When and Why Naïve Diversification Works: A Simple Diagnostic Strategy

We explain the long-standing puzzle of naïve diversification with a simple, testable condition: equal weighting is minimum-variance optimal when the forecast-error covariance matrix has a uniform eigenstructure. This "Golden Criterion" drives a two-stage adaptive strategy that dynamically blends naive and optimized weights based on the empirical distance from this condition. Applied to U.S. equity premium forecasting, the method delivers consistent out-of-sample gains in forecast accuracy, utility, and Sharpe ratios. Diversity-driven shrinkage dominates at short horizons, while optimized weights regain their edge at longer horizons, offering clear horizon-dependent guidance for portfolio construction.

Source: arXiv:2607.11054v1 - http://arxiv.org/abs/2607.11054v1 PDF: https://arxiv.org/pdf/2607.11054v1 Original Link: http://arxiv.org/abs/2607.11054v1