This article presents a mean-variance framework for likelihood-ratio tests of asset pricing models. A pricing model is tested by examining the position of one or more reference portfolios in sample mean-standard-deviation space. Included are tests of both single-beta and multiple-beta relations, with or without a riskless asset, using either a general or a specific alternative hypothesis. Tests with a factor that is not a portfolio return are also included. The mean-variance framework is illustrated by testing the zero-beta CAPM, a two-beta pricing model, and the consumption-beta model.

We analyze a unique dataset that includes the full demand schedules of 27 Israeli IPOs that were conducted as nondiscriminatory (uniform price) auctions. To the best of our knowledge, this is the first time the whole demand schedule for any asset is described. The demand schedules are relatively flat around the auction clearing price: The average elasticity is 27. The elasticity is low when the return distribution contains a large unique component. We also find a significant average abnormal return of 4.5% on the first trading day and a positive correlation between the abnormal return and the elasticity of demand.

The incorporation of diverse information into asset prices is empirically examined in an actual securities market with multiple rounds of trade. Using prices of Israeli index and nominal bonds of equal maturity, we calculate implied expectations of inflation that has already occurred but for which the official statistic has not yet been announced. Learning is defined as the convergence of these expectations to the actual level of inflation in the period after the end of the month but before the announcement of the official statistic. We find that the variance of the inflation expectation errors decreases with trading days in this period. The decline in the variance suggests that investors learn, by repeatedly observing prices, about the distribution of other investors' information. We also find a positive relation between the dispersion of relative price changes and the size of the inflation‐expectation errors on the first round of trade. The correlation diminishes as investors learn about the distribution of inflation information in the economy.

A Bayesian approach is used to investigate a sample’s information about a portfolio’s degree of inefficiency. With standard diffuse priors, posterior distributions for measures of portfolio inefficiency can concentrate well away from values consistent with efficiency, even when the portfolio is exactly efficient in the sample. The data indicate that the NYSE–AMEX market portfolio is rather inefficient in the presence of a riskless asset, although this conclusion is justified only after an analysis using informative priors. Including a riskless asset significantly reduces any sample’s ability to produce posterior distributions supporting small degrees of inefficiency.