The consumption based asset pricing model: A note on potential tests and applications

Breeden's demonstration that Merton's multi-beta capital asset pricing model can be collapsed into a single-beta model where betas are computed with respect to aggregate consumption is an important theoretical advance. Nonetheless, Breeden's model retains many of the empirical problems that beset Merton's earlier version. In general the consumption betas will be nonstationary, so that the state variables must be observable for the model to be estimated.     

Cash demand,liquidation costs and capital market equilibrium under uncertainty

In this paper, the portfolio and the liquidity planning problems are unified and analyzed in one model. Stochastic cash demands have a significant impact on both the composition of an individual's optimal portfolio and the pricing of capital assets in market equilibrium. The derived capital asset pricing model with cash demands and liquidation costs shows that both the market price of risk and the systematic risk of an asset are affected by the aggregate cash demands and liquidity risk. The modified model does not require that all investors hold an identical risky portfolio as implied by the Sharpe-Lintner-Mossin model. Furthermore, it provides a possible explanation for the noted discrepancies between the empirical evidence and the prediction of the traditional capital asset pricing model.     

Time preference and capital asset pricing models

Results of the theory of individual optimal consumption-investment choice under uncertainty are extended to a class of intertemporally dependent preferences for consumption streams. These results are then used to show that with intertemporally dependent preferences, which are more realistic than the separable time-additive preference structure, Merton's (1973) multi-beta intertemporal capital asset pricing model is still valid, but it can no longer be collapsed to Breeden's (1979) single consumption-beta model.     

Optimum consumption and portfolio rules with money as an asset

This article generalizes Merton's optimum consumption and portfolio rules in continuous time by introducing money as a capital asset and allowing for uncertain inflation. Assuming that prices are log-normally distributed, a three-funds theorem is derived and the introduction of money is shown not to change the form of the standard inflation-adjusted CAPM but to change the market price of risk. The individual's consumption-portfolio problem is completely solved under uncertain inflation if his utility function is iso-elastic in its arguments. Comparative statics are used to assess the influence of changes in exogenous parameters on the individual's optimal rules.     

Habit-based asset pricing with limited participation consumption

We calibrate and estimate a consumption-based asset pricing model with habit formation using limited participation consumption data. Based on survey data of a representative sample of American households, we distinguish between assetholder and non-assetholder consumption, as well as the standard aggregate consumption series commonly used in the CCAPM literature. We show that assetholder consumption outperforms non-assetholder and aggregate consumption data in explaining bond returns, bond yields, and the volatility of bond yields. We further show that the high volatility of assetholder consumption enables the model to explain the equity premium puzzle and the risk-free rate puzzle simultaneously for a reasonable value of relative risk aversion.     

Optimal multi-period consumption and investment with short-sale constraints

This article examines agents’ consumption-investment problem in a multi-period pure exchange economy where agents are constrained with the short-sale of state-dependent risky contingent claims. In equilibrum, agents hold options written on aggregate consumption in their optimal portfolios. Furthermore, under the specific case of quadratic utility, the optimal risk-sharing rule derived for the pricing agent leads to a multifactor conditional consumption-based capital asset pricing model (CCAPM), where excess option returns appear as factors.     

Measuring portfolio performance and the empirical content of asset pricing models

Recent work by Richard Roll has challenged the worth of portfolio performance measures based on the capital asset pricing model. This paper demonstrates that Roll's conclusions are due to his focusing on a ‘truly’ ex-ante efficient index. Using a choice and information theoretic framework, we show that an appropriate index is efficient relative to the probabilities assessed by the ‘market’. Residual analyses and portfolio performance tests, using such an index, yield meaningful results for a wide class of information structures. Roll's primary criticisms, however, relate to tests of the asset pricing model itself. We argue that these criticisms are vastly overstated.     

