Exact arbitrage, well-diversified portfolios and asset pricing in large markets

For a market with an atomless continuum of assets, we formulate the intuitive idea of a “well-diversified” portfolio, and present a notion of “exact arbitrage”, strictly weaker than the more conventional notion of “asymptotic arbitrage”, and necessary and sufficient for the validity of an APT pricing formula. Our formula involves “essential” risk, one based on a specific index portfolio constructed from factors and factor loadings that are endogenously extracted to satisfy an optimality property involving a finite number of factors. We illustrate how our results can be translated to markets with a large but finite number of assets.     

Generic inefficiency of equilibria in the general equilibrium model with incomplete asset markets and infinite time

Summary. We consider a Lucas asset-pricing model with heterogeneous agents, exogenous labor income, and a finite number of exogenous shocks. Although agents are infinitely lived, endowments and dividends are time-invariant functions of the exogenous shock alone and are thus restricted to lie in a finite-dimensional space; genericity analysis can be conducted on sets of zero Lebesgue measure. When financial markets are incomplete, that is, there are fewer financial securities than shocks, we show that generically in individual endowments all competitive equilibria are Pareto inefficient. Received: November 22, 1999; revised version: March 4, 2002 RID="*" ID="*" We are grateful to an anonymous referee for very insightful comments on earlier drafts.     

The evolution of debt and equity markets in economic development

Summary. As noted by Gurley and Shaw, there is a typical pattern of economic development in which the evolution of the financial system is an essential aspect of the growth process. We focus on one component of this evolution: the increasing importance of equity markets as an economy grows. We develop a growth model where capital accumulation is financed externally through a combination of debt and equity. We illustrate why equity market activity might grow – often very rapidly – as an economy develops. We also illustrate why access to equity markets may not be needed in the early stages of economic development. Received: December 30, 1997; revised version: May 26, 1998     

Moral hazard and general equilibrium in large economies

Summary. The paper analyzes a two period general equilibrium model with individual risk, aggregate uncertainty and moral hazard. There is a large number of households, each facing two individual states of nature in the second period. These states differ solely in the household's vector of initial endowments, which is strictly larger in the first state (good state) than in the second state (bad state). In the first period each household chooses a non-observable action. Higher levels of action give higher probability of the good state of nature to occur, but lower levels of utility. Households' utilities are assumed to be separable in action and the aggregate uncertainty is independent of the individual risk. Insurance is supplied by a collection of firms who behave strategically and maximize expected profits taking into account that each household's optimal choice of action is a function of the offered contract. The paper provides sufficient conditions for the existence of equilibrium and shows that the appropriate versions of both welfare theorems hold. Received: December 7, 1998; revised version: October 25, 1999     

Symmetry and order in the portfolio allocation problem

Summary. This research studies the role of multivariate distribution structures on random asset returns in determining the optimal allocation vector for an expected utility maximizer. All our conclusions pertain for the set of risk averters. By carefully disturbing symmetry in the distribution of the, possibly covarying, returns, we ascertain the ordinal structure of the optimized allocation vector. Rank order of allocations is also established when a permutation symmetric random vector is mapped into the returns vector through location and scale shifts. It is shown that increased dispersion in the vectors of location and scale parameters benefit, ex-ante, investors as does a decrease in the rank correlation coefficient between the location and scale parameter vectors. Revealed preference comparative static results are identified for the location and scale vectors of asset returns. For most issues addressed, we arrive at much stronger inferences when a safe asset is available. Received: August 8, 2000; revised version: January 8, 2001     

Competitive and core allocations in large economies with differential information

Summary. We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is “irreducible”, then a competitive equilibrium, in the sense of Radner (1968, 1982), exists. Moreover, the set of competitive equilibrium allocations coincides with the “private core” (Yannelis, 1991). We also show that the “weak fine core” of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy. Received March 22, 2000; revised version: May 1, 2000