Ambiguity and the Historical Equity Premium

45 Pages Posted: 16 May 2011

See all articles by Fabrice Collard

Fabrice Collard

University of Berne - Department of Economics

Sujoy Mukerji

Queen Mary University of London; International Centre for Economic Research (ICER)

Kevin Sheppard

University of Oxford - Department of Economics; University of Oxford - Oxford-Man Institute of Quantitative Finance

Jean-Marc Tallon

Paris School of Economics

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Date Written: May 9, 2011

Abstract

This paper assesses the quantitative impact of ambiguity on the historically observed equity premium. We consider a Lucas-tree pure–exchange economy with a single agent where we introduce two key non- standard assumptions. First, the agent’s beliefs about the dividend/consumption process is ambiguous, i.e., she is uncertain about the exact probability distribution governing the realization of future dividends and consumption. Second, the agent’s preferences are sensitive to this ambiguity, a property formalized using the smooth ambiguity model. The consumption and dividend process is assumed to evolve according to a hidden state model, popularized by Bansal and Yaron (2004), where a persistent latent state variable describes temporary shocks to the mean of consumption growth prospects. We further extend the model to allow for uncertainty about the magnitude of the persistence of the latent state. The agent’s beliefs are am- biguous due to the uncertainty about the conditional mean of the probability distribution on consumption and dividends in the next period. We show that in this model ambiguity is endogenously dynamic, for example, increasing during recessions. This results in an endogenously volatile and (counter-)cyclical equity premium. We calibrate the level of ambiguity aversion to match only the first moment of the risk-free rate in data, and ambiguity to match the uncertainty conditional on the historical growth path, and evaluate the model using moderate levels of risk aversion. We find that this simple modification of a Lucas-tree model accounts for a large part of the historical equity premium, both in terms of its level and variation over time.

Keywords: Ambiguity Aversion, Asset pricing, Equity premium puzzle

JEL Classification: G12, E21, D81, C63

Suggested Citation

Collard, Fabrice and Mukerji, Sujoy and Sheppard, Kevin Keith and Tallon, Jean-Marc, Ambiguity and the Historical Equity Premium (May 9, 2011). Available at SSRN: https://ssrn.com/abstract=1836297 or http://dx.doi.org/10.2139/ssrn.1836297

Fabrice Collard

University of Berne - Department of Economics ( email )

Schanzeneckstrasse 1
Bern, CH-3001
Switzerland

HOME PAGE: http://fabcol.free.fr

Sujoy Mukerji (Contact Author)

Queen Mary University of London ( email )

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London, London E1 4NS
United Kingdom

International Centre for Economic Research (ICER)

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Viale Settimio Severo, 63
10133 Torino
Italy

Kevin Keith Sheppard

University of Oxford - Department of Economics ( email )

Manor Road Building
Manor Road
Oxford, OX1 3BJ
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

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Oxford, Oxfordshire OX2 6ED
United Kingdom
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HOME PAGE: http://www.oxford-man.ox.ac.uk

Jean-Marc Tallon

Paris School of Economics ( email )

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