Investment strategy performance under tracking error constraints

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Recent (2018) evidence identifies the increased need for active managers to facilitate the exploitation of investment opportunities found in inefficient markets. Typically, active portfolios are subject to tracking error (TE) constraints. The risk-return relationship of such constrained portfolios is described by an ellipse in mean-variance space, known as the constant TE frontier. Although previous work assessed the performance of active portfolio strategies on the efficient frontier, this article uses several performance indicators to evaluate the outperformance of six active portfolio strategies over the benchmark – subject to various TE constraints – on the constant TE frontier.

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    • Figure 1. (a) Efficient frontier, TE frontier and constant TE frontier and (b) efficient frontier, TE frontier and constant TE frontier and capital market line (CML) in mean/standard deviation space
    • Figure 2. TE frontier, constant TE frontier and portfolio strategies
    • Figure 3. Intra-correlation and diversification ratio subject to a TE = %V
    • Figure 4. The empirical identification of applying brute force mathematics on the MD and MIC portfolios to be constrained by TE
    • Figure 5. (a) Loci of the six portfolio strategies with respect to changes in their risk/return relationships for increasing TEs and (b) an enlarged section of Figure 4(a)
    • Figure 6. Performance evaluation of the six portfolio strategies with respect to their (a) Sharpe ratios and (b) M2 ratios for incremental increases in TE
    • Figure 7. (a) Performance of the six portfolio strategies with respect to their IRs and (b) correlation of benchmark and each strategy’s returns, as a function of TE
    • Figure 8. The loci of possible (a) Sharpe ratios, (b) M2 ratios and (c) IRs – as a function of portfolio risk – for increasing TEs
    • Figure 9. The loci of possible (a) Sharpe ratios, (b) M2 ratios and (c) IRs – as a function of portfolio return – for increasing TEs
    • Figure 10. Explanation of performance ratio plateaus as TE →9%→15%→18%. The efficient frontier is the darker grey line to which the CML is tangent
    • Table 1. Stylized input data