High-Dimensional Mean-Variance Spanning Tests

ArXiv ID: 2403.17127 “View on arXiv”

Authors: Unknown

Abstract

We introduce a new framework for the mean-variance spanning (MVS) hypothesis testing. The procedure can be applied to any test-asset dimension and only requires stationary asset returns and the number of benchmark assets to be smaller than the number of time periods. It involves individually testing moment conditions using a robust Student-t statistic based on the batch-mean method and combining the p-values using the Cauchy combination test. Simulations demonstrate the superior performance of the test compared to state-of-the-art approaches. For the empirical application, we look at the problem of domestic versus international diversification in equities. We find that the advantages of diversification are influenced by economic conditions and exhibit cross-country variation. We also highlight that the rejection of the MVS hypothesis originates from the potential to reduce variance within the domestic global minimum-variance portfolio.

Keywords: Mean-Variance Spanning, Hypothesis Testing, Cauchy Combination Test, Minimum-Variance Portfolio, Portfolio Optimization, Equities

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced statistical methods including robust Student-t tests, batch-mean procedures, and the Cauchy combination test for high-dimensional spanning, indicating high mathematical density. It demonstrates strong empirical rigor through Monte Carlo simulations, application to real equity data for international diversification, and detailed discussion of implementation challenges.
  flowchart TD
    A["Research Goal<br>Test Mean-Variance Spanning<br>in High Dimensions"] --> B["Methodology<br>Robust Student-t + Cauchy Combination"]
    B --> C["Input Data<br>Stationary Asset Returns<br>Test Assets > Time Periods"]
    C --> D["Computational Process<br>1. Individual Moment Tests<br>2. P-value Aggregation"]
    D --> E["Key Findings<br>Superior Power vs. State-of-Art<br>Diversification Benefits Vary by Economy<br>Rejection Driven by Variance Reduction"]