Implied market volatility (as measured by VIX) is determined by a reflexive loop between the derivative and underlying markets based on future estimate of realized volatility of the underlying + characteristic movements of the underlying. There are of course many more factors that affect the VIX--such as skew of implied volatility curve, day of the week, holidays in a given month, upcoming events that could impact the market--just to name a few.

Ok, I apologize if I am losing the interest of the readers with confusing terminology or definitions. I will keep it as simple as possible from hereon. In a nutshell, an investor could get a good sense of whether VIX is cheap or expensive based on simple analysis of 1) Various GARCH model estimates and 2) Median Curve of VIX dependent on (NYSEARCA:SPY) prices in relation to its various moving averages. Please allow me to walk you through this process.

The first step involves looking at estimates of future realized volatility. V-Lab is an excellent website to get up-to-date estimates on the S&P500 Index based on various GARCH models (the second link is to Wikipedia for technical definitions of GARCH). In V-Lab, click on SPX, and several analyses of S&P500 Index will show. I like to look at EGARCH return series (just a personal preference). The graph below is from V-Lab, and shows EGARCH vol prediction for future realized volatility of the S&P500 Index. As of July 4, 2012, the value was 15.68%.

One should then compare this number to the At-The-Money [ATM] implied volatility level of July/August S&P500 Index options, depending on number of days to go before expiration. Since we are about half way though July month expiration, we could average July ATM implied volatility of 14% and August ATM implied volatility of 15% to get 14.5%. ATM implied volatility numbers can be found in Morningstar's website under "Options" tab for SPY.

Usually, volatility values from EGARCH model are higher than implied volatility values of ATM options. The reason is that investors would rather buy options than sell them, given a 50/50 outcome of a gain vs. a loss, because the potential payout of unlimited gain and limited risk is far more attractive. Furthermore, if the EGARCH model estimate of 15.68% proves to be accurate, options theory tells us that one could purchase ATM options straddle at an average 14.5% volatility level and dynamically scalp deltas at 15.68% volatility level for a theoretical profit. Commissions, slippage and other costs could eliminate any profits, but these costs are very low for market makers. To market makers, the current situation would be like owning free options, and free options are always good. **Based on realized (future estimate) volatility analysis, I would say that current implied volatility levels are cheap or undervalued.**

The second step is to look at median values of VIX dependent on where SPY prices are relative to its various moving averages. The chart below shows analysis that I conducted. Median value represents 50/50 probability of VIX being above or below a specified level based on historical data.

For example, since 1994, shown in black & grey, when SPY prices were in an uptrend and above moving averages, the median VIX level was around 18%, while when SPY prices were in correction and below the moving averages, the median levels were between 22-26%. I would say that the 20-day, 50-day, & 200-day moving averages are most widely followed.

I also included two other plots showing "distinct" periods when VIX remained high or low for extended periods of time. Between 2003-2007, shown in blue & cyan, VIX levels remained low. The median VIX level when SPY prices were above its moving averages was around 13.6%, while when SPY prices were below its moving averages, median VIX levels ranged from 16.4-24.4%. On the other hand, between 2008-2011, shown in red & orange, VIX levels remained high. The median VIX levels during this period were 20.5% and 26-31%, respectively.

I believe the long-term median VIX values in black & grey are more befitting to the current market environment in 2012. Therefore, **based on probability analysis, the current VIX level of 16.6 is low compared to the 18% level, indicating 50/50 probability.**

Finally, the third chart below shows the graph of VIX relative to my own Fair Volatility Estimate [FVE] Indicator. FVE takes into calculation the future realized volatility estimate and characteristic movements of SPY as well as other factors in a visually simple indicator. According to FVE, VIX is clearly undervalued.

Now that we have walked through this process and determined that VIX is cheap or undervalued based on 1) estimate of future realized volatility and 2) historical probability, how can we make money off of this analysis?

Unfortunately, VIX is not an instrument one could realistically trade. There are instruments that have been created based on VIX futures, but these instruments have complex idiosyncrasies of their own. Let us look at iPath S&P500 VIX short-Term Futures ETN (NYSEARCA:VXX), because it is by far the most popular VIX-related instrument available to retail investors.

Let us assume that, based on our previous analysis, we believe with high likelihood that VIX would rise to the 19 level (14% higher than the July 3rd closing value of 16.66) quickly and remain at that level until the morning of July 18th. VIX July futures and options expire and settle at the spot VIX level on the morning of July 18th. At first glance, a 14% rise in VIX within 2 weeks appears to be a very attractive situation to go long VXX. **However, investors should not buy VXX as a bet on rising volatility until the following analysis is conducted.**

VXX is an exchange traded note that holds a daily rolling position of first two month VIX futures. The current price levels of July and August VIX futures prices are 17.7 and 20.2, respectively, as of July 3rd. Since we are about half-way through July expiration, VXX would be holding about 1/2 July VIX futures and 1/2 August VIX futures in its portfolio. If VIX were to rise to 19 level and remain there by VIX settlement, that would mean that the expected percentage rise or fall of VXX from current level would be 0.5*(19/17.7) + 0.5*(**20**/20.2) - 0.25*(20.2/17.7-1).

How did I come up with the above calculation? The first part is the expected percentage gain/loss of July VIX futures. The second part is the expected percentage gain/loss of August VIX futures, with 20 being the expected price of August VIX futures at July expiration. Front month VIX futures on average trade 5-6% higher than the spot VIX, with a full month to go before expiration. Finally, the third part of the equation takes into account contango in VIX futures and the cost of daily roll that VXX ETN incurs from selling July VIX futures to Buy August VIX futures, and the assumption that the current steepness in the contango would subside by 50%.

If we plug in the numbers, we would get 99.6% or a 0.4% decline in VXX price. **As shocking as it may seem, even if VIX were to rise to the 19 level by July 18th, based on our forecast, the forecasted price of VXX, which closed at 13.90 on July 3rd, is expected to fall 0.4% to 13.85.** Some of the assumptions made in our calculation could change, but this clearly illustrates how much of a disadvantage it is to buy and hold VXX for any extended period of time. Unless we were confident that VIX would rise much higher above 20 level within 2 weeks, it would not be worthwhile to buy VXX, either as a portfolio hedge or as a bet on rising volatility for periods of more than a couple of days.

Perhaps the best strategy given the current volatility environment and our analysis of both VIX and VXX above would be to buy VIX July Futures (17.70 closing on July 3rd). Another (superior risk adjusted) strategy would be to buy July VIX futures and sell either August or September VIX futures as a spread. When VIX rises, front month VIX futures should rise a greater percentage than back month futures. For investors without commodities accounts, a similar strategy would be to buy VXX and sell (NYSEARCA:VXZ) in equal dollar amounts. VXX holds front two month VIX futures contracts, while VXZ holds fourth, fifth, sixth and seventh month VIX futures contracts. Once again, the logic that front month VIX futures should rise greater than back month VIX futures applies. Furthermore, even if VIX were not to rise, VXZ should fall by a greater percentage than VXX. This VXX/VXZ pairs trade takes advantage of the current steepness of VIX futures contango along its term structure, and is a bet this steepness will level off. One needs to be careful when executing this pairs trade, because VXZ is not very liquid, thus the bid/ask spread is relatively wide.

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