RT Journal Article
SR Electronic
T1 Using Lagrangian Relaxation to Obtain Small Portfolios
JF The Journal of Portfolio Management
FD Institutional Investor Journals
SP 75
OP 79
DO 10.3905/JPM.2009.35.2.075
VO 35
IS 2
A1 Leonid Kopman
A1 Shucheng Scott Liu
A1 Dong Shaw
YR 2009
UL https://pm-research.com/content/35/2/75.abstract
AB Investors with small portfolios, or a limited number of securities in their portfolios, may benefit from a new portfolio optimization method. Placing a limit on the number of assets in a portfolio turns the ordinary mean variance portfolio optimization problem into a challenging puzzle, especially for larger investment universes. In response, practitioners typically employ either enumerative methods, such as branch-and-bound based on quadratic programming relaxation, or heuristic methods. Both approaches have their respective disadvantages in that quadratic programming–based branch-and-bound may fail to solve large problems in reasonable time and heuristics may produce solutions of unknown quality. The new method presented by the authors can be used to solve smaller problems to optimality. For larger problems, the method produces good heuristic solutions along with a useful estimate of their quality; that is, the distance from the optimum. The computational results are promising.TOPICS: Portfolio construction, accounting and ratio analysis, statistical methods