Numerical Solution for the Minimum Semivariance Portfolio Optimization Problem in R: The Semicov Package

Abstract

Exact analytical solutions to the problem of computing a minimum semivariance portfolio cannot be obtained due to the endogeneity of the semicovariance matrix. However, when the number of assets is small, the weights for such a portfolio can be determined numerically. This paper presents the R package semicov, which provides a function that implements a numerical algorithm to minimize the semivariance of a portfolio with up to five assets. A function that estimates the approximation of the semicovariance matrix as in Estrada (2008) is also included in the package.

Keywords: semivariance, numerical solution, portfolio optimization

JEL Classification: C65, G11