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

: In a model of a nancial market with an atomless continuum of assets, we give a precise and rigorous meaning to the intuitive idea of a \well-diversi ed" portfolio and to a notion of \exact arbitrage". We show this notion to be necessary and su cient for an APT pricing formula to hold, to be strictly weaker than the more conventional notion of \asymptotic arbitrage", and to have novel implications for the continuity of the cost functional as well as for various versions of APT asset pricing. We further justify the idealized measure-theoretic setting in terms of a pricing formula based on \essential" risk, one of the three components of a tri-variate decomposition of an asset's rate of return, and based on a speci c index portfolio constructed from endogenously extracted factors and factor loadings. Our choice of factors is also shown to satisfy an optimality property that the rst m factors always provide the best approximation. We illustrate how the concepts and results translate to markets with a large but nite number of assets, and relate to previous work.

On the welfare costs of business-cycle fluctuations and economic-growth variation in the 20th century and beyond

The main objective of this paper is to propose a novel setup that allows estimating separately the welfare costs of the uncertainty stemming from business-cycle uctuations and from economic-growth variation, when the two types of shocks associated with them (respectively,transitory and permanent shocks) hit consumption simultaneously. Separating these welfare costs requires dealing with degenerate bivariate distributions. Levis Continuity Theorem and the Disintegration Theorem allow us to adequately de ne the one-dimensional limiting marginal distributions. Under Normality, we show that the parameters of the original marginal distributions are not afected, providing the means for calculating separately the welfare costs of business-cycle uctuations and of economic-growth variation. Our empirical results show that, if we consider only transitory shocks, the welfare cost of business cycles is much smaller than previously thought. Indeed, we found it to be negative - -0:03% of per-capita consumption! On the other hand, we found that the welfare cost of economic-growth variation is relatively large. Our estimate for reasonable preference-parameter values shows that it is 0:71% of consumption US$ 208:98 per person, per year.