Fast Algorithm For the Markowitz Critical Line Method

摘要

The critical line method developed by the Nobel Prize winner H. Markowitz is a classical technique for the construction of a minimum-variance frontier within the paradigm of “the expected return–risk” (mean–variance) and finding minimum portfolios. Considerable interest has recently been attracted to the development of a fast algorithm for the construction of the minimum-variance frontier. In some works, such algorithms have been used to find statistically stable optimal portfolios. An algorithm based on the critical line method has recently been proposed by Andras Niedermayer and Daniel Niedermayer. Its testing showed that it is faster than all similar algorithms known before by several orders of magnitude. In this paper, we present an algorithm for constructing the minimum- variance frontier for the Markowitz problem with the condition of nonnegativity of the optimal port- folio, which requires about half as many operations as the Niedermayers’ algorithm. To this end, we had to perform a more thorough analytical and geometric study of the Markowitz problem.