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...

Portfolio managers have long suspected that the risk forecast of an optimized portfolio tends to be optimistic. Many have identified the culprit as estimation error in the covariance matrix. Forecasts based on historical asset covariance matrices are particularly sensitive to this error. The bias is reduced dramatically by using a factor model. Even so, factor models still tend to under-forecast the risk of optimized portfolios, especially the risk coming from factors. In this paper, we show...

Portfolio managers have long suspected that the risk forecast of an optimized portfolio tends to be optimistic. Many have identified the culprit as estimation error in the covariance matrix. Forecasts based on historical asset covariance matrices are particularly sensitive to this error. The bias is reduced dramatically by using a factor model. Even so, factor models still tend to under-forecast the risk of optimized portfolios, especially the risk coming from factors. In this paper, we show...

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...

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.