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Minimum-allocation robustness conjecture in portfolio optimization

Establish whether imposing a minimum per-asset allocation constraint (for example, requiring each selected stock to receive at least 5% of the portfolio) increases the robustness of optimal portfolios in portfolio optimization models, measured by reduced sensitivity of allocations to small perturbations in return and covariance inputs, relative to unconstrained formulations such as the Maximum Drawdown linear program and classical Markowitz models.

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Background

The paper introduces a Maximum Drawdown (MD) linear program and a mixed-integer linear programming (MILP) variant that enforces a minimum 5% allocation for any selected stock. A sensitivity experiment perturbs returns (inducing changes in the covariance matrix) and measures robustness by the average absolute percentage change in positive allocations.

Results show markedly improved robustness for the constrained MD (MILP) model (3.7% average change) compared to Markowitz (approximately 38–42%) and unconstrained MD (47.1%). Based on this evidence, the authors suggest that minimum-allocation constraints may reduce overfitting and improve robustness, but note that deeper analysis is needed to make the claim conclusive.

References

Therefore, it seems that a simple way to increase the robustness of any given portfolio optimization model is to require a minimum allocation for each selected stock (at the expense of turning the portfolio optimization model into a MILP, but it seems this is not necessarily an issue for problems with a size and structure similar to ours, especially with today's solvers and computational power). Naturally, the previous claim would require a deeper analysis to be more conclusive, but it seems at least a reasonable conjecture in light of the evidence we have and the intuitive connection with overfitting.

Constrained Max Drawdown: a Fast and Robust Portfolio Optimization Approach (2401.02601 - Dorador, 5 Jan 2024) in Subsection 4.3 Sensitivity analysis (after Table 3)