Decreasing the Computational Workload in Portfolio Optimization

Abstract

This chapter illustrates the usage of the market indices for the estimation of parameters of the portfolio problem. It is derived an evaluation algorithm for decreasing the computational workload in definition and solution of portfolio optimization problem. The algorithm applies numerical relations, which lead to transformation of the classical portfolio problem to optimization one, which contains parameters from Capital Market Theory. The decreasing of the computational workload results from the inclusion of beta coefficient. Thus, the estimation of the asset characteristics is not performed by individual assessment of each asset return. The characteristics are found only by estimation of the market index and next evaluations according to relations of the asset risks and returns. This considerably decreases the amount of evaluations for the covariance matrix of the portfolio problem. The algorithm is illustrated by solution of portfolio problem with indices and mutual funds from the Bulgarian Stock Exchange. The obtained results support the decision making for investments on stock exchanges.