Composition of wealth,conditioning information,and the cross-section of stock returns

Value stocks covary with aggregate consumption more than growth stocks during periods when financial wealth is low relative to consumption. However, the conditional value premium does not exhibit such countercyclical behavior. Consequently, a one-factor conditional consumption-based asset pricing model can be rejected without making any arbitrary assumptions on the dynamics of the price of risk or the conditional moments. Empirical evidence is somewhat more consistent with a consumption-based model augmented with an aggregate wealth growth factor, which can be motivated by either recursive preferences or relative wealth concerns.     

Seasonality and Consumption-Based Asset Pricing

Most of the evidence on consumption-based asset pricing is based on seasonally adjusted consumption data. The consumption-based models have not worked well for explaining asset returns, but with seasonally adjusted data there are reasons to expect spurious rejections of the models. This paper examines asset pricing models using not seasonally adjusted aggregate consumption data. We find evidence against models with time-separable preferences, even when the models incorporate seasonality and allow seasonal heteroskedasticity. A model that uses not seasonally adjusted consumption data and nonseparable preferences with seasonal effects works better according to several criteria. The parameter estimates imply a form of seasonal habit persistence in aggregate consumption expenditures.     

Idiosyncratic Consumption Risk and the Cross Section of Asset Returns

This paper investigates the importance of idiosyncratic consumption risk for the cross‐sectional variation in asset returns. We find that besides the rate of aggregate consumption growth, the cross‐sectional variance of consumption growth is also a priced factor. This suggests that consumers are not fully insured against idiosyncratic consumption risk, and that asset returns reflect their attempts to reduce their exposure to this risk. The resulting two‐factor consumption‐based asset pricing model significantly outperforms the CAPM, and its performance compares favorably with that of the Fama–French three‐factor model.     

Asset pricing and energy consumption risk

This paper proposes energy consumption in the US as a new measure for the consumption capital asset pricing model. We find that (i) industrial energy growth produces reasonable values for the relative risk aversion coefficient and the implied risk-free rate; (ii) compared to alternative consumption measures, industrial energy performs well in explaining the cross-sectional variation in stock returns with the lowest implied risk aversion and pricing errors; (iii) the industrial energy consumption risk model performs equally well as the Fama–French three-factor model in the cross-sectional asset pricing tests; and (iv) total energy consumption risk is priced in the presence of the Fama–French factor risks.     

Good‐Specific Habit Formation and the Cross‐Section of Expected Returns

I study asset prices in a general equilibrium framework in which agents form habits over individual varieties of goods rather than over an aggregate consumption bundle. Goods are produced by monopolistically competitive firms whose elasticities of demand depend on consumers' habit formation. Firms that produce goods with a high habit level relative to consumption have low demand elasticities, set high prices for their product, have low expected returns on their stock, and have low asset pricing betas and stock return volatilities. I find supportive evidence for these predictions in the data.     

BUSINESS CYCLES AND STOCK MARKET RETURNS: EVIDENCE USING INDUSTRY-BASED PORTFOLIOS

Much evidence has emerged recently that suggests stock returns are predictable. In representative agent consumption-based asset pricing models, asset returns are related to aggregate output and consumption through changes in the intertemporal marginal rate of substitution. An alternative view is that the amount of variation required in the intertemporal marginal rate of substitution is too large to be rationally explained. We shed further light on this debate by investigating whether the stock returns of certain sectors of the economy can predict future market returns even after controlling for the information contained in the aggregate market index. In the consumption-based models, aggregate output and consumption affect the discount rates of all assets synchronously; no particular sectoral return should have any more predictive ability than the others. We find evidence that the stock returns of five industry-based portfolios have significant information about future market returns that is not in the market index. This stylized empirical result is not consonant with existing models relating output to stock returns.     

A model of international asset pricing

In this paper an intertemporal model of international asset pricing is constructed which admits differences in consumption opportunity sets across countries. It is shown that the real expected excess return on a risky asset is proportional to the covariance of the return of that asset with changes in the world real consumption rate. (World real consumption does not, in general, correspond to a basket of commodities consumed by all investors.) The model has no barriers to international investment, but it is compatible with empirical facts which contradict the predictions of earlier models and which seem to imply that asset markets are internationally segmented.     

