Creating better tracking portfolios with quantiles

Abstract

Tracking error is a ubiquitous tool among active and passive portfolio managers, widely used for fund selection, risk management, and manager compensation. This paper shows that traditional measures of the tracking error are incapable of detecting variations in skewness and kurtosis. As a solution, this paper introduces a new class of Quantile Tracking Errors (QuTE), which measures differences in the quantiles of return distributions between a tracking portfolio and its benchmark. Through an extensive simulation study, this paper shows that QuTE is six times more sensitive than traditional tracking measures to skewness and three times more sensitive to kurtosis. The QuTE statistic is robust to various calibrations and can easily be customized. By using the QuTE tracking measure during the Dot Com bubble and the Great Recession, this paper finds differences between the DIA and its benchmark, the DJIA, that otherwise would have gone undetected. Quantile based tracking provides a robust method for relative performance measurement and index portfolio construction.

Keywords

• index fund
• index tracking
• portfolio tracking
• quantile
• tracking error