• Both the Financial Turbulence and Systemic Risk indicators are currently hosted here.
  • Python script and documentation.


  • In A Nutshell
  • Financial Turbulence Indicator
  • Systemic Risk Indicator
  • The Dataset
  • The Sales Pitch (or, “How These 2 Indicators Can Make / Save You Money”)

In A Nutshell

This project illustrates 2 unique approaches for measuring financial risk.

The Financial Turbulence Indicator measures the turbulence of global financial markets across time. This matters because:

  1. We can predict the future path of financial turbulence, since financial turbulence is highly persistent across time.
  2. You can save money by predicting turbulent financial conditions before they occur, since financial asset prices tend to fall during turbulent periods (as opposed to non-turbulent periods).

Both of these claims are discussed by Mark Kritzman and Yuanzhen Li in their paper titled “Skulls, Financial Turbulence, and Risk Management” (2010).

The Systemic Risk Indicator measures the systemic risk embedded in global financial markets across time. This matters because if systemic risk is high, then global financial markets are “tightly coupled” with each other, suggesting that financial shocks are prone to propagate more quickly and broadly. Mark Kritzman, Yuanzhen Li, Sebastien Page, and Roberto Rigobon support this claim in “Principal Components as a Measure of Systemic Risk” (2010).

A Helpful Analogy: “3 Little Pigs”

Using this analogy, Systemic Risk deals with whether your house is made of straw, sticks, or bricks. Turbulence deals with how hard the big bad wolf is blowing at your house. Therefore Systemic Risk does not necessarily indicate that a financial crisis is imminent, only that global markets are more susceptible to bouts of turbulence.

The rest of this article will proceed as follows.

  • For both indicators, we will discuss their original calculations and use cases (as suggested by their creators), as well as my personal modifications to the calculations.
  • Next, we will review the dataset used to calculate both indicators.
  • Lastly, we will analyze the behavior of both indicators during previous financial crises. This exercise will showcase how by prudently interpreting both indicators, an investor could have mitigated his losses in prior crises.

Financial Turbulence Indicator

Kritzman and Li (2010) present “a mathematical measure of financial turbulence” based on the Mahalanobis Distance.

Qualitatively: financial turbulence is a condition where

  • Asset prices move by an uncharacteristically large amount.
  • Asset prices movements violate the existing correlation structure (the “decoupling of correlated assets” and the “convergence of uncorrelated assets”).

If both conditions are satisfied, turbulence will be higher than if only one of the conditions are satisfied.


From “Skulls, Financial Turbulence, and Risk Management” (2010)

Use cases for Financial Turbulence include stress-testing investment portfolios, building turbulence-resistant investment portfolios, and scaling exposure to risk. More details in Kritzman and Li (2010).

This article focuses on the “scaling exposure to risk” use case.

My personal modifications to the calculation. In Equation (2) above, the left-hand-side of the equation is called “Raw Turbulence” in my Turbulence Chart. In order to create a smoother, more interpretable turbulence metric, I calculated the exponentially weighted moving average (EWMA) of the “Raw Turbulence” series, and call it “Turbulence”. This means that every data point in the “Turbulence” series is equal to the EWMA across *all* the previous “Raw Turbulence” values, where more recent “Raw Turbulence” values are given a higher weight. The decay factor “alpha” is set such that the half-life of each value’s weight is 12 weeks (12 weeks is approximately the length of 1 fiscal quarter).

Systemic Risk Indicator

Kritzman, Li, Page, and Rigobon (2010) introduce “a measure of implied systemic risk called the absorption ratio”.

Qualitatively: high systemic risk exists if global asset price movements can be *mostly* explained by a small number of independent factors.

Quantitatively: the absorption ratio (AR) equals the fraction of the total variance of a set of asset returns explained or “absorbed” by a fixed number of eigenvectors (of the asset return covariance matrix).

From “Principal Components as a Measure of Systemic Risk” (2010)

The main use case for the AR is to indicate market fragility in various ways. More details in Kritzman, et al. (2010).

This article focuses on using the AR to provide context for interpreting the Turbulence Index.

My personal modifications to the calculation. First, I calculate the asset return covariance matrix over a 250-week window (250 weeks is approximately 5 years). This window shifts forward for each new data point. Second, instead of using the AR formula above, the “Systemic Risk” series in my Systemic Risk Chart is the Gini coefficient of all the eigenvalues for the asset return covariance matrix. This way, we don’t have to arbitrarily choose the number of eigenvectors in the numerator of the AR formula above.

The Dataset

Both indicators can theoretically be calculated across any pool of financial assets. To choose which assets to include in my pool, I used the following criteria:

  1. Encompass all major global financial markets. Therefore, my asset pool includes 6 international stock market indices.
  2. Include asset classes that describe several investor risk-return dimensions. For instance:
  • US Assets vs. International Assets
  • Stocks (risky) vs. US Treasuries (“risk-free”)
  • Aggressive Industries (cyclical) vs. Defensive Industries (counter-cyclical)
  • Small Market Capitalization (more risky) vs. Large Market Capitalization (less risky)
  • Long Term debt (more risky) vs. Short Term debt (less risky)
  • High Yield debt (more risky) vs. Investment Grade debt (less-risky)

With these considerations in mind, the final asset pool is:

The Sales Pitch (or, “How These 2 Indicators Can Make / Save You Money”)

Using these 2 indicators as “early warning signals” for financial crises, investors can achieve higher absolute returns with less volatility.

The remainder of this article will illustrate the hypothetical “Turbulence-based Strategy” in the chart above.

Consider an investor who can make the following 3 choices:

  1. Be 100% invested in the U.S. stock market (S&P 500 Index).
  2. Be 50% invested in the U.S. stock market.
  3. Be 0% invested in the U.S. stock market (the investor is holding cash).

Let’s step into the shoes of this investor, starting in November 1996.



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