Consumption-based Asset Pricing Model Research Articles

Time-varying risk aversion and unexpected inflation

We formulate a consumption-based asset pricing model in which aggregate risk aversion is time-varying in response to both news about consumption growth (as in a habit formation model) and news about inflation. We estimate our model and explore its pricing implications for the term structure of interest rates and the cross-section of stock returns. Our empirical results support the hypothesis that aggregate risk aversion varies in response to news about inflation. The induced time-variation in risk aversion does not appear to proxy for inflation uncertainty or economic growth.

Testable implications of consumption-based asset pricing models with incomplete markets

This paper studies the testable implications of consumption-based asset pricing models with incomplete markets when idiosyncratic income shocks are permanent. It is shown that the theory places no testable restrictions (beyond absence of arbitrage) on either the macroeconomic data or the first N moments of the cross-sectional distribution of consumption growth even if the one-period utility function (degree of risk aversion) is known. More precisely, this paper shows that any “observed” joint process of aggregate consumption, arbitrage-free asset returns, and N moments of the cross-sectional distribution of consumption growth is an equilibrium outcome for some pure discount factor and some process of individual income. The proof is based on the construction of a personal-disaster process (process of extreme idiosyncratic events) which allows for arbitrary variations in idiosyncratic risk without affecting the first N moments of the cross-sectional distribution of consumption growth.

Consumption, Housing Rents and Housing Price: A Test Of A Real Estate Pricing Model Using Hong Kong Data

The present study investigates whether Hong Kong's volatile real estate market is consistent with a non–linear consumption–based–asset–pricing model. It finds that the asset–pricing model is not rejected for some types of properties. However, the differentials between the returns to residential properties and risk–free rate are too large to be explained by the model.

Consumption asset pricing with stable shocks—exploring a solution and its implications for mean equity returns

We study the consumption based asset pricing model due to Lucas (Econometrica 46 (1978) 1429). The exogenous endowment sequence is modeled as a linear stochastic process driven by stable shocks in an otherwise standard framework. The Gaussian process emerges as a special case. We derive exact analytical solutions for asset prices and returns, and provide conditions under which these exist. We also study the ability of the model to generate realistic values of observed mean rates of return.

Comparing Consumption–Based Asset–Pricing models

We make use of a recently developed method to estimate the intertemporal marginal rate of substitution consistent with the fluctuations of asset return data from the Toronto Stock Exchange. These estimates are then used to evaluate various parametric specifications for preferences often used in empirical studies of consumption and asset returns. In contrast to existing studies, we are able to perform a formal statistical comparison of these models. We consider six extensions of the usual power utility model, and we find that none can be said to be a demonstrable improvement on the standard model. Comparaison de modèles de prix des actifs fondés sur la consommation. Les auteurs utilisent une méthodologie développée récemment pour calibrer le taux marginal de substitution inter–temporel compatible avec les fluctuations des rendements sur les actifs enregistrées au Toronto Stock Exchange. Ces estimations sont utilisées pour évaluer diverses spécifications paramétriques souvent utilisées dans les études empiriques de la consommation et des rendements sur les actifs. Contrairement à ce qui est présenté dans les études existantes, les auteurs font une comparaison statistique formelle de ces modèles. Ils considèrent six extensions du modèle d’utilité et trouvent qu’aucune ne constitue une amélioration significative du modèle standard.

Asset Returns in an Endogenous Growth Model with Incomplete Markets

This paper studies the testable implications of consumption-based asset pricing models with incomplete markets when idiosyncratic income shocks are permanent and not lognormally distributed. It is shown that the theory places no testable restrictions (beyond absence of arbitrage) on either the macroeconomic data or the first N moments of the cross-sectional distribution of consumption (income) growth. More precisely, this paper shows that any observed joint process of aggregate consumption, arbitrage-free asset returns, and N moments of the cross-sectional distribution of consumption growth is an equilibrium outcome for some incomplete-markets economy (some pure discount factor and process of individual income). The proof is based on the construction of a personal-disaster process (process of extreme idiosyncratic events) which allows for arbitrary variations in idiosyncratic risk without affecting the first N moments of the cross-sectional distribution of consumption growth.

Generalized spectral estimation of the consumption-based asset pricing model

This paper provides a framework for estimating parameters of a wide class of dynamic rational expectations models in the frequency domain. The approach is particularly useful for models that are meant to match the data only in limited ways. Specifically, this holds when interest is focused on a subset of frequencies. The estimation strategy generalizes band spectrum regression to more general settings and allows for more general loss functions. A noteworthy special case involves whitening estimators which force estimated innovations to be close to white noise. These estimators can be understood as minimizing a set of moment conditions which grows with sample size and which are typically implied by RE models.

