Enhanced Index Tracking-an Extension of the Elton and Gruber (1976) Model

Abstract

Aims: The purpose of the study is to make a case for the development of middle-range models for use in developing markets by modifying the Elton and Gruber (1976) model to come up with semi-optimized index-tracking models with desirable tracking and excess return features. Study Design:  Non-experimental empirical design. Place and Duration of Study: Zimbabwe, Department of Finance and Department of Insurance and Actuarial Science, covering the period between February 2009 and June 2010. Methodology: We use weekly data of 71 industrial closing prices from the Zimbabwe Stock Exchange (ZSE) for the period starting February 2009 to June 2010 to compare the return and tracking performance of the adapted models against simple capitalization-based tracking models. Results: We find that the semi-optimized models yield tracking and excess return results that are not statistically significantly different from simple capitalization-based models, at the 1% significance level, yet only utilizing about half as many stocks. Conclusion: The use of semi-optimized index-tracking models has potential to significantly reduce transaction costs while keeping tracking error within reasonable limits. However, their use results in inferior excess return performance on a risk-adjusted basis when compared to simple capitalization-based models. The use of the correlation coefficient in filtering stocks to include in a tracking portfolio yields superior tracking error results but inferior excess return results compared to the use of the ratio of beta to idiosyncratic risk. Portfolios with higher Active Share measures produce poorer tracking error and excess return results compared to lower Active Share portfolios. The use of passive portfolio management strategies on the ZSE is supported by our findings.