Comparative issues in large-scale mean–variance efficient frontier computation

One of the functions of a portfolio management system is to return quickly an efficient frontier. However, in the large-scale problems (1000 to 3000 securities) that are beginning to appear with greater frequency, the task of computing the mean–variance efficient frontier, even when all constraints are linear, can range from the significant to the prohibitive. For ease of reference, we call mean–variance problems with all linear constraints Markowitz problems. With little on the time to compute a Markowitz-problem efficient frontier in the literature, we conduct experiments that involve varying problem sizes, methods employed, and optimizers used to present an overall picture of the situation and establish benchmarks in the large-scale arena. One of the conclusions of the experiments is the superiority of the class of techniques that would fall under the title of parametric quadratic programming.