Is VIX at Appropriate Level?

 - On Friday, June 1, 2012, S&P500 Index closed below its 200-day Simple Moving Average.  Why is this significant?  Many investors look at the 200-day moving average as the "unofficial" gauge to declare whether the US stock market is in a "Bull" or "Bear" market.  Many technical analysts also believe 200-day moving average serves as a strong support or resistance level.

-One facet of the equity markets where the significance of whether the S&P500 Index is above or below its 200-day moving average is in Volatility measures or specifically VIX.  I ran some analysis on SPDR S&P500 (SPY) ETF and VIX to determine the statistical probability of VIX levels dependent on whether SPY prices are higher or lower than its 200-day moving average.  The results are shown on the first graph.

- The solid blue-line represents on any given trading day, the probability that VIX would be higher than a specific level when SPY is greater than its 200-day MA since January of 1994.  The blue-dash line represents the same figures but the period since January of 2008.  The reason I chose to look at the time period since January 2008 is because the financial crisis of 2008 and the current crisis affecting Europe (and the rest of the world) are considered to be part of the same phenomenon.  The red line and red-dash line represent probability of VIX being higher than a specified level, except this time the condition being SPY below its 200-day MA.


 - The results are not surprising but highly informative. On Friday, June 1, 2012, the value of VIX was at 26.66.  According to my analysis, the probability that VIX would be higher than 26 level is only 7.18% when SPY is higher than its 200-day MA but jumps to 48.17% when SPY is below its 200-day MA since 1994.  These figures jump even higher when looking at time period since 2008, 9.57% and 64.57%, respectively.  If we consider 50/50 probability to determine the appropriate VIX level, then the current VIX level of 26.66 is not too far off from the "appropriate" level calculated to be between 25.5 and 30.3.

- Now, just because in one trading day, SPY penetrated below its 200-day moving average does not make the "appropriate" VIX level jump from 18-20 range when SPY is higher than its 200-day MA to 25.5 to 30.3 range when SPY is below its 200-day MA.  Rather, VIX moves in a time-series or trend and its outcome is not binary.  However, I do believe that the US equity markets and VIX levels are at a point of inflection. The price trend of SPY in the near-term (few days to a few weeks) could determine whether VIX continues to soar or plunges back down.

- There are other methods to measure the "appropriate" level of VIX.  Based on options theory, the theoretical value of options or "appropriate" implied volatility level of options should not be too far off from the estimated value of future, actual or realized volatility level of the underlying instrument.  Traditionally, historical volatility has been used as a gauge to estimate future realized volatility.  The second chart is a graph from IVolatility.com (http://www.ivolatility.com/) and shows the trend of the IVolatility's calculation of mean implied volatility levels on SPY options (in yellow) compared to the 30-day historical volatility trend of SPY (in blue).  According to values from IVolatility.com, the mean Implied Volatility Index was at 23.77% on Friday, June 1, 2012, while 30-day historical volatility level was at 14.42.

- GARCH models are more sophisticated ways of estimating future volatility of the underlying.  V-Lab posts updated figures of estimated future realized volatility levels of thousands of underlying instruments and indices (http://vlab.stern.nyu.edu/).  According the V-Lab, the 1-month predicted realized volatility of the S&P500 Index is 17.07 (third graph shows the trend of V-Lab's GARCH model estimate), compared to at-the-money implied volatility level of around 20 for S&P500 Index June/July options.

- Based on historical volatility or GARCH model measures, one could conclude that implied volatility levels of SPY or S&P500 Index options are in-line or "appropriate" or even slightly overvalued.  If the discrepancy between estimated future volatility and implied volatility levels got too out of line, options traders would buy of sell options to raise or lower the implied volatility levels to profit from what is known as volatility arbitrage.

- Finally, there is another model that I have developed, called "Fair Value Estimate" (FVE) Model.  Instead of trying to estimate future realized volatility of SPY or S&P500 Index, FVE calculates the "appropriate" VIX level on any given moment based on price action of SPY.  Because FVE Model's focus is on the VIX, it has been an indispensible tool for me to analyze the VIX and price levels of VIX-related instruments, such as VIX futures and VXX.

- The fourth graph shows a chart of VIX in comparison to FVE Indicator (in red) since 1993.  Currently, the FVE Model is indicating that VIX is overvalued and significantly so.  The top indicator, also in red, is a filter showing instances when VIX was spiking up and FVE was 20% lower than VIX since 1993.  What is of significance is that each and everytime VIX experienced a significant uptrend, FVE had either led or was concurrent with the rise in VIX.  Furthermore, every time VIX was over 20% higher than FVE Indicator's value, VIX reached its top and began dropping within a week period.  The exception was in 1998.  In August 14, 1998, VIX was 34.75 or 25.5% higher than FVE Indicator's value of 25.87.  Instead of dropping, VIX continued rising to a top of 45.74 on October 8, 1998 before ultimately returning to the 20 level.  This time period coincided with the Russian Financial Crisis and Fed's bailout of Long-term Capital Management.

- In conclusion, I presented four different methods of analysis on the VIX.  Based on the SPY being above or below its 200-day moving average, I presented probabilities that VIX could easily move either above 30 level or back down to below 20 level.  That would undoubtedly depend on developments (or lack thereof) coming out of Europe and possible action by central banks.  I also presented three different models to calculate the "appropriate" level of VIX.  The models are indicating that VIX could be "overvalued" or at best appropriately valued, which is slightly a contrarian view given all the uncertainty surrounding Europe and global economy's health.  Regardless of what transpires in the coming days, US markets are at a point of inflection.