Expected Returns and Habit Persistence

Using a consumption-based asset pricing model with infinite-horizon nonlinear habit formation, Campbell and Cochrane (1999) show that low consumption in surplus of habit should forecast high expected returns. This article argues that the finite-horizon linear habit model also implies an inverse relation between expected returns and surplus consumption. This article also presents empirical evidence, which indicates that expected returns on stocks and bonds vary with surplus consumption implied by the habit models. The volatility of returns and the reward to volatility are also related to surplus consumption. However, less than 30% of the predictable variation of expected returns, using standard lagged information variables, is attributed to surplus consumption.

Expected Returns and Habit Persistence

Using a consumption-based asset pricing model with infinite-horizon nonlinear habit formation, Campbell and Cochrane (1999) show that low consumption in surplus of habit should forecast high expected returns. This article argues that the finite-horizon linear habit model also implies an inverse relation between expected returns and surplus consumption. This article also presents empirical evidence, which indicates that expected returns on stocks and bonds vary with surplus consumption implied by the habit models. The volatility of returns and the reward to volatility are also related to surplus consumption. However, less than 30 percent of the predictable variation of expected returns, using standard lagged information variables, is attributed to surplus consumption.

Conditioning Information and Variance Bounds on Pricing Kernels

We show how to use conditioning information optimally to construct a sharper unconditional Hansen-Jagannathan (1991) bound. The approach in this paper is different from that of Gallant, Hansen and Tauchen (1990), but both approaches yield the same bound when the conditional moments are known. Unlike Gallant, Hansen and Tauchen, our approach is robust to misspecification of the first and second conditional moments. Potential applications include testing dynamic asset pricing models, studying the predictability of asset returns, diagnosing the accuracy of competing models for the first and second conditional moments of asset returns, dynamic asset allocation and mutual fund performance measurement. The illustration in this article starts with the familiar Hansen-Singleton (1983) setup of an autoregressive model for consumption growth and bond and stock returns. Our innovation is to add time-varying volatility to the model. Both an unconstrained version and a version with the restrictions of the standard consumption-based asset pricing model imposed serve as the data-generating processes to illustrate the behavior of the bounds. In the process, we discover and explore an interesting empirical phenomenon: asymmetric volatility in consumption growth.

The Consumption Risk of the Stock Market

OVER THE PAST century in the United States, the average annual return on the stock market has exceeded that on short-term government bonds by 6 percentage points. The natural economic explanation for the premium on equity is the greater risks associated with investing in the stock market. However, the large premium that we observe cannot be explained by the canonical, consumption-based asset pricing model. Risk is best measured as the extent to which a return alters marginal utility. Since marginal utility is closely related to consumption, and consumption moves little with returns, the measured risk of the stock market is small. (1) One common informal interpretation of this equity premium puzzle is that stocks are a good deal. In this view, the model is taken as a reasonably accurate description of optimal behavior and a poor description of actual behavior. This normative view of the model and the data implies that households should increase their holdings of equity and even borrow to invest in the stock market. (2) Such thinking has also entered important areas of public policy, most notably in proposals to allow funds from the Social Security system--whether the current $1 trillion surplus in the trust fund or the entire $10 trillion in implicit liabilities--to be invested in the stock market rather than entirely in government bonds as is currently done. The positive view of the equity premium puzzle is that we simply do not understand asset prices. Since the puzzle was discovered, economists' efforts to find a model that rationalizes the premium have yielded little success. That is, there is as yet no model of a household investment problem with reasonable levels of risk aversion that explains the variation in returns over time, and the difference in returns between stocks and bonds in particular. This leaves economists largely unable to model investment behavior and largely unable to provide policymakers with guidance for the diversification of the Social Security system. This paper proposes an understanding of the risk-return trade-off between stocks and bonds that departs from the canonical model in two ways. First, I ignore many issues in asset pricing and focus solely on the ultimate risk to consumption of a given portfolio choice. That is, rather than measure the risk to consumption as the contemporaneous response of consumption to returns on the stock market, this paper measures the risk as the medium-term impact of stock market returns on consumption. (3) Second, in addition to studying the medium-term risk of equity as measured by aggregate consumption data, I follow Gregory Mankiw and Stephen Zeldes and ask whether the risk of equity justifies its return for the subset of households that hold equity. (4) The main finding of the paper is that the medium-term risk of equity is much greater than the contemporaneous risk, both for the representative household and for the representative stock. holder. For households that hold equity, the medium-term risk is largely sufficient to justify the high relative return of equity. Measuring the risk of equity as the medium-term impact of a return on consumption has several appealing features. First, this approach maintains the assumption that the primary determinant of utility is the level of consumption. This assumption is intuitive and has proved useful and successful in many other branches of economics. Second, this approach is consistent with the theory of portfolio choice in that the medium-term risk and the contemporaneous risk should be approximately the same according to the canonical model. Most important, the medium-term risk is a better measure of the true risk of the stock market under a wide class of extant models used in the study of household consumption and saving. If consumption responds with a lag to changes in wealth, then the contemporaneous covariance of consumption and wealth understates the risk of equity, and the medium-term risk provides the correct measure. …

Consumption Asset Pricing with Stable Shocks - Exploring a Solution and Its Implications for the Equity Premium Puzzle

We study the consumption based asset pricing model due to Lucas (1978). The exogenous endowment sequence is modeled as a linear stochastic process driven by stable shocks in an otherwise standard framework. The Gaussian process emerges as a special case. We derive exact analytical solutions for asset prices and returns, and provide conditions under which these exist. We also study the implications of the model for the equity premium puzzle.

