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Estimating a Continuous-Time Asset Pricing Model with State-Dependent Risk Aversion

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  • Gordon, Stephen

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  • St-Amour, Pascal

Abstract

We propose a consumption-based capital asset pricing model in which the representative agent's preferences display state-dependent risk aversion. Since a common factor - the state of the world - influences both stock prices and preferences, we obtain a valuation equation in which the vector of excess returns on equity includes both consumption risk as well as the risk associated with variations in preferences. We develop a simple model that can be estimated without specifying the functional form linking risk aversion with state variables. Our estimates are based on Markov chain Monte Carlo estimation of exact discrete-time parametrizations for linear diffusion processes. Since consumption risk is not forced to account for the entire risk premium, our results contrast sharply with estimates from models in which risk aversion is state-independent. We find that relaxing fixed risk preferences yields estimates for relative risk aversion that are (i) reasonable by usual standards, (ii) correlated with both consumption and returns and (iii) indicative of an additional preference risk of holding the assets. Nous proposons un modèle d'agent représentatif de valorisation d'actifs dans lequel les préférences de l'agent sont caractérisées par une aversion contingente au risque. Dans la mesure où un facteur commun - l'état du monde - influence à la fois les prix des actifs et les préférences, nous retrouvons une équation d'Euler où les rendements excédentaires incorporent le risque de consommation et le risque de variations des préférences. Nous développons un modèle simple pouvant être estimé sans avoir à spécifier la forme fonctionnelle reliant l'aversion au risque aux variables d'état. Nos estimations sont basées sur des chaînes markoviennes de Monte-Carlo utilisant des vraisemblances exactes pour des processus de diffusion. Puisque les risques de consommation seuls ne suffisent plus à expliquer les primes de risques, nos estimations diffèrent sensiblement des résultats obtenus avec des préférences non-contingentes. En particulier, les coefficients d'aversion au risque sont (i) raisonnables par rapport aux valeurs acceptées, (ii) corrélés avec la consommation et les rendements et (iii) cohérents avec l'hypothèse de risque additionnel.

Suggested Citation

  • Gordon, Stephen & St-Amour, Pascal, 1997. "Estimating a Continuous-Time Asset Pricing Model with State-Dependent Risk Aversion," Cahiers de recherche 9711, Université Laval - Département d'économique, revised 08 Jun 1998.
  • Handle: RePEc:lvl:laeccr:9711
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    File URL: http://www.ecn.ulaval.ca/w3/recherche/cahiers/1997/9711.pdf
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    Cited by:

    1. Pascal St-Amour & Stephen Gordon, 2000. "A Preference Regime Model of Bull and Bear Markets," American Economic Review, American Economic Association, vol. 90(4), pages 1019-1033, September.

    More about this item

    Keywords

    Asset pricing models; Bayesian analysis; continuous-time econometric models; data augmentation; equity premium puzzle; Markov-Chain Monte-Carlo; risk aversion; state-dependent preferences;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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