S&P 500's Daily Returns Vs Daily VIX Change.
The daily changes have been plotted by sorting the data from the highest daily increase in VIX to highest daily fall. This plot clearly conveys a high negative correlation between the daily movements of these 2 indices -- as the Fear index (VIX) increases, the S&P 500 index falls.
Using VIX to predict S&P Volatility
By definition, VIX is an indication of expected market volatility in the next 30 days. Plotting standard deviation of the 30-day forward S&P standard deviation (Y) against VIX (X) on that day, indicates a decently correlated graph. Correlations between these were found to be 72%. VIX can't explain about a quarter of the volatility we observe in S&P over the next 30-days.
While VIX only indicates expected volatility and doesn't claim to predict S&P returns, I still went ahead and tried to plot 30-day forward S&P returns (Y) against VIX (X). As expected, I found that VIX can only explain about 5.8% of the 30-day forward returns of S&P. The plot indicates a poor correlation.
Analysis was based on daily closing values of VIX and S&P indices from 05-2004 to 11-2024.
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