Volatility and correlation-based systemic risk measures in the US market

• This paper tests some systemic risk measures based on correlation matrices using Granger-causation of the S&P 500 and the VIX indexes.
• This paper deepens the discussion around eigenvalues entropies in Finance, showing some theoretical considerations about the impact of negative correlations.
• The indicators are shown to Granger-cause the S&P 500 in all windows observed, but they do not necessarily Granger-cause the VIX.
• Their impact on the returns is highly dependent on the selected window.

This paper deals with the problem of how to use simple systemic risk measures to assess portfolio risk characteristics. Using three simple examples taken from previous literature, one based on raw and partial correlations, another based on the eigenvalue decomposition of the covariance matrix and the last one based on an eigenvalue entropy, a Granger-causation analysis revealed some of them are not always a good measure of risk in the S&P 500 and in the VIX. The measures selected do not Granger-cause the VIX index in all windows selected; therefore, in the sense of risk as volatility, the indicators are not always suitable. Nevertheless, their results towards returns are similar to previous works that accept them. A deeper analysis has shown that any symmetric measure based on eigenvalue decomposition of correlation matrices, however, is not useful as a measure of “correlation” risk. The empirical counterpart analysis of this proposition stated that negative correlations are usually small and, therefore, do not heavily distort the behavior of the indicator.