*fear index*or the

*fear gauge*and represents a measure of the stock market's expectation of volatility of the S&P 500 Index over the next 30 day period. The VIX generally has a negative correlation to price returns of the S&P 500 Index.

The VIX is the second major volatility index created. The first major volatility index, now referred to as "VXO," was created in 1993 and represents a measure of the implied volatility of S&P 100 index options. The creators of the VXO index retroactively determined its closing values dating back to January 2, 1986. VXO was the most widely-followed volatility until the VIX was created in 2003 to track the implied volatility of S&P 500 index options. Closing values for the VIX index were retroactively determined dating back to January 2, 1990.

The VIX is calculated and reported in real-time by the Chicago Board Options Exchange. The VIX represents a weighted blend of prices for a range of options on the S&P 500 index. The VIX is calculated as the square root of the par variance swap rate for a 30 day term initiated on today's date. The VIX represents the volatility of a variance swap, not a volatility swap. A variance swap may be perfectly statically replicated through vanilla puts and calls whereas a volatility swap requires dynamic hedging. The VIX is the square-root of the risk neutral expectation of the S&P 500 variance over the next 30 calendar days and is quoted as an annualized standard deviation.

The chart below (click on the chart for a larger view) shows closing values for the VIX dating between January 2, 1990 and October 18, 2013. As shown, during this time period the VIX closed at values ranging from 9.31 (achieved on 12/13/1993) to 80.86 (achieved on 11/20/2008), with an average closing value of 20.25.

Several additional indexes have been derived from the VIX. Among them are the VIX Short Term Futures Index and the VIX Short Term Futures Inverse Daily Index. Both of these derivative indexes were created in 2007 and closing values for these indexes were retroactively determined dating back to December 20, 2005.

The VIX Short Term Futures Index utilizes prices of the next two near-term VIX futures contracts to replicate a position that rolls the nearest month VIX futures to the next month on a daily basis in equal fractional amounts. This results in a constant one-month rolling long position in first and second month VIX futures contracts.

The VIX Short Term Futures Inverse Daily Index measures the performance of the inverse (determined daily and on a percentage basis) of the VIX Short-Term Futures Index. Accordingly, if the VIX Short Term Futures Index rises 2% during a trading session, the VIX Short Term Futures Inverse Daily Index is designed to drop 2% (e.g., the inverse sign of the percentage movement of the underlying index).

The VIX Short Term Futures Index has experienced a strong downward bias in price movement since its creation as a result of contango. "Contango" refers to a situation where a longer term future has a higher price than a short term future. The VIX Short Term Futures Index replaces one-month futures with two-month futures - this process is commonly referred to as a future roll. If the two-month future is trading at a higher price than the one-month future, the value of the VIX Short Term Futures Index may decrease as a result of this futures roll. However, there are occasions during which the price of the two-month future is less expensive than the price of the one-month future such that the futures roll increases the value of the VIX Short Term Futures Index - this situation is known as "backwardation."

If the spot price of the VIX increases, the VIX Short Term Futures Index will normally also increase unless the VIX Short Term Futures Index is in a state of contango. Based on my own observations, the VIX Short Term Futures Index is normally around 30-40% as volatile as the VIX index. Accordingly, if the VIX spot price increases 10% in a day, the VIX Short Term Futures Index will often rise 3-4% unless the VIX Short Term Futures Index is in a state of significant contango.

When the price of the VIX is below its long-term average of 20.25, the VIX Short Term Futures Index is usually in a state of contango. However, when the price of the VIX is much higher than its long-term average of 20.25, the VIX Short Term Futures Index is usually in a state of backwardation.

The charts below show linear and log views of the daily closing values of the VIX Short Term Futures Index between December 20, 2005 and October 18, 2013. During this period of time, the VIX Short Term Futures Index plummeted from a value of 100,000 to a value of 1,319.20, a drop of about 98.68%, or an annualized drop of about 42%.

As shown in the charts above, the VIX Short Term Futures Index has been a terrible speculative investment. Although it has risen sharply during several periods of time, it is clear the strong downward bias of the index quickly wipes out accumulated gains over time. A heavily traded ETN with the symbol VXX tracks the VIX Short Term Futures Index.

The VIX Short Term Futures Inverse Daily Index, on the other hand, has experienced a strong upward bias since its creation. Between December 20, 2005 and October 18, 2013, the VIX Short Term Futures Inverse Daily Index rose from a value of 100,000 to a value of 393,853.39, an increase of about 293.85%, or an annualized increase of about 19%. This return is all the more impressive considering that the worst financial crisis since the Great Depression occurred during this time period. As a point of reference, the total return of S&P 500 Index was about 63.7% during the same time period, or an annualized gain of about 6.5%.

I was able to obtain daily closing values for the VIX Short Term Futures Inverse Daily Index dating back to January 11, 2008. I obtained daily closing values for the VIX Short Term Futures Index dating between December 20, 2005 and January 10, 2008 and used this data to estimate the daily returns for the VIX Short Term Futures Inverse Daily Index dating back to December 20, 2005. The charts below show a combination of (a) estimated daily closing values for the VIX Short Term Futures Index between December 20, 2005 and January 10, 2008; and (b) the actual daily closing values for the VIX Short Term Futures Index between January 11, 2008 and October 18, 2013.

As shown in the charts above, the VIX Short Term Futures Inverse Daily Index has been a fantastic speculative investment. Although it has fallen sharply during several periods of time, it is clear the strong upward bias of the index quickly overcomes index drops over time. There are two popular investment vehicles for capturing the gains of the VIX Short Term Futures Inverse Daily Index: (a) the Proshares Short VIX Short-Term Futures ETF (symbol: SVXY); and (b) the VelocityShares Daily Inverse VIX Short-Term ETN (symbol: XIV).

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