Knowledge that Transforms

This paper relates the value of additional information to asset prices in a pure exchange setting. The price structure of interest revolves around a “pricing‐hypothesis”: the prices in an economy with less information are unbiased estimators of the prices that would obtain in a more informative economy. Two basic results are developed. First, if the incremental information is useless then the pricing‐hypothesis applies. Second, if the pricing hypothesis is assumed valid, then the information is valuable in a weak sense. The results are also considered in the context of empirical research. The case is made for viewing statistical tests of association between prices and signals as tests of the social value of information.

This paper presents a method for solving the mean‐variance portfolio selection problem that is applicable to the case where the number of securities is nondenumerably infinite. Necessary conditions for the existence of an optimal portfolio density are obtained and an expression for the efficient frontier is derived. The conditions for the existence of an optimal portfolio of continuously maturing bonds when their covariance matrix is singular are used to derive an arbitrage‐free bond pricing equation. A method for estimating the covariance matrix and the associated efficient frontier is presented.

Through the use of laboratory market methodology, the effect of a futures market on the time path of asset prices is studied and competing models of asset pricing are analyzed. With replication of market conditions, the predictions of rational expectations equilibrium model are relatively accurate whether or not futures markets are present. However, the presence of futures markets increases the speed with which an efficient equilibrium is achieved. While this more rapid adjustment can increase the variance of spot market prices as they move to equilibrium, this increased variance reflects efficiency gains due to better information.

This paper values options on assets whose returns, over a finite interval of time, are generated by a binomial process. It shows that a simple valuation relationship, between the option and the underlying stock, obtains if investors have preference functions that belong to a particular class, even if opportunities to hedge do not exist. One particular application of the theory is in the case where the stock price over a finite interval could increase by an amount, fall by the same amount, or stay at the same level. The results in this paper may be viewed as the foundation of the preference-based approaches to obtaining a risk neutral valuation relationship.