Approximate p-values of predictive tests for structural stability

We approximate the p-values for the non-standard asymptotic null distribution of predictive tests proposed by Ghysels et al. (Journal of Econometrics,1997;82:209–233). The p-value response surfaces are approximated by a parametric function using the methodology proposed by Hansen (Journal of Business and Economic Statistics, 1997;15:60–67). We illustrate the use of the approximate p-values through an application to consumption based asset pricing models.

Crash states and the equity premium: Solving one puzzle raises another

Abstract This paper examines the behavior of asset returns as predicted by the consumption-based capital asset pricing model within an artificial economy that includes a low probability, crash state in consumption and dividends. It is demonstrated that the behavior of agents' intertemporal marginal rate of substitution in such an economy is consistent with the Hansen and Jagannathan (1991) frontier even though the consumption process in the model is calibrated to actual data, preferences are time separable, and agents' relative risk aversion is restricted to moderate levels. Moreover, as demonstrated by Rietz (1988), the crash-state economy can replicate the mean of excess returns on equity, i.e. the equity premium. However, the model severely underpredicts the volatility of excess returns.

The empirical relationship between aggregate consumption and security prices in Australia

This paper provides an empirical examination of the consumption-based capital asset pricing model (CCAPM) using Australian data. Multivariate tests of the CCAPM using actual quarterly consumption data indicate good support for the CCAPM. In a second phase of tests, the maximum correlation portfolio (MCP) is used to proxy the consumption variable using monthly data. Generally, the results of these tests are very mixed. Finally, for non-nested tests of the CCAPM versus the CAPM the evidence favours the traditional CAPM using quarterly data, but is inconclusive using monthly data.

The Cyclical Behavior of Interest Rates

This paper investigates the behavior of the term structure of interest rates over the business cycle. In contrast to prior studies that measure the business cycle by the simple growth in aggregate economic activity, we consider an alternative measure: the deviation of aggregate economic activity from its potentially stochastic trend. We show that incorporating both an independent trend and cyclical component in consumption improves the efficiency in estimating consumption-based asset pricing models. We also find that the term spread is more informative about future changes in stochastically detrended real gross domestic product (GDP) than future growth rates in real GDP.

Approximating the Asset Pricing Kernel

This paper tests a simple consumption-based asset pricing model by approximating the true asset pricing kernel using low-order orthonormal polynomials based on the model's state variables. Approximated kernels based solely on next period's consumption growth are not rejected by overall measures of model fit, but they produce statistically and economically large pricing errors. Approximated kernels that are based on two quarters of future consumption growth and technology shocks have substantially improved overall fit. In particular, the best of these kernels are capable of eliminating the small firm effect.

Risk and International Parity Conditions: A Synthesis from Consumption Based Models

Built on a consumption-based capital asset pricing model, this paper presents a coherent theoretical framework from which the main international parity conditions are derived. These conditions represent market equilibria characterized by the equality of gross returns after adjustment for risk premia. The spectrum of assets treated is broadened to include equity markets. The parity conditions obtained from the model are then used to characterize the relationships for the pricing of risks encountered in international finance. Only two fundamental types of aggregate risk matter when pricing any asset: equity risk and foreign exchange rate risk. The relative riskiness of an asset can then be approximately measured by a linear combination of equity and foreign exchange risk premia. [F30, G12]

EQUITY-PREMIUM AND RISK-FREE-RATE PUZZLES AT LONG HORIZONS

The failure of consumption-based asset pricing models to match the stochastic properties of the equity premium and the risk-free rate has been attributed by some authors to frictions, transaction costs, or durability. However, such frictions primarily would affect the higher-frequency data components: Consumption-based pricing models that concentrate on long-horizon returns should be more successful. We consider two consumption-based models: time-separable utility, and the habit model of Constantinides. We estimate a vector ARCH model that includes the pricing kernel and the equity return, and use the fitted model to assess the model's implications for the equity premium and for the risk-free rate. Neither model performs well at a quarterly horizon, but at longer horizons the Constantinides model can match the mean and the variance of the observed equity premium, captures time variation of the equity premium, and can better match the observed risk-free rate. We conclude that the equity-premium and risk-free-rate puzzles are primarily problems for shorter-horizon returns.

Is the real interest rate unstable? Some new evidence

Prior studies typically report that real Treasury bill returns have a unit root. The unit-root findings are not consistent with the long-run Fisher effect and consumptionbased asset pricing models. This study examines a data set of ex ante real returns on US Treasury bills and commercial papers. The statistical analysis employs a new modified Dickey-Fuller test, whc has better power than standard unit-root tests. In contrast to previous findings, strong evidence of stationarity is found for all the real return series under examination. Implications of the results are discussed.