Large-scale MV efficient frontier computation via a procedure of parametric quadratic programming

Despite the volume of research conducted on efficient frontiers, in many cases it is still not the easiest thing to compute a mean–variance (MV) efficient frontier even when all constraints are linear. This is particularly true of large-scale problems having dense covariance matrices and hence they are the focus in this paper. Because standard approaches for constructing an efficient frontier one point at a time tend to bog down on dense covariance matrix problems with many more than about 500 securities, we propose as an alternative a procedure of parametric quadratic programming for more effective usage on large-scale applications. With the proposed procedure we demonstrate through computational results on problems in the 1000–3000 security range that the efficient frontiers of dense covariance matrix problems in this range are now not only solvable, but can actually be computed in quite reasonable time.