Testing for the Minimum Mean-Variance Spanning Set

TL;DR

This paper introduces a new method for accurately estimating the minimum spanning set of risky assets that define the mean-variance efficient frontier, with strong theoretical guarantees and practical applications.

Contribution

It develops a novel estimation and inference procedure for the MSS, providing identification conditions and asymptotic properties, validated through simulations and empirical analysis.

Findings

Factor momentum and stock return factors are key drivers of mean-variance efficiency.

The proposed estimator reliably identifies the true MSS with high confidence levels.

Empirical analysis ranks the importance of various factors in asset allocation.

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.