Learning and Asset Prices Under Ambiguous Information

University of St.Gallen Economics Discussion Paper No. 2005-03

66 Pages Posted: 23 Sep 2004

See all articles by Paolo Vanini

Paolo Vanini

University of Basel

Markus Leippold

University of Zurich; Swiss Finance Institute

Fabio Trojani

University of Geneva; University of Turin - Department of Statistics and Applied Mathematics; Swiss Finance Institute

Multiple version iconThere are 2 versions of this paper

Date Written: September 2004

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.

Keywords: Financial equilibria, knightian uncertainty, model misspecification, robust decision making

JEL Classification: C60, C61, G11

Suggested Citation

Vanini, Paolo and Leippold, Markus and Trojani, Fabio, Learning and Asset Prices Under Ambiguous Information (September 2004). University of St.Gallen Economics Discussion Paper No. 2005-03, Available at SSRN: https://ssrn.com/abstract=594401 or http://dx.doi.org/10.2139/ssrn.594401

Paolo Vanini

University of Basel ( email )

Petersplatz 1
Basel, CH-4003
Switzerland

Markus Leippold

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Fabio Trojani (Contact Author)

University of Geneva ( email )

Geneva, Geneva
Switzerland

University of Turin - Department of Statistics and Applied Mathematics ( email )

Piazza Arbarello, 8
Turin, I-10122
Italy

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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