• Mark Kritzman and Yuanzhen Li
  • Financial Analyst Journal, 2010
  • A version of this paper can be found here
  • Want to read our summaries of academic finance papers? Check out our Academic Research Insight category

What are the Research Questions

When hunting for diversity, the typical investor considers only average correlations. However, when measuring an asset’s diversification benefits utilizing average correlations tend to mislead investors. For example, when both U.S. and non-U.S. equities produce returns greater than one standard deviation above their means (ie when times are good), their correlation equals –17 percent; but when both markets produce returns more than one standard deviation below their means (ie when things are bad and you want diversification), their correlation rises to +76 percent (based on monthly returns from 1970 to 2008). So on utilizing average correlations, it appears as though non-U.S. equities produce the diversification benefit investors are looking for. It is this period of financial turbulence, the periods in which investors are most interested in diversification, that the authors investigate specifically.

  1. First, the authors identify the empirical features of financial turbulence.
  2. Secondly, they investigate what the possible applications are for this measure?

What are the Academic Insights?

By utilizing a measure of financial turbulence,(1) which was originally developed by Mahalanobis (1927, 1936) to analyze characteristics of human skulls(2), the authors find:

  1. There are two particular features that are interesting:
    • Returns to risk assets are substantially lower during turbulent periods than during non-turbulent periods, irrespective of the source of turbulence.
    • Financial turbulence is highly persistent. Although we may not be able to anticipate the initial onset of financial turbulence, once it begins, it usually continues for a period of weeks as the markets digest it and react to the events causing the turbulence.

  2. The authors show a couple of possible practical applications:
    • Stress Test Portfolios: Investors often use value at risk (VaR) to measure a portfolio’s exposure to loss but the conventional approach for measuring VaR uses the full-sample covariance matrix to compute the portfolio’s standard deviation. The authors suggest measuring exposure to losses more reliably by estimating covariance from the turbulent subperiods when losses are more likely to occur.
    • Build Turbulence Resistant portfolios: Use modified mean-variance optimization by blending the turbulent subsample covariance with the full-sample covariances in proportion to their sample sizes
    • Enhance the performance of certain risky strategies by using turbulence as a filter for scaling exposure to risk.

Why does it matter?

This study shows that a mathematically derived measure of financial turbulence, which measures the statistical unusualness of a set of returns given their historical pattern of behavior, coincides with well known episodes of market turbulence. This measure of financial turbulence can be applied in a variety of useful ways.

The Most Important Chart from the Paper

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are un-managed, do not reflect management or trading fees, and one cannot invest directly in an index.


Based on a methodology introduced in 1927 to analyze human skulls and later applied to turbulence in financial markets, this study shows how to use a statistically derived measure of financial turbulence to measure and manage risk and to improve investment performance.

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About the Author: Wesley Gray, PhD

Wesley Gray, PhD
After serving as a Captain in the United States Marine Corps, Dr. Gray earned an MBA and a PhD in finance from the University of Chicago where he studied under Nobel Prize Winner Eugene Fama. Next, Wes took an academic job in his wife’s hometown of Philadelphia and worked as a finance professor at Drexel University. Dr. Gray’s interest in bridging the research gap between academia and industry led him to found Alpha Architect, an asset management firm dedicated to an impact mission of empowering investors through education. He is a contributor to multiple industry publications and regularly speaks to professional investor groups across the country. Wes has published multiple academic papers and four books, including Embedded (Naval Institute Press, 2009), Quantitative Value (Wiley, 2012), DIY Financial Advisor (Wiley, 2015), and Quantitative Momentum (Wiley, 2016). Dr. Gray currently resides in Palmas Del Mar Puerto Rico with his wife and three children. He recently finished the Leadville 100 ultramarathon race and promises to make better life decisions in the future.

Important Disclosures

For informational and educational purposes only and should not be construed as specific investment, accounting, legal, or tax advice. Certain information is deemed to be reliable, but its accuracy and completeness cannot be guaranteed. Third party information may become outdated or otherwise superseded without notice.  Neither the Securities and Exchange Commission (SEC) nor any other federal or state agency has approved, determined the accuracy, or confirmed the adequacy of this article.

The views and opinions expressed herein are those of the author and do not necessarily reflect the views of Alpha Architect, its affiliates or its employees. Our full disclosures are available here. Definitions of common statistics used in our analysis are available here (towards the bottom).

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