The impacts of the coronavirus on the global economy: Part III The Global Financial Turbulence Score and the VIX

I have taken another pulse of the stock markets by recalculating the global financial turbulence scores using the latest weekly benchmark indices and compared them to the VIX, a volatility index, published by the Chicago Board Options Exchange (CBOE). An option is a contract that gives its owner the right to buy (in the case of a call option) or to sell (in the case of a put option) an underlying asset (e.g., a stock) at a specified price and date. The CBOE is the world's largest options exchange. Figure 1, below, plots both the turbulence scores and the VIX. The VIX is also known fear index.

Figure 1: Global Financial Turbulence Scores and VIX, Jan 8, 2000 - Mar 21, 2020

The global financial turbulence score is backward-looking, as it is based on historical benchmark indices. On the other hand, the VIX is an implied volatility index, as it is the market expectation of the next 30-day fluctuations in the S&P 500 that results from solving numerically an option pricing model. While the VIX has the advantage of being forward-looking, it has the disadvantage of being derived from a theoretical model that might not always hold true empirically.

At the end of last week (i.e., on March 20), both the turbulence score and the fear index went down, respectively, from 12.9 to 9.4 and from 66.04 to 61.59. This means that, even if the global financial crisis caused by the outbreak of the COVID-19 is still going on, stock markets became less volatile and investors that were betting on the future evolution of stock prices by trading options also became somewhat less pessimistic. Since the outbreak of the COVID-19, the highest values of both the turbulence score and the fear index were recorded on March 13. (Recall that trading paused on March 9 and 12 on the New York Stock Exchange, as its benchmark S&P 500 plunged below the 7% threshold of the market-wide circuit breakers.) Both the turbulence score and the fear index date the on-going financial crisis back to February 21, where their values rose sharply, respectively, from 1.4 to 6.2 and from 17.08 to 40.11.

It appears in Figure 1 that there is a co--movement between the turbulence score and the fear index. In general, when stock markets are very turbulent, investors are also very pessimistic about the future. For example, during the 2007-08 financial crisis and the on-going health crisis, both time series reach a peak. However, during the oil price crash, the turbulence index quadrupled going from 2.74 to 11.57 on January 9, 2015, whereas the fear index only rose from 17.55 to 20.95 (which represents a 19.3% increase). On November 10, 2017, whereas the turbulence score was decreasing, the fear index rose. Figure 2 shows the scatter plot of both time series.

Figure 2: Scatter Plot of the Global Financial Turbulence Scores and the VIX, Jan 8, 2000 - Mar 21, 2020

The correlation coefficient between the turbulence score and the fear index is .64. However, as it appears in Figure 1, during quiet periods, the relationship between these two time series is not as strong as it is during turbulent periods.

Dataset and Code

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The Latest Global Financial Turbulence Scores.

Date	Score
Feb 14, 2020	1.36
Feb 21, 2020	6.23
Feb 28, 2020	3.68
Mar 6, 2020	9.74
Mar 13, 2020	12.89
Mar 20, 2020	9.37

The components indices of the global financial turbulence score

(1) NYA: the New York Stock Exchange composite index, (2) IXIC: the NASDAQ composite, (3) N225, the Tokyo Stock Exchange average index, (4) FTAS, the London Stock Exchange FTSE all share, (5) HSI, the Hong Kong Stock Exchange index, (6) N150, the Euronext Next 150 index, (7) GSPTSE, the Toronto Stock Exchange composite index, (8) BSESN, the Bombay Stock Exchange sensitive index, (9) GDAXI, the Frankfurt Stock Exchange performance index, (10) AXJO, the Australian Securities Exchange S&P 200, (11) SSMI, the SIX Swiss exchange mid-cap index, and (12) IBOVESPA, the Brazil Stock Exchange index.

Formula

$$d_t² = (r_t - μ ) Σ ^-1 (r_t - μ )',

where $d$ denotes the turbulence score, the vector $r$_t lists the current growth rates of the benchmark indices, the vector $$ μ their historical averages, and $$ Σ designates their variance-covariance matrix. For further details, see Mark Kritzman and Li Yuanzhen (2010).