Extended Viewer

Leonid Kopman

Research and Insights

Articles by Leonid Kopman

    Treatment of Fixed Transaction Costs in Barra Optimizer

    Research Report | Apr 13, 2011 | Leonid Kopman, Scott Liu

    This paper deals with fixed transaction costs in the context of portfolio optimization. These are transaction costs that do not depend on the traded amount. We show how such costs need to be taken into account during the portfolio optimization process, and describe the algorithm Barra Optimizer uses to address the costs. Computational results demonstrate the performance of the algorithm.

    Lagrangian Relaxation Procedure for Cardinality - Constrained Portfolio Optimization

    Research Report | Nov 30, 2010 | Leonid Kopman, Scott Liu, Dong Shaw

    This paper studies a portfolio-selection problem subject to a cardinality constraint, that is, the number of securities in a portfolio is restricted to a certain limit. The problem is formulated as a cardinality-constrained quadratic programming problem, and a dedicated Lagrangian relaxation method is developed. In contrast to many existing Lagrangian relaxation methods, the approach presented in the paper is able to take advantage of the special structure of the objective function rather...

    Risk Target Optimization

    Research Report | Dec 8, 2009 | Leonid Kopman, Scott Liu

    As an alternative to mean-variance portfolio optimization, Barra Optimizer offers users an option to run risk target optimization. Instead of risk being controlled implicitly with the risk aversion parameters, the risk target is explicitly specified by the user. When the risk target is achievable and efficient, the optimized portfolio will have risk (or tracking error) equal to the specified target. The risk target may be too low due to the problem constraints; it may also be too high, that...

    Maximizing the Sharpe Ratio and Information Ratio in Barra Optimizer

    Research Report | Jun 1, 2009 | Leonid Kopman, Scott Liu

    In this paper we introduce a new feature of the Barra Optimizer -- the ability to maximize the Sharpe Ratio (SR) and the Information Ratio (IR).  We discuss the portfolio optimization problems that focus on SR and IR, their properties and relationship to the standard mean-variance portfolio optimization problem, and the methods the Barra Optimizer utilizes to solve them.

    Using Lagrangian Relaxation to Obtain Small Portfolios

    Research Report | Jun 1, 2008 | Leonid Kopman, Shucheng Liu, Dong Shaw

    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....

    Portfolio Construction in Europe: Screening Versus Optimization

    Research Report | Jun 1, 2005 | Leonid Kopman, Elizabeth Penades

    We compared Screening and Optimization approaches to portfolio construction for the European market using the methodology found in Grinold and Kahn [1999] and Muller [1993]. We obtained similar results to those we previously saw in the US market. Optimization clearly outperformed the screening methods, producing the best IRs in 10 out of 12 cases. The worst-performing method was Cap-Weighted Screening. This is because the wide variation in market capitalization within the constructed...