An analysis and verification of a benchmark replication on the basis of Tracking Error methodology

by Jiří VALECKÝ

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JEL classification

  • Portfolio Choice; Investment Decisions
  • Mathematical Methods; Programming Models; Mathematical and Simulation Modeling: General

Keywords

Benchmark, replication, restructuring, tracking error, transaction costs

Abstract

The aim of the paper is to perform an analysis and compare the accuracy of a benchmark replication using various replication methods of Tracking Error methodology. On the historical data and under the existence of the proportional transactions costs, we verify the impact of stocks number in portfolio and transaction costs on the selected replication methods of passive and active asset management strategies, namely replication with daily and controlled restructuring and the method with penalization of transaction costs. We also determined which selected replication method is the most precise in the sense of benchmark replication and we give several general recommendations for benchmark replication strategy including the eligible proportion of replicating portfolio on the market capitalization with respect to the target replication accuracy. Firstly, the Tracking Error methodology and its application in asset management are presented and optimization problem of particular replication methods is formulated in the next part of the paper. In the application part, the replication accuracy is analyzed and the quality of benchmark replication is verified on the Czech index PX-GLOB during the period of the year 2007. It emerged during our experiment that under the condition of passive asset management strategy the replicating portfolios with the proportion of the market capitalization on the benchmark at the level 70 – 85 % give very good results. Moreover we conclude that the method with penalization of transaction costs is the most precise replication method from the selected and analyzed methods of active assets management strategy.