**By Keith H. Black, PhD, CFA, CAIA**

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The CBOE Volatility Index (VIX) measures the implied volatility on S&P 500 Index options with a 30 day forward expiration. Widely termed the “fear gauge,” the VIX rises rapidly when stock prices fall, but declines when stock prices rise.

The Chicago Board Options Exchange (CBOE) lists both call and put options on the S&P 500 Index. These options vary across strike prices and expiration dates. VIX is simply the average of the implied volatilities of all options listed in the two months closest to expiration. Because the weight between the two expiration months changes every day to maintain a 30 day constant maturity, VIX is not directly tradable.

Options prices are often calculated using the Black-Scholes options pricing formula. The variables that determine the option’s price are the time to expiration, strike price, index price, interest rates, dividends and volatility. At any given time, all of these factors, with the exception of volatility, are known quantities. In order to determine the level of volatility implied in the option’s price, an options calculator is used.

The implied volatility is the market’s best estimate of the annualized standard deviation of the price changes of the stock market over the coming 30 day period. From 1993 to 2011, VIX has ranged from below 10% to over 80%, but has been between 14.3% and 24.6% approximately half of the time. While VIX averaged 20.8% over the last eighteen years, volatility has been significantly higher over the last three years, averaging 27.7% between 2008 and 2011. When market volatility is expected to increase, such as during periods of corporate earnings announcements and political risk, options prices and VIX tend to increase.

While stock and options prices are not normally distributed, the normal distribution can be used to understand the implications of market volatility estimates. For example, at 10% volatility, and the S&P 500 Index at 1300, the market is estimating approximately a 68% probability that the S&P 500 Index will trade between 1170 and 1430 one year from today, which is one standard deviation away from the current Index level. At 30% volatility, the range of outcomes is much wider, with a 68% probability that next year’s stock market level will be between 910 and 1690.

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VIX consistently shows a negative correlation to returns on the S&P 500 Index, averaging -0.63 since 1993 and -0.83 over the three months ending December 2011. A long position in VIX, then, is frequently used to hedge positions in stock market investments. The volatility of VIX is very high, averaging 99% since 1993, while the volatility of the S&P 500 has averaged less than 20% over the same time period. A little VIX, then, goes a long way, so investors are encouraged to trade VIX at a smaller size than their typical stock position. Leveraged VIX products have an even higher volatility.

VIX rises rapidly when the S&P 500 declines, but falls more slowly when the S&P 500 rises. While the hedge ratio can vary with the exchange-traded product, as well as over time, the front month futures may have a beta of -1.7 to the S&P 500 index, while second month futures may have a beta of -1.2.

Empirical evidence shows that VIX, and market volatility, are mean reverting. This means that when VIX is at extremely high levels, it is likely to move lower, while it is likely to move higher when trading at extremely low levels.

*Keith Black has more than twenty years of financial market experience, serving approximately half of that time as an academic and half as a trader and consultant to institutional investors. He currently serves as Associate Director of Curriculum for the CAIA Association. During his most recent role at Ennis Knupp + Associates, Keith advised foundations, endowments and pension funds on their asset allocation and manager selection strategies in hedge funds, commodities and managed futures.*

*He is the author of the book “Managing a Hedge Fund,” as well as the co-author of the 2012 editions of the CAIA Level I and Level II textbooks. Dr. Black was named to Institutional Investor magazine’s list of “Rising Stars of Hedge Funds” in 2010. He earned a BA from Whittier College, an MBA from Carnegie Mellon University, and a PhD from the Illinois Institute of Technology. Dr. Black previously served as an assistant professor and senior lecturer at the Illinois Institute of Technology.*

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## 3 Comments

August 17, 2012 at 4:05 pm## Gaston