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Estimation risk and the implicit value of index-tracking

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  • Brian Clark
  • Chanaka Edirisinghe
  • Majeed Simaan

Abstract

We study [Roll, R., A mean/variance analysis of tracking error. J. Portfolio Manage., 1992, 18, 13–22.] conjecture that there exists an implicit value in index-tracking (IVIT) relative to forming mean-variance (MV) optimal portfolios under estimation error. We derive an analytical definition for the opportunity cost facing the MV investor who does not index-track. Our findings indicate that the opportunity cost is positive and statistically significant. The existence of an IVIT (positive opportunity cost) is strongly associated with a reduction in the portfolio's induced estimation risk under index-tracking relative to an MV-efficient portfolio of equal target mean return. Under high estimation error cases, increased IVIT translates to higher risk-adjusted returns, lower volatility, higher Sharpe-ratio, lower turnover, and larger certainty equivalent returns. Empirically, a one standard deviation increase in IVIT translates to an annual increase of 4%–5% in the out-of-sample Sharpe-ratio and a 6%–15% decrease in the monthly turnover.

Suggested Citation

  • Brian Clark & Chanaka Edirisinghe & Majeed Simaan, 2022. "Estimation risk and the implicit value of index-tracking," Quantitative Finance, Taylor & Francis Journals, vol. 22(2), pages 303-319, February.
  • Handle: RePEc:taf:quantf:v:22:y:2022:i:2:p:303-319
    DOI: 10.1080/14697688.2021.1959631
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    Cited by:

    1. Lassance, Nathan & Vrins, Frédéric, 2023. "Portfolio selection: A target-distribution approach," European Journal of Operational Research, Elsevier, vol. 310(1), pages 302-314.
    2. Ling, Aifan & Li, Junxue & Wen, Limin & Zhang, Yi, 2023. "When trackers are aware of ESG: Do ESG ratings matter to tracking error portfolio performance?," Economic Modelling, Elsevier, vol. 125(C).

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