Global investment flows illustrated with a circuit board world map.

Diversify Your Investments: Unlocking Global Opportunities for Higher Returns

Beau Callahan in Business & Economy December 2025 • 4 min read.

"A comprehensive look at mean-variance spanning tests and how they can help you build a more robust investment portfolio by exploring international diversification."

In today's interconnected world, investment opportunities extend far beyond domestic borders. Savvy investors are increasingly looking to international diversification as a way to enhance returns and mitigate risk. But how do you know if adding international assets will genuinely improve your portfolio? That's where mean-variance spanning (MVS) tests come in. These powerful tools help determine whether adding new assets, particularly those from foreign markets, significantly improves the efficiency of your investment portfolio.

Traditional investment strategies often focus on familiar domestic markets. However, these markets can be susceptible to local economic downturns or industry-specific shocks. By diversifying internationally, investors can tap into different growth cycles, industries, and economic conditions, potentially smoothing out returns and reducing overall volatility. MVS testing provides a rigorous framework for evaluating the potential benefits of this diversification.

This article explores the world of mean-variance spanning tests, explaining their methodology, benefits, and practical applications. We'll delve into how these tests help investors make informed decisions about international diversification, ultimately leading to more robust and potentially more profitable investment portfolios.

Understanding Mean-Variance Spanning (MVS) Tests

Global investment flows illustrated with a circuit board world map.

At its core, an MVS test helps determine if adding a set of "test assets" (e.g., international stocks) to your existing "benchmark assets" (e.g., domestic stocks) improves your portfolio's efficient frontier. The efficient frontier represents the set of portfolios that offer the highest expected return for a given level of risk, or the lowest risk for a given level of expected return. The MVS test examines whether the test assets can create a new efficient frontier that outperforms the original.

MVS testing hinges on the concept of the two-fund separation theorem. This theorem suggests that all investors, regardless of their risk preferences, can achieve an optimal portfolio by combining two "funds": a risk-free asset and a portfolio of risky assets. MVS testing essentially checks if the test assets have zero weight in the maximum Sharpe ratio portfolio and the global minimum-variance portfolio of all assets. If they do, it suggests that these assets don't add value to the portfolio.

Sharpe Ratio: Measures risk-adjusted return, indicating how much excess return you receive for each unit of risk taken.
Global Minimum-Variance Portfolio: The portfolio with the lowest possible risk (variance) for a given set of assets.
Efficient Frontier: The set of portfolios offering the highest expected return for each level of risk.

In essence, MVS tests help investors determine if the potential benefits of adding international assets—such as higher returns or lower risk—are statistically significant, or simply due to chance.

The Future of Investment Strategies

As global markets become increasingly integrated, understanding and applying advanced portfolio optimization techniques like mean-variance spanning tests will be crucial for achieving superior investment outcomes. By embracing these tools, investors can move beyond traditional strategies and unlock the full potential of international diversification. Whether you're a seasoned professional or just starting your investment journey, exploring global opportunities with the guidance of MVS testing can lead to a more resilient and prosperous financial future.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: 10.2139/ssrn.4703023,

Title: High-Dimensional Mean-Variance Spanning Tests

Subject: stat.me q-fin.gn q-fin.pm q-fin.st

Authors: David Ardia, Sébastien Laurent, Rosnel Sessinou

Published: 25-03-2024

Everything You Need To Know

What are mean-variance spanning (MVS) tests, and how can they benefit my investment strategy?

Mean-variance spanning (MVS) tests are tools used to assess whether adding a new set of assets, like international stocks, to an existing portfolio improves its efficiency. They help determine if these 'test assets' enhance the efficient frontier, which represents portfolios offering the highest expected return for a given risk level. By using MVS tests, investors can make informed decisions about international diversification, potentially leading to more robust and profitable investment portfolios. MVS tests are about statistically validating if the perceived benefits are real rather than coincidental.

Why is international diversification important for investment portfolios, and how do MVS tests play a role in it?

International diversification is crucial because it allows investors to tap into different growth cycles, industries, and economic conditions, reducing overall portfolio volatility. Domestic markets are susceptible to local economic downturns, whereas international diversification provides exposure to varied economic environments. Mean-variance spanning (MVS) tests provide a rigorous framework for evaluating whether adding international assets truly enhances the efficient frontier of a portfolio. MVS tests help validate the benefits of diversification beyond just the intuition, offering statistical evidence to support investment decisions.

Can you explain the core concept behind mean-variance spanning tests in terms of benchmark and test assets?

At its core, a mean-variance spanning (MVS) test helps determine if adding a set of 'test assets' (e.g., international stocks) to your existing 'benchmark assets' (e.g., domestic stocks) improves your portfolio's efficient frontier. The efficient frontier represents the set of portfolios that offer the highest expected return for a given level of risk, or the lowest risk for a given level of expected return. The MVS test examines whether the test assets can create a new efficient frontier that outperforms the original. If the 'test assets' improve the Sharpe ratio and reduce risk, it may be a worthwhile portfolio enhancement.

How does the two-fund separation theorem relate to mean-variance spanning tests, and what implications does it have for portfolio optimization?

Mean-variance spanning (MVS) testing hinges on the concept of the two-fund separation theorem, which suggests that all investors can achieve an optimal portfolio by combining a risk-free asset and a portfolio of risky assets, regardless of their risk preferences. MVS testing checks if the 'test assets' have zero weight in the maximum Sharpe ratio portfolio and the global minimum-variance portfolio of all assets. If the test assets have zero weight, it suggests that they don't add value to the portfolio. In essence, MVS testing assesses whether the potential benefits of adding international assets are statistically significant, or simply due to chance. This has implications for portfolio optimization, as it provides a framework for making informed decisions about asset allocation.

What are the key metrics or concepts, such as Sharpe Ratio, Global Minimum-Variance Portfolio, and Efficient Frontier, that are essential for understanding mean-variance spanning tests, and how do they influence investment decisions?

Several key metrics are essential for understanding mean-variance spanning tests. The Sharpe Ratio measures risk-adjusted return, indicating the excess return received for each unit of risk taken. The Global Minimum-Variance Portfolio is the portfolio with the lowest possible risk for a given set of assets. The Efficient Frontier represents the set of portfolios offering the highest expected return for each level of risk. MVS tests evaluate whether adding new assets improves these metrics. If adding international assets increases the Sharpe Ratio, shifts the Efficient Frontier outward, or reduces the Global Minimum-Variance, it supports the decision to diversify internationally. These metrics help investors quantify the potential benefits of diversification, aiding in making data-driven investment decisions.