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When and Why Na\"ive Diversification Works: A Simple Diagnostic Strategy

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  • Han Feng
  • Difang Huang
  • Jue Wang
  • Zhengjun Zhang

Abstract

We explain the long-standing puzzle of na\"ive 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.

Suggested Citation

  • Han Feng & Difang Huang & Jue Wang & Zhengjun Zhang, 2026. "When and Why Na\"ive Diversification Works: A Simple Diagnostic Strategy," Papers 2607.11054, arXiv.org.
    • Handle: RePEc:arx:papers:2607.11054
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    File URL: https://arxiv.org/pdf/2607.11054
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