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INTRODUCTION
A frequent question that arises in portfolio management is how to construct a portfolio of securities that will best mimic the performance of a benchmark index. A passive investment strategy may indicate that the objective of the portfolio is to track the benchmark as closely as possible, while an active investment strategy will mandate that the portfolio outperform the benchmark. The practitioner literature abounds with many approaches to this problem ranging from the standard step-wise regression through neural networks to genetic algorithms. Unfortunately, most of these applications are numerical in nature and do not yield much intuition into how to build a replicating portfolio that is compact and correlates highly with its benchmark.
Roll (1992) is an example of an early paper targeted at practitioners arguing against some common practices of fixing a target portfolio volatility while tracking a benchmark. He shows that unless the portfolio manager gets the volatility right ex ante , the replicating portfolio will do a poor job of tracking the index. Ammann and Zimmermann (2001) illustrate the use of position limits on the underlying basis assets and report that this constraint produces very small tracking errors in practice. In the same spirit, Jorion (2003) demonstrates how additional constraints such as limits on the value-at-risk may be necessary to align the incentives of portfolio managers and investors. Bertrand (2010) modifies the Jorion (2003) result by holding the investor's risk aversion parameter fixed and allowing the tracking error to vary. Stutzer (2003) finds that in equilibrium the benchmarks may become priced risk factors when fund managers try to replicate or outperform the benchmarks. Furthermore, Baker et al (2011) demonstrate how delegated portfolio management can flatten the capital market line.
Another stream of research has targeted the problem based on various econometrics techniques and by trying out different objective functions. Rudolf et al (1999) argue against using a mean squared error loss function and in favor of mean absolute deviations between the benchmark and the replicating portfolio returns. They show convincing evidence that this loss function results in more stable portfolio weights that are less sensitive to outliers. Various statistical techniques have been applied toward the objective of benchmark index replication ranging from time series clustering (Focardi and Fabozzi, 2004) to...