Optimal omega-ratio portfolio performance constrained by tracking error

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The mean-variance framework coupled with the Sharpe ratio identifies optimal portfolios under the passive investment style. Optimal portfolio identification under active investment approaches, where performance is measured relative to a benchmark, is less well-known. Active portfolios subject to tracking error (TE) constraints lie on distorted elliptical frontiers in return/risk space. Identifying optimal active portfolios, however defined, have only recently begun to be explored. The Ω – ratio considers both down and upside portfolio potential. Recent work has established a technique to determine optimal Ω – ratio portfolios under the passive investment approach. The authors apply the identification of optimal Ω – ratio portfolios to the active arena (i.e., to portfolios constrained by a TE) and find that while passive managers should always invest in maximum Ω – ratio portfolios, active managers should first establish market conditions (which determine the sign of the main axis slope of the constant TE frontier). Maximum Sharpe ratio portfolios should be engaged when this slope is > 0 and maximum Ω – ratios when < 0.

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    • Figure 1. Ω frontier, analogous capital market line, and location of the optimal Ω portfolio
    • Figure 2. Orientation of relevant components in Oct-05. TE = 6% and rf = 7.0%. The Ω – ratio as a function of risk is shown as a solid black line, tied to the right-hand axis (the maximum Ω – ratio on this curve is indicated). All other elements are linke
    • Figure 3. Orientation of relevant components in Oct-14. TE = 6% and rf = 5.8%
    • Figure 4(a)-(b). Ω frontiers and (b) maximum Ω(τ) for Oct-00 – Oct-05 and Oct-09 – Oct-14
    • Figure 5. Weights in optimal, unconstrained Ω portfolios for Oct-00 – Oct-05 and Oct-09 – Oct-14
    • Figure 6(a). Return/risk profiles for relevant portfolios as a function of TE (percentages indicate TE values)
    • Figure 6(b). Sharpe ratios versus TE for Oct-00 – Oct-05
    • Figure 7(a). Return/risk profiles for relevant portfolios as a function of TE
    • Figure 7(b). Sharpe ratios versus TE for Oct-14
    • Figure 8. Benchmark weight deviations for relevant portfolios in (a) Oct-00 – Oct-05 and (b) Oct-09 – Oct-14
    • Figure 9. Asset K’s deviation in weight from the benchmark for the relevant portfolios in (a) Oct-00 – Oct-05 and (b) Oct-09 – Oct-14
    • Conceptualization
      Wade Gunning
    • Data curation
      Wade Gunning
    • Formal Analysis
      Wade Gunning
    • Investigation
      Wade Gunning
    • Methodology
      Wade Gunning
    • Software
      Wade Gunning
    • Validation
      Wade Gunning, Gary van Vuuren
    • Writing – original draft
      Wade Gunning
    • Project administration
      Gary van Vuuren
    • Supervision
      Gary van Vuuren
    • Writing – review & editing
      Gary van Vuuren