Creating better tracking portfolios with quantiles

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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.

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    • Figure 1. Scaled ATE, TER, RMSTE and TEV sensitivity plots
    • Figure 2. Scaled TER and QuTER sensitivity plots
    • Figure 3. Granularity of grid for the QuTER statistic
    • Figure 4. Effect of varying weights on QuTER
    • Figure 5. DIA and DJIA returns
    • Figure 6. Comparing the benchmark and tracking portfolio
    • Figure 7. Return differences (TE) of DIA and DJIA
    • Figure 8. Difference in 3-year moments rolled through time for DIA and DJIA
    • Figure 9. TER and QuTER (3-year rolling window)
    • Figure 10. Return distribution of MSCI-EM and EEM
    • Figure 11. Return differences (TE) of EEM and MSCI-EM
    • Figure 12. Difference in 3-year moments rolled through time for EEM and MSCI-EM
    • Figure 13. QuTER and TER (3-year rolling window)
    • Table 1. Simulation study design
    • Table 2. Sensitivity of TER and QuTER
    • Table 3. QuTER and TER regression
    • Table 4. Statistical comparison of DJIA and DIA
    • Table 5. (Quantile) Tracking errors
    • Conceptualization
      Mike Aguilar, Anessa Custovic
    • Formal Analysis
      Mike Aguilar, Anessa Custovic, Ziming Huang
    • Investigation
      Mike Aguilar, Anessa Custovic, Ruyang Chengan, Ziming Huang
    • Methodology
      Mike Aguilar, Anessa Custovic, Ziming Huang
    • Resources
      Mike Aguilar
    • Supervision
      Mike Aguilar
    • Writing – original draft
      Mike Aguilar, Anessa Custovic, Ruyang Chengan
    • Writing – review & editing
      Mike Aguilar, Ziming Huang
    • Data curation
      Anessa Custovic, Ruyang Chengan, Ziming Huang
    • Project administration
      Anessa Custovic
    • Software
      Anessa Custovic, Ruyang Chengan, Ziming Huang
    • Visualization
      Anessa Custovic, Ruyang Chengan, Ziming Huang
    • Validation
      Ruyang Chengan