In this paper, a general treatment of identifying the set of unbiased estimators of N-period mean returns is advanced and a new unbiased estimator, which promises near-minimum variance and minimal computation, is formulated. The new estimator is also equally applicable to other processes of compound growth.

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.

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.