We propose a new modeling framework to study the asset pricing implications of learning under ambiguity aversion. In a continuous time partial information Lucas economy, we characterize analytically equilibrium equity returns and make the following observations. First, learning under ambiguity aversion implies an equilibrium discount for ambiguity, if and only if relative risk aversion is below one or, equivalently, the elasticity of intertemporal substitution (EIS) is above one. In this case, ambiguity aversion increases conditional equity premia and volatilities. Second, equilibrium interest rates are lower, irrespective of risk aversion. Third, no time-invariant relation between excess returns and conditional variances exists. Therefore, estimated relations between excess returns and equity conditional variances are highly time varying and have an indeterminate sign. Fourth, estimates of the EIS based on standard Euler equations for equity returns are strongly downward biased in a setting of learning and ambiguity aversion. Therefore, an EIS well above one can be consistent with estimates of EIS well below one. Fifth, ambiguity does not resolve asymptotically. Finally, using realistic model parameters, we show that a low risk aversion and a moderate amount of ambiguity are consistent with the equity premium, the low interest rate, and the excess volatility puzzles.

Leippold, Markus; Vanini, Paolo; Trojani, Fabio (2008). *Learning and Asset Pricing under Uncertainty.* Review of Financial Studies, 21(6):2565-2597.

## Abstract

We propose a new modeling framework to study the asset pricing implications of learning under ambiguity aversion. In a continuous time partial information Lucas economy, we characterize analytically equilibrium equity returns and make the following observations. First, learning under ambiguity aversion implies an equilibrium discount for ambiguity, if and only if relative risk aversion is below one or, equivalently, the elasticity of intertemporal substitution (EIS) is above one. In this case, ambiguity aversion increases conditional equity premia and volatilities. Second, equilibrium interest rates are lower, irrespective of risk aversion. Third, no time-invariant relation between excess returns and conditional variances exists. Therefore, estimated relations between excess returns and equity conditional variances are highly time varying and have an indeterminate sign. Fourth, estimates of the EIS based on standard Euler equations for equity returns are strongly downward biased in a setting of learning and ambiguity aversion. Therefore, an EIS well above one can be consistent with estimates of EIS well below one. Fifth, ambiguity does not resolve asymptotically. Finally, using realistic model parameters, we show that a low risk aversion and a moderate amount of ambiguity are consistent with the equity premium, the low interest rate, and the excess volatility puzzles.

## Citations

## Additional indexing

Item Type: | Journal Article, refereed, original work |
---|---|

Communities & Collections: | 03 Faculty of Economics > Department of Banking and Finance |

Dewey Decimal Classification: | 330 Economics |

Language: | English |

Date: | 2008 |

Deposited On: | 11 Apr 2013 08:54 |

Last Modified: | 05 Apr 2016 16:28 |

Publisher: | Oxford University Press |

ISSN: | 0893-9454 |

Official URL: | http://rfs.oxfordjournals.org/content/21/6/2565.short |

Other Identification Number: | merlin-id:4473 |

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