Abstract
Index tracking seeks to minimize the unsystematic risk component by imitating the movements of a reference index. Partial index tracking only considers a subset of the stocks in the index, enabling a substantial cost reduction in comparison with full tracking. Nevertheless, when heterogeneous investment profiles are to be satisfied, traditional index tracking techniques may need different stocks to build the different portfolios. The aim of this paper is to propose a methodology that enables a fund's manager to satisfy different clients’ investment profiles but using in all cases the same subset of stocks, and considering not only one particular criterion but a compromise between several criteria. For this purpose we use a mathematical programming model that considers the tracking error variance, the excess return and the variance of the portfolio plus the curvature of the tracking frontier. The curvature is not defined for a particular portfolio, but for all the portfolios in the tracking frontier. This way funds’ managers can offer their clients a wide range of risk-return combinations just picking the appropriate portfolio in the frontier, all of these portfolios sharing the same shares but with different weights. An example of our proposal is applied on the S&P 100.
Highlights
The increasing popularity of passive portfolio techniques is probably due to the difficulty to model and predict the evolution of stock markets (Jarrett, Schilling 2008; Teresiene 2009; Aktan et al 2010)
The disadvantages of full tracking include the high portfolio management and transaction costs, as well as the need to invest in all the stocks in the index despite they might have a minor weight in the index composition
A restrictive view of the costs associated with tracking portfolios has been discussed in numerous academic papers (Connor, Leland 1995; Canakgoz, Beasley 2003) and the drawbacks are usually addressed through mathematical programming models
Summary
The increasing popularity of passive portfolio techniques is probably due to the difficulty to model and predict the evolution of stock markets (Jarrett, Schilling 2008; Teresiene 2009; Aktan et al 2010). Works that make use of multivariate analysis techniques include: Focardi and Fabozzi (2004), Dose and Cincotti (2005), Corielli and Marcellino (2006) All these papers are characterized by the search for a single portfolio, characterized up to three possible parameters: tracking error variance, excess return and volatility of returns, which represent reliability, profitability and risk (Rutkauskas, Stasytyte 2007). With the difference that instead of looking for the portfolio with the least volatility for a given return, managers try to obtain the portfolio with the minimum tracking error variance for a given level of return in excess of the index. The second constraint ensures that the total investment in the tracking portfolio is the same as the index – and so the sum of positive and negative deviations is compensated
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