In this paper, we introduce the Multiple-Period Optimization (MPO) - a new feature in the Barra Optimizer.

How would a quantitative portfolio manager replicate the performance of a stock index, knowing it would be impractical to hold every asset in the index, or to trade only a few shares of a stock?  One approach might be to apply cardinality and threshold constraints using the Barra Optimizer.  While these constraints are valuable tools, they are often difficult to manage, since they render portfolio optimization problems discrete and non-convex. In this paper, we present MSCI’s...

Jacobs and Levy recently published a series of papers on “leverage aversion” and the benefits of incorporating it in the traditional Markowitz Mean-Variance Optimization.  They emphasize the uniqueness of leverage risk, in contrast to volatility risk.  Their debate with Markowitz has sparked renewed interest in the theory and application of long-short optimization.  In this Research Insight, we point out that MSCI has been a pioneer in long-short portfolio...

In this Research Insight, we show how the Barra Optimizer uniquely handles round lot optimization. With our technique, a successfully returned “optimal” portfolio will be feasible under all the user-imposed constraints. By comparison, post-optimization roundlotting is simple and straightforward, yet the resulting portfolio may violate one or more constraints. This paper explains how the Barra Optimizer offers both optimal roundlotting and post-optimization roundlotting to help...

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.

Trade paring constraints enable portfolio managers to control the number of trades when constructing and rebalancing their portfolios. Allowing users to set trade paring constraints is a new feature in the Barra Optimizer (first available in Aegis 4.4 and also in Barra Open Optimizer 1.2). Portfolio optimization problems involving trade paring constraints are difficult to solve. In this paper, we show that the integrated trade paring approach in the Barra Optimizer, which consists of two...

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...

In this paper, we examine the influences of risk aversion on various aspects of portfolio optimization.  Our main message is that the risk aversion parameters in the Barra Optimizer provide users with the flexibility to control or adjust the risk levels of their optimal portfolios.  They are valuable tools for portfolio managers to explore and customize their portfolio optimization results and investment processes.

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...

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.