Asset Pricing in Heterogeneous Economies

ETH Zurich Department of Mathematics Working Paper

149 Pages Posted: 14 Jul 2005

See all articles by Yvan Lengwiler

Yvan Lengwiler

University of Basel - Faculty of Business and Economics (WWZ)

Semyon Malamud

Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute

Eugene Trubowitz

Swiss Federal Institute of Technology Zurich

Date Written: July 1, 2005

Abstract

We extend the Lucas asset pricing tree economy to a heterogeneous population. Perturbative methods are applied to explicitly calculate the second order response of returns to heterogeneity. We determine the status of various stylized facts. For example, we find that the equity premium always varies counter cyclically and that a sufficiently positive correlation between risk aversion and patience increases the risk premium and decreases the interest rate, thus giving another perspective on the equity premium and the risk-free rate puzzles. This motivates us to make a concrete social prediction. We also give a complete description of the infinite horizon behavior. First, there exists a (generically) unique agent who eventually consumes everything at infinite horizon. Second, there is another agent whose preferences determine the expected return rate of holding equity forever. There is a third agent whose preferences determine the very long end of the interest rate term structure. Finally, there is a fourth agent who determines the price of long maturity call options. It is shown that a large equity premium will result if the preferences of these dominant agents are sufficiently different. Moreover, arbitrarily small changes in the composition of the population can lead to large (discontinuous) changes of long (infinite) horizon expected returns. It is also shown that the conventional representative agent picture leads to incorrect predictions about the infinite horizon limit.

Keywords: Heterogeneity, equity premium puzzle, stylized facts, infinite horizon

JEL Classification: E0, E1, E2, G0, G1

Suggested Citation

Lengwiler, Yvan and Malamud, Semyon and Trubowitz, Eugene, Asset Pricing in Heterogeneous Economies (July 1, 2005). ETH Zurich Department of Mathematics Working Paper. Available at SSRN: https://ssrn.com/abstract=755984 or http://dx.doi.org/10.2139/ssrn.755984

Yvan Lengwiler (Contact Author)

University of Basel - Faculty of Business and Economics (WWZ) ( email )

Peter Merian-Weg 6
PO Box
Basel, CH-4002
Switzerland
+41 61 267 3369 (Phone)

HOME PAGE: http://wwz.unibas.ch/lengwiler

Semyon Malamud

Ecole Polytechnique Federale de Lausanne ( email )

Lausanne, 1015
Switzerland

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

Swiss Finance Institute

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

Eugene Trubowitz

Swiss Federal Institute of Technology Zurich ( email )

Lausanne CH-1001
Switzerland

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