Knowledge that Transforms

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.

Changes in six-month bill rates over semiannual periods in the 1960s and 1970s are successfully related to expected changes and to surprises. The latter include unanticipated changes in expected inflation, in the growth of industrial production and base money, and in inflation uncertainty. Estimation of the basic equation through the middle of 1983 does not suggest any change in structure. Moreover the equation "explains" 60 percent of the extraordinarily high level of real rates since late 1980, largely owing to an excess of unexpected net increases in anticipated inflation over actual increases.

Bradford Cornell, Purchasing Power Parity as a Trading Strategy: Discussion, The Journal of Finance, Vol. 39, No. 3, Papers and Proceedings, Forty-Second Annual Meeting, American Finance Association, San Francisco, CA, December 28-30, 1983 (Jul., 1984), pp. 724-725