Consumption capital asset pricing model

What Is Consumption Capital Asset Pricing Model?

The Consumption Capital Asset Pricing Model (CCAPM) is an asset pricing model that posits an asset's expected return is determined by its covariance with aggregate consumption growth, rather than covariance with the market portfolio. It is an extension of the traditional Capital Asset Pricing Model (CAPM) and falls under the broader field of financial economics. The core idea behind the Consumption Capital Asset Pricing Model is that investors seek to smooth their consumption over time. Therefore, they will demand a higher expected return premium for assets that pay out more during times of low consumption (e.g., recessions) because these assets would make their consumption more volatile. Conversely, assets that perform well when consumption is already high (and marginal utility is low) will command lower expected returns.

History and Origin

The foundational concepts of the Consumption Capital Asset Pricing Model were laid by seminal research in the late 1970s. Robert Lucas's 1978 paper, "Asset Prices in an Exchange Economy," and Douglas Breeden's 1979 work, "An Intertemporal Capital Asset Pricing Model," are widely credited for developing the model¹⁴. While the earlier CAPM operated in a single-period, static setting, the Consumption Capital Asset Pricing Model offered a more dynamic, multi-period framework, recognizing that the ultimate purpose of holding wealth is to provide for future consumption.

A key motivation for the development of the Consumption Capital Asset Pricing Model was to address observed anomalies in financial markets, most notably the "equity premium puzzle." This puzzle, prominently highlighted by Rajnish Mehra and Edward Prescott in their 1985 work, refers to the historical observation that equities have significantly outperformed relatively risk-free assets like Treasury bills over long periods, by a margin that seemed too large to be explained by standard economic models given reasonable levels of risk aversion¹², ¹³. The Consumption Capital Asset Pricing Model attempted to provide a more robust theoretical explanation for asset returns by linking them directly to investors' consumption patterns and utility for consumption.

Key Takeaways

• The Consumption Capital Asset Pricing Model (CCAPM) links an asset's expected return to its sensitivity to aggregate consumption growth.
• It suggests investors demand higher returns for assets that reduce their ability to smooth consumption over time.
• The model uses a "consumption beta" to measure an asset's systematic risk related to consumption volatility.
• CCAPM is an intertemporal model, considering consumption decisions across multiple periods, unlike the static CAPM.
• Despite its theoretical appeal, the Consumption Capital Asset Pricing Model faces empirical challenges in fully explaining observed market phenomena, particularly the equity premium puzzle.

Formula and Calculation

The Consumption Capital Asset Pricing Model expresses the expected real return on a risky asset in terms of its consumption beta. The expected risk premium on an asset is proportional to its consumption beta.

The formula for the expected risk premium according to the CCAPM is:

$E[R_i] - R_f = \beta_i^C \cdot \lambda_C$

Where:

• ( E[R_i] ) = Expected return on asset (i)
• ( R_f ) = Risk-Free Rate
• ( \beta_i^C ) = Consumption Beta for asset (i)
• ( \lambda_C ) = Market price of consumption risk, reflecting investors' aggregate risk aversion.

The consumption beta (( \beta_i^C )) measures how sensitive an asset's return is to changes in aggregate consumption growth. It is formally defined as:

$\beta_i^C = \frac{Cov(R_i, \Delta C / C)}{Var(\Delta C / C)}$

Where:

• ( Cov(R_i, \Delta C / C) ) = Covariance between the asset's return ((R_i)) and the growth rate of aggregate consumption (( \Delta C / C ))
• ( Var(\Delta C / C) ) = Variance of the aggregate consumption growth rate

This consumption beta is analogous to the market beta in the traditional CAPM, but instead of relating an asset's returns to the market portfolio, it relates them to changes in aggregate consumption.

