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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 proprietary paring heuristics employed by the Bara Optimizer that deal with cardinality and threshold constraints, explaining how these heuristics have consistently outperformed alternative portfolio construction techniques in both passive and active portfolio management cases. We also use real-world examples to provide details on two component heuristics—one is the "build-up" heuristic, which emphasizes feasibility; the other is the "pare-down" heuristic, which stresses optimality.
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