Universal Bounds for Asset Prices in Heterogeneous Economies

Abstract

We establish universal bounds for asset prices in heterogeneous complete market economies with scale invariant preferences. Namely, for each agent in the economy we consider an artificial homogeneous economy, populated solely by this agent and calculate the homogeneous price of an asset in each of this economies. Dumas (1989) conjectured that the risk free rate in the heterogeneous economy must lie in the interval determined by the minimal and maximal of the homogeneous prices. We show that the answer depends on the risk aversions of the agents in the economy: the upper bound holds when all risk aversions are smaller than one and the lower bound holds when all risk aversions are larger than one. The bounds almost never hold simultaneously. Furthermore, we prove these bounds for arbitrary assets.

Keywords: heterogeneity, asset prices, yield curve, bounds

JEL Classification: D91, E43, G12