Estimating the Minimum Mean-Variance Spanning Set

Summary

The paper studies how to identify the smallest subset of risky assets that can span the mean-variance efficient frontier of a larger universe. It sets out conditions for identifying that subset and introduces an estimation and inference procedure designed to cover the true set with probability approaching one and to converge at a chosen confidence level.

Monte Carlo simulations are reported as evidence of strong finite-sample performance. An empirical application compares individual-stock momentum and factor-momentum strategies with established stock-return factors. The findings identify factor momentum, some stock-momentum strategies, and several return factors as important contributors to mean-variance efficiency; the analysis also examines and ranks their contributions. The document provides no details about the sample, specific assets, estimation choices, or robustness checks, so the empirical conclusions cannot be assessed beyond this overview.

Key ideas

• The minimum spanning set is the smallest risky-asset subset that spans a portfolio universe’s mean-variance efficient frontier.
• Identification conditions define when this subset can be recovered.
• The proposed method estimates the set and provides inference with asymptotic coverage and convergence guarantees.
• Monte Carlo simulations are used to assess finite-sample performance.
• An application ranks the contributions of stock momentum, factor momentum, and established return factors to mean-variance efficiency.

Tags

# Testing for the Minimum Mean-Variance Spanning Set


# Testing for the Minimum Mean-Variance Spanning Set









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.