Asset Pricing in Heterogeneous Economies
ETH Zurich Department of Mathematics Working Paper
149 Pages Posted: 14 Jul 2005
Date Written: July 1, 2005
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
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