Fast computation of efficient portfolios

Antonio Marcos Duarte, Jr.

Abstract

ABSTRACT

In this paper the author seeks to generate the set of efficient portfolios of securities. Efficient portfolios are those that maximize the expected return for a given level of expected risk, and minimize the expected risk for a given level of expected return. An approach that unifies six portfolio optimization methodologies is proposed. Choosing between these six portfolio optimization methodologies is as simple as giving values (0 or 1) to three parameters. Interior point algorithms are used to generate the set of efficient portfolios exploring computational aspects such as the sparsity of the large- scale linear systems that need to be solved. The resulting methodology is easy to implement, is sound from the theoretical point of view, and allows a very fast generation of the set of efficient portfolios. Randomly generated problems are used to illustrate the computational performance of the methodology when applied to problems with different numbers of securities and scenarios.