Interpreting the Consumption Capital Asset Pricing Model

Interpreting the Consumption Capital Asset Pricing Model centers on understanding how an asset's payoff stream correlates with investors' aggregate consumption. The model suggests that assets that provide high returns when aggregate consumption is low (e.g., during a recession when people are consuming less) are less desirable. This is because such assets would exacerbate the decline in an investor's utility function from consumption. Therefore, investors will demand a higher expected return as compensation for holding assets that correlate positively with bad consumption states, implying higher consumption risk.

Conversely, assets that yield higher returns when aggregate consumption is also high are more appealing. These assets help smooth consumption by providing payoffs when they are most valued (i.e., when marginal utility of consumption is high, meaning consumption is low). However, the CCAPM predicts that assets with low or negative correlation with consumption growth should offer lower expected returns because they act as a form of consumption insurance. The model provides a framework for asset valuation by connecting expected returns to macroeconomic variables related to consumption rather than just market indices.

Hypothetical Example

Consider two hypothetical companies: "Stable Foods Inc." (SFI), a consumer staples company, and "Luxury Yachts Corp." (LYC), a manufacturer of high-end yachts.

Assume the following:

• Risk-free rate (( R_f )) = 2%
• Market price of consumption risk (( \lambda_C )) = 5%

We analyze their consumption betas:

• Stable Foods Inc. (( \beta_{SFI}^C )): During economic downturns, when overall consumption growth is low, demand for essential goods like food remains relatively stable. Thus, SFI's returns might be less correlated with drastic swings in aggregate consumption. Let's say its consumption beta is 0.5.
  Expected Risk Premium for SFI: ( E[R_{SFI}] - R_f = 0.5 \cdot 5% = 2.5% )
  Expected Return for SFI: ( E[R_{SFI}] = 2% + 2.5% = 4.5% )

• Luxury Yachts Corp. (( \beta_{LYC}^C )): Sales of luxury items are highly sensitive to economic cycles and consumption trends. During periods of low aggregate consumption growth, demand for luxury yachts would likely plummet, leading to significantly lower returns for LYC. Therefore, LYC's returns would be highly correlated with aggregate consumption growth. Let's assume its consumption beta is 1.8.
  Expected Risk Premium for LYC: ( E[R_{LYC}] - R_f = 1.8 \cdot 5% = 9.0% )
  Expected Return for LYC: ( E[R_{LYC}] = 2% + 9.0% = 11.0% )

In this hypothetical scenario, the Consumption Capital Asset Pricing Model suggests that investors would demand a much higher expected return for holding Luxury Yachts Corp. stock compared to Stable Foods Inc., because LYC's returns are more sensitive to fluctuations in overall consumption, thereby exposing investors to greater consumption risk. This highlights how the CCAPM attempts to price assets based on their contribution to an investor's overall consumption smoothing objective, aiding in diversification based on consumption risk.

Practical Applications

While often challenging to implement empirically due to difficulties in accurately measuring aggregate consumption, the Consumption Capital Asset Pricing Model offers valuable theoretical insights and finds applications in various areas of finance:

• Asset Pricing Research: It provides a theoretical framework for understanding how risk related to consumption affects asset prices. Researchers use it to analyze and develop more sophisticated asset pricing models, often incorporating factors like habit formation or long-run risks in consumption growth to better explain observed market anomalies¹⁰, ¹¹.
• Macroeconomic Linkages: The Consumption Capital Asset Pricing Model explicitly connects financial markets with real economic activity through aggregate consumption. This linkage helps economists and policymakers understand how changes in economic conditions and consumer behavior might influence asset returns and investment decisions.
• Risk Management and Portfolio Construction: Although direct application for individual investors is limited, institutional investors and academic researchers can use the principles of CCAPM to think about portfolio construction in terms of managing exposure to macroeconomic consumption risk. It implies that diversifying away from market risk might not be enough; one also needs to consider consumption-related systematic risk.
• Understanding Puzzles: The model is central to the ongoing academic debate surrounding the Equity Premium Puzzle and other asset pricing anomalies. It highlights the discrepancy between theoretical predictions and historical market returns, prompting further research into consumer preferences and market frictions⁹. The Federal Reserve Bank of San Francisco has published on the persistency of this puzzle, underscoring the CCAPM's role in the discussion⁸.

