Studies on Design of Index Fund and its Properties

点击翻译按钮获取中文摘要

This study is concerned with a traditional asset allocation of the Markowitz type and develops an efficient algorithm to design an index fund with given number of securities that locally minimizes the tracking error between the benchmark portfolio and the index fund. When the benchmark portfolio is on the frontier, some interesting findings on the properties of the index fund with minimizing tracking error are derived. These findings are illustrated by simple numerical examples.Moreover, some cross-sectional relationships between the benchmark portfolio (for examples, market portfolio and Nikkei 225) and its index fund which play central roles in portfolio theory and asset allocation. Emphases are on some analytical properties of these efficient frontier portfolios on the frontier curve with the tracking error being defined as the mean square error of portfolio return. Those relations and properties are similar to the existing ones under the traditional correlation tracking error. They provide useful information for empirical studies on CAPM and index fund construction.Many problems are left for future research. In particular, clarifying the practical implications of the tracking error and investing the relationship between various costs and the number of securities included in the index fund are important fields.