Inside Volatility Trading: Breaking Down the VIX Index and its Correlation to the S&P 500 Index

Scott Bauer

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June 21, 2022

The VIX® Index is a financial benchmark designed to be an up-to-the minute market estimate of expected volatility in the S&P 500 Index and is calculated by using the midpoint of real-time S&P 500® Index (SPX) option bid/ask quotes. The VIX Index generally tends to have an inverse relationship with the S&P 500 Index and historically when the S&P 500 Index declines the VIX Index generally tends to increase. Simply put, the VIX Index tells us the level of expected volatility of the S&P 500 Index for the next 30 days, with a 68% confidence level, or a one standard deviation of the normal probability curve.

Although the VIX Index isn’t expressed as a percentage, it can be understood as one. For example, if the VIX Index is at 28, this represents an expected annualized change with a 68% probability of less than 28% in the S&P 500 Index, in either direction. With the S&P 500 Index trading at 3,900 (as of June 10^th), this correlated into a projected range of 2,808 – 4,992 over the next year. Calculating potential movement in the S&P 500 Index using the VIX Index on a shorter basis is a bit more complicated. The expected volatility for a single month can be calculated from this figure by dividing the VIX Index level of 28 not by 12 (since there are 12 months in a year), but by the square root of 12 (approximately 3.46). This would imply a move of 8.09% over the next month or a range of approximately 3,585 – 4,215 during that time frame. Similarly, expected volatility for a week would be 28 divided by the square root of 52 or 7.21. This implies a move of 3.88% over the next week or a range of approximately 3,749 – 4,051. (Source: Six Figure Investing)

Since the VIX Index uses calendar day annualization (365 days) rather than many historical/realized volatility measurements which use trading day annualization (252 days), the daily expected volatility is calculated by taking the current VIX Index level divided by the square root of 365. With the VIX Index at 28, the daily expected volatility is 28 divided by 19.1. This implies a daily move of approximately 1.46%. As mentioned above, while the VIX Index generally tends to move in the opposite direction of the S&P 500 Index, this relationship is not always maintained. In fact, about 20% of the time, the VIX Index and S&P 500 Index move in the same direction. (Source: macroption)

Using data from Barchart I created a comparison of the daily move in the S&P 500 Index (close to close) to the VIX Index, from January 3 – June 10 of this year. The average daily move in absolute terms in the S&P 500 Index during this time was approximately 1.24% which correlates to a VIX Index level of slightly lower than 24. (24/19.1). The average daily reading for the VIX Index during the same period was 26.04.

S&P 500 Index vs. VIX Index Implied Move

^{Source: Barchart}

In summary, the comparison between the VIX Index and movement in the S&P 500 Index is close, about an 80% correlation, which confirms the reality of the two generally tending to move in opposite directions most of the time. In addition, the correlation generally tends to remain relatively stable throughout different market conditions. For more information on the CBOE VIX please reference https://www.cboe.com/tradable_products/vix/

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