Testing for the Minimum Mean-Variance Spanning Set

ArXiv ID: 2501.19213 “View on arXiv”

Authors: Unknown

Abstract

This paper explores the estimation and inference of the minimum spanning set (MSS), the smallest subset of risky assets that spans the mean-variance efficient frontier of the full asset set. We establish identification conditions for the MSS and develop a novel procedure for its estimation and inference. Our theoretical analysis shows that the proposed MSS estimator covers the true MSS with probability approaching 1 and converges asymptotically to the true MSS at any desired confidence level, such as 0.95 or 0.99. Monte Carlo simulations confirm the strong finite-sample performance of the MSS estimator. We apply our method to evaluate the relative importance of individual stock momentum and factor momentum strategies, along with a set of well-established stock return factors. The empirical results highlight factor momentum, along with several stock momentum and return factors, as key drivers of mean-variance efficiency. Furthermore, our analysis uncovers the sources of contribution from these factors and provides a ranking of their relative importance, offering new insights into their roles in mean-variance analysis.

Keywords: Minimum Spanning Set (MSS), Mean-Variance Efficient Frontier, Asset Pricing, Factor Momentum, Statistical Inference, Equities

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail
  • Why: The paper presents advanced econometric theory, including set inference, moving block bootstrap, and step-down procedures, resulting in high math complexity; its Monte Carlo simulations under AR-GARCH and real-data application to momentum factors demonstrate significant data/implementation effort.
  flowchart TD
    A["Research Goal: Identify Minimum<br>Mean-Variance Spanning Set MSS"] --> B["Methodology:<br>Develop Estimation & Inference Procedure"]
    B --> C["Data Inputs:<br>Simulations & Empirical Stock/Factor Returns"]
    C --> D["Computational Process:<br>Estimate MSS Coverage & Convergence"]
    D --> E["Key Findings:<br>Factor Momentum & Stock Factors<br>Drive Efficiency"]