Understanding the Relationship between VIX and the S&P 500 Index Volatility

We study the VIX Index, often referred to as “the investor's fear gauge,” relative to the observed volatility of the S&P 500 Index to investigate the relationship between these two measures of financial markets variability and to understand the directionality of their influence on one another. Calculated as a weighted average of put and call options on the S&P 500 Index, the VIX is considered as a forecasting indicator of the S&P 500 Index's volatility over a one-month period. We examine the daily VIX and S&P 500 Index volatility data for the 20-year period between 1990 and 2009 and find that VIX lags the S&P 500 one-month volatility for the period that we study. Furthermore, we analyze the VIX Index and the S&P 500 volatility for different time periods, when the financial markets exhibit: (i) higher level of stability with volatility below two standard deviations from the mean and (ii) lower stability regimes, with volatilities above two standard deviations from the mean. We find that in general, the VIX overestimates the S&P 500 Index volatility during the stable financial market regimes, and underestimates the S&P 500 Index volatility throughout high volatility periods