When and Why Naïve Diversification Works: A Simple Diagnostic Strategy
arXiv:2607.11054
The paper identifies a simple condition—called the Golden Criterion—under which equal‑weight portfolios are minimum‑variance optimal, and proposes an adaptive two‑stage strategy that blends naive and optimized weights based on how closely the forecast‑error covariance meets this condition, showing out‑of‑sample improvements in equity‑premium forecasts and portfolio performance.
Abstract
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.
134 pages, 22 figures