Factor pricing in a finite economy

Prior theoretical derivations of the Arbitrage Pricing Theory (APT) bound an aggregate measure of the deviation of mean asset returns from that predicted by a linear pricing equation. It is conceivable, given this bound, that some assets might be badly mispriced by the model. In this paper, a more intuitive derivation of the factor pricing equation is presented which describes the deviation on an asset by asset basis. The deviation is shown to be small for assets in a realistic finite economy and is arbitrarily close to zero for those assets with arbitrarily small size relative to aggregate wealth. It follows that the linear pricing equation provides a good approximation for the mean returns of all traded assets.     

Time Variation in the Covariance between Stock Returns and Consumption Growth

The conditional covariance between aggregate stock returns and aggregate consumption growth varies substantially over time. When stock market wealth is high relative to consumption, both the conditional covariance and correlation are high. This pattern is consistent with the “composition effect,” where agents' consumption growth is more closely tied to stock returns when stock wealth is a larger share of total wealth. This variation can be used to test asset‐pricing models in which the price of consumption risk varies. After accounting for variations in this price, the relation between expected excess stock returns and the conditional covariance is negative.     

Consumption Fluctuations and Expected Returns

This paper introduces a novel consumption-based variable, cyclical consumption, and examines its predictive properties for stock returns. Future expected stock returns are high (low) when aggregate consumption falls (rises) relative to its trend and marginal utility from current consumption is high (low). We show that the empirical evidence ties consumption decisions of agents to time variation in returns in a manner consistent with asset pricing models based on external habit formation. The predictive power of cyclical consumption is not confined to bad times and subsumes the predictability of many popular forecasting variables.     

Hidden persistent disasters and asset prices

This study analyzes the effects of agents’ learning about hidden persistent economic disasters on asset prices. In this study, it is assumed that aggregate consumption follows a hidden Markov regime-switching process and a representative agent infers the current regime, normal regime, or disaster regime, sequentially from the realized path of the past consumption process. In this setting, the fluctuation in the agent’s posterior probabilities of the disaster regime augments the volatility of equity returns. By utilizing the stochastic differential utility, this study demonstrates that the current model can help resolve many asset pricing puzzles including the equity premium puzzle, equity volatility puzzle, and risk-free rate puzzle simultaneously. Further, the current model predicts the counter-cyclical pattern in the equity premium and equity-return volatility on the normal regime, although asset returns are negative and highly volatile during disasters. The study also demonstrates that, if the agent’s preferences are restricted to time-additive power utility, the consideration of hidden persistent disasters deepens the asset pricing puzzles.     

“Lucas” in the Laboratory

We study the Lucas asset pricing model in a controlled setting. Participants trade two long‐lived securities in a continuous open‐book system. The experimental design emulates the stationary, infinite‐horizon setting of the model and incentivizes participants to smooth consumption across periods. Consistent with the model, prices align with consumption betas and comove with aggregate dividends, particularly so when risk premia are higher. Trading significantly increases consumption smoothing compared to autarky. Nevertheless, as in field markets, prices are excessively volatile. The noise corrupts traditional generalized method of moment tests. Choices display substantial heterogeneity, with no subject representative for pricing.     

Housing,consumption and asset pricing

This paper considers a consumption-based asset pricing model where housing is explicitly modeled both as an asset and as a consumption good. Nonseparable preferences describe households’ concern with composition risk, that is, fluctuations in the relative share of housing in their consumption basket. Since the housing share moves slowly, a concern with composition risk induces low frequency movements in stock prices that are not driven by news about cash flow. Moreover, the model predicts that the housing share can be used to forecast excess returns on stocks. We document that this indeed true in the data. The presence of composition risk also implies that the riskless rate is low which further helps the model improve on the standard CCAPM.