: Stock Fund
The stock fund's returns are highly correlated with the overall economic cycle. In periods of strong economic growth, when aggregate consumption is high, the stock fund performs exceptionally well. However, during recessions, when there are significant economic shocks and aggregate consumption falls, the stock fund's value declines sharply.

Scenario 2: Bond Fund
The bond fund, consisting mainly of government bonds, offers a more stable return profile, largely uncorrelated with the economic cycle. Its returns are consistent whether the economy is booming or in a downturn.

CCAPM Interpretation:
From a Consumption-Based Asset Pricing Model perspective, Sarah would view the stock fund as inherently riskier relative to her consumption needs. Even though it offers high returns during good times, those returns come when her consumption is already high, and extra income provides less additional utility. The poor performance during recessions, when her consumption might be low and she needs income most, significantly reduces its appeal. To compensate for this, Sarah would demand a substantially higher expected return from the stock fund compared to the bond fund. The bond fund, by providing more consistent returns regardless of the economic state, helps Sarah achieve her goal of consumption smoothing, making it a relatively more desirable asset even if its average returns are lower.

Practical Applications

While the Consumption-Based Asset Pricing Model (CCAPM) faces empirical challenges, its theoretical framework offers valuable insights and practical applications in several areas of finance and economics:

Understanding Risk Premia: The CCAPM provides a rigorous theoretical basis for understanding why different assets carry different risk premia. It shifts the focus from purely statistical measures of risk (like volatility) to economic risk based on how an asset's payoff correlates with aggregate consumption. This helps investors conceptualize systematic risk in a broader economic context.
Macro-Finance Research: The model serves as a cornerstone for academic research in macro-finance, guiding studies on the links between real economic activity (like consumption growth) and asset prices. Researchers use variations of the CCAPM to explore phenomena such as the determinants of the risk-free rate, the relationship between inflation and asset returns, and the impact of demographic shifts on saving and investment.
Long-Term Investment Planning: For long-term investors focused on achieving specific consumption goals (e.g., retirement planning), the CCAPM emphasizes aligning investment strategies with their lifetime consumption needs. It suggests that portfolios should be constructed to provide more wealth during periods of low consumption, even if it means accepting lower average returns during boom times. This is closely tied to the concept of consumption smoothing.⁵
Asset Allocation Strategies: Although not used directly for day-to-day trading, the CCAPM's insights can inform strategic asset allocation decisions, particularly for institutional investors or endowments with long investment horizons. By considering the aggregate consumption implications of various asset classes, they can design portfolios that better insulate consumption from economic shocks.
Central Bank Policy: Monetary policy decisions by central banks, such as adjustments to interest rates, aim to influence economic activity, including consumption. The CCAPM provides a theoretical lens through which policymakers can consider the impact of these changes on asset valuations and, consequently, on household wealth and spending behavior.

Limitations and Criticisms

Despite its theoretical elegance, the Consumption-Based Asset Pricing Model (CCAPM) has faced substantial empirical challenges and criticisms. The most prominent limitation is its inability to adequately explain the historically observed equity premium, a phenomenon famously dubbed the "equity premium puzzle" by Mehra and Prescott.⁴ Standard calibrations of the CCAPM, using realistic levels of risk aversion and observed consumption volatility, predict a much smaller difference between equity returns and the risk-free rate than has been observed in actual financial markets over the long run.³

Other criticisms and limitations include:

Smoothness of Consumption Data: Aggregate consumption data, particularly for non-durable goods and services, tends to be much smoother than asset returns. The CCAPM requires that fluctuations in consumption drive significant variations in returns, which is often not borne out by the data. This discrepancy makes it difficult for the model to capture the volatility observed in asset prices.
Representative Agent Assumption: The model typically assumes a "representative agent" who embodies the preferences and consumption patterns of all investors. This simplification ignores investor heterogeneity, market imperfections, and individual-specific economic shocks, which can significantly influence investment decisions and asset prices.
Preferences and Utility Function: The standard CCAPM often relies on specific forms of the utility function, such as power utility. Researchers have explored alternative preference structures, like habit formation or recursive utility, to try and resolve the equity premium puzzle and other empirical anomalies.²,¹ While some of these modifications can improve the model's fit, they often introduce additional complexity or rely on parameters that are difficult to estimate or intuitively interpret.
Liquidity and Transaction Costs: The model generally assumes frictionless markets, ignoring liquidity constraints, transaction costs, and portfolio adjustment costs that investors face in the real world. These factors can influence asset demand and pricing in ways not captured by the basic CCAPM.

Consumption-Based Asset Pricing Model vs. Capital Asset Pricing Model

The Consumption-Based Asset Pricing Model (CCAPM) and the Capital Asset Pricing Model (CAPM) are both fundamental frameworks in asset pricing theory, but they differ significantly in their core assumptions and the type of risk they emphasize.

The CAPM, an earlier and more widely used model, posits that an asset's expected return is determined by its covariance with the overall market portfolio. The key risk in the CAPM is "market risk" or systematic risk, measured by beta, which represents an asset's sensitivity to movements in the broad market. Investors are assumed to be concerned with the mean and variance of their portfolio returns.

In contrast, the CCAPM argues that investors are concerned not with the variance of their portfolio returns directly, but with the variance of their consumption. Therefore, the relevant measure of risk for an asset is its covariance with aggregate consumption growth. An asset is considered riskier if its returns are low when consumption is low (and vice-versa). The CCAPM provides a more fundamental, microeconomic grounding for risk and return, linking asset prices directly to investor preferences for consumption smoothing across different states of the world. While the CAPM is an equilibrium model, the CCAPM is often seen as a more general and theoretically richer framework because it derives asset prices from basic principles of utility maximization and macroeconomic aggregates, whereas the CAPM takes the existence of a market portfolio as given.

FAQs

What is the main idea behind the Consumption-Based Asset Pricing Model?

The main idea is that investors ultimately care about their consumption, not just wealth. Therefore, the riskiness of an asset is determined by how its returns correlate with aggregate consumption growth. Assets that provide high returns when consumption is already high (and thus money is less valuable) are less desirable and require higher expected returns, while assets that provide returns when consumption is low (when money is most valuable) are more desirable and require lower expected returns.

How does the CCAPM define risk?

In the Consumption-Based Asset Pricing Model, risk is defined by an asset's covariance with aggregate consumption growth. Assets that pay off poorly when consumption is low are considered risky because they exacerbate periods of hardship. This is distinct from traditional measures of risk like volatility.

What is the "equity premium puzzle" in relation to CCAPM?

The "equity premium puzzle" refers to the empirical observation that historically, stocks have yielded a much higher return than risk-free assets, a difference that the standard CCAPM struggles to explain. The model, with commonly accepted parameters for risk aversion and consumption volatility, predicts a much smaller equity premium than what has been observed in real financial markets.

Is the Consumption-Based Asset Pricing Model used by everyday investors?

No, the Consumption-Based Asset Pricing Model is primarily an academic and theoretical framework used in advanced financial research and economic modeling. Unlike models such as the Capital Asset Pricing Model (CAPM), it is not typically used by everyday investors for practical portfolio construction or individual security selection due to the difficulty in measuring and forecasting aggregate consumption growth and its complex relationship with individual asset returns.

What is consumption smoothing?

Consumption smoothing is the economic concept that individuals prefer to maintain a relatively stable level of consumption over their lifetime, even when their income fluctuates. They achieve this by saving during periods of high income and dissaving (or borrowing) during periods of low income. The CCAPM is built on the premise that investors make investment decisions with this goal in mind.