An analysis of a mean-variance enhanced index tracking problem with weights constraints

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In this paper, the authors deal with a mean-variance enhanced index tracking (EIT) problem with weights constraints. Using a shrinkage approach, they show that constructing the constrained EIT portfolio is equivalent to constructing the unconstrained EIT portfolio. This equivalence allows to study the effect of weights constraints on the covariance matrix and on the EIT portfolio. In general, the effects of weights constraints on the EIT portfolio are different from those observed in the case of global minimum variance portfolio. Finally, the authors present a numerical asset allocation example, where the S&P 500 index is used as the market index to be tracked using a portfolio composed of ten stocks, in which the constrained EIT portfolio shows a satisfactory performance when compared to the unconstrained case.

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    • Figure 1. Cumulative monthly portfolio values, obtained by the constrained EIT portfolio ω~ and by the unconstrained EIT portfolio , ω* considering an in-sample analysis
    • Figure 2. Cumulative monthly portfolio values, obtained by the constrained EIT portfolio ω~ and by the unconstrained EIT portfolio , ω* considering an out-of-sample analysis
    • Figure 3. Cumulative monthly portfolio values, obtained by rebalancing the weights ω~ and ω* during the out-of-sample period
    • Table 1. Elements of the perturbation matrix, Δ i, j, related to the optimized weights ω~i and ω~j
    • Table 2. Market parameters and optimal solution for the unconstrained EIT problem (ω*)
    • Table 3. Results for the constrained EIT problem, with weights constraints 0.10 ≤ ωi ≤ 0.30
    • Table 4. Solutions for the unconstrained EIT problem, ω*, for the constrained EIT problem with 0.1 ≤ ωi ≤0.3, ω~ and for the unconstrained EIT problem with ri = 0.02 and β i = 1.0, ω-