Limitations and Criticisms

Despite its theoretical elegance and ability to generalize the CAPM, the Consumption Capital Asset Pricing Model faces significant limitations and criticisms, primarily concerning its empirical performance:

• Measurement of Aggregate Consumption: A major practical hurdle is the accurate measurement of "aggregate consumption" in a way that aligns with the model's theoretical requirements. Reported consumption data, often from national accounts, may not fully capture the short-term, high-frequency changes in consumption relevant to investors' decisions, leading to measurement errors that hinder empirical testing⁶, ⁷.
• The Equity Premium Puzzle: Even with the CCAPM, the model has struggled to fully resolve the equity premium puzzle. To match the historically observed equity premium, the model often requires implausibly high levels of risk aversion on the part of investors, far exceeding what economists generally consider reasonable⁴, ⁵. This suggests that the model might be missing other important factors influencing asset returns or that the underlying assumptions about investor utility function and market equilibrium are too simplistic³.
• Oversimplification of Preferences: The Consumption Capital Asset Pricing Model typically assumes a representative agent with simple, time-separable preferences. This simplification may not capture the complexities of real-world investor behavior, such as habit formation (where current utility depends on past consumption) or various behavioral biases that influence financial decisions².
• Limited Empirical Success: While theoretically appealing, empirical tests of the Consumption Capital Asset Pricing Model have often yielded mixed results, showing that it does not consistently outperform simpler models, particularly when accounting for measurement issues in consumption data¹. This has led to the development of alternative asset pricing models.

Consumption Capital Asset Pricing Model vs. Capital Asset Pricing Model

The Consumption Capital Asset Pricing Model (CCAPM) and the Capital Asset Pricing Model (CAPM) are both foundational frameworks within portfolio theory for determining the expected return on a risky asset. Their key difference lies in the fundamental source of risk they use to explain these returns.

While the CAPM is widely taught and applied due to its simplicity and relative ease of implementation, the Consumption Capital Asset Pricing Model offers a more theoretically grounded perspective by linking asset returns directly to fundamental economic forces and investor utility for consumption. However, the practical challenges of measuring consumption and its limited empirical success in fully explaining market anomalies have meant that the CCAPM has seen more application in academic research on the stochastic discount factor than in everyday financial analysis.

FAQs

What is the main idea behind the Consumption Capital Asset Pricing Model?

The main idea is that investors care most about their consumption. Therefore, assets that provide returns that help smooth an investor's consumption over time are more desirable and will command lower expected returns. Conversely, assets whose returns fluctuate significantly with aggregate consumption (making consumption more volatile) are riskier and require higher expected returns.

How does consumption risk differ from market risk?

Market risk (as in the CAPM) refers to the risk associated with the overall stock market. Consumption risk (as in the CCAPM) refers to the risk an asset poses to an investor's ability to maintain a smooth path of consumption. An asset with high consumption risk tends to perform poorly when overall economic consumption is low, thereby magnifying the adverse impact on an investor's ability to consume.

Why is the Consumption Capital Asset Pricing Model difficult to test?

The primary difficulty in testing the Consumption Capital Asset Pricing Model stems from the challenge of accurately measuring "aggregate consumption" in real-time and with sufficient frequency. Economic data on consumption is often subject to reporting lags, revisions, and may not fully capture the nuances of short-term consumption changes that drive investor behavior and asset prices.

Has the Consumption Capital Asset Pricing Model replaced the CAPM?

No, the Consumption Capital Asset Pricing Model has not replaced the CAPM in widespread practical application. While CCAPM offers a more robust theoretical foundation linking asset prices to fundamental economic variables, its empirical performance has been limited, particularly in solving the Equity Premium Puzzle. The CAPM, despite its simpler assumptions, remains a popular tool due to its relative ease of use and long-standing presence in financial education and practice.