Rebalancing Issues in Tracking Error Variance Minimization

Abstract

The paper focuses on portfolio selection based on the approach to index tracking minimizing tracking error variance. The idea of this approach is to replicate a suitably chosen financial index as a convex linear combination (i.e. portfolio) of pre-selected assets that are components of the given synthetic financial index. In this approach, a tracking portfolio that performs as best as the financial index serving the function of benchmark and follows its path of returns is constructed and sought. However, a question arises whether the replication portfolio found under the tracking error variance minimization strategy should be left without alterations (non-rebalanced) or adjusted in respect to market movements (or rebalanced). This is of practical implications as rebalancing induces undesirable transaction costs, and the investor must choose whether he will rebalance his portfolio on a regular periodic basis. In the paper, under the tracking error variance minimization approach, practical aspects of both the buy-and-hold strategy and the rebalancing strategy are investigated with respect to net returns (returns including transaction costs) and to portfolio volatility.