Tracking-Error Models for Multiple Benchmarks: Theory and Empirical Performance
Posted: 25 May 2016 Last revised: 4 Oct 2018
Date Written: June 30, 2012
We propose a new multiple-benchmark tracking-error model for the portfolio selection problem. We construct a strategy to track the performance of the highest return from a set of benchmarks, by minimizing a quadratic loss function. The portfolio rule constructed this way retains features of the linear combination rule, with weights mainly determined by the probability that each benchmark portfolio attains the highest return among all the benchmark portfolios considered. We use this approach to deal with the issue of estimation errors in portfolio construction. A common strategy here is to use a re-sampling technique to construct portfolios from the data, and use the average of the portfolio weights as the solution. We can view each portfolio constructed from sampling as a benchmark, and use the tracking error method proposed in this paper to enhance the performance of any portfolio selection method. We perform comprehensive numerical experiments with various empirical data sets to demonstrate that our approach can consistently provide higher net Sharpe ratio (even after accounting for transaction cost), higher net aggregate return, smaller tracking error, and lower turnover rates in out-of-sample performance, compared to twelve different benchmark portfolios proposed in the literature, including the equally weighted portfolio (the 1/n strategy).
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