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Wednesday, July 4, 2012

Probability Analysis of VIX (in greater detail)

In the previous post "Assumptions Behind FVE Model", I wrote that implied volatility is a reflexive function of realized volatility of the underlying + statistical relationships on supply & demand of options based on characteristic movement of the underlying.  Basically, an investor could get a good sense of the "appropriate" value of VIX based on the analysis of 1) realized (future estimate) volatility & 2) characteristic movement of the underlying.  I am going to walk through this process.

First, using various GARCH models, one could calculate an annualized volatility number of the future volatility of the underlying from 1 week to 1 month out.  In the case of S&P500 Index, the following link (http://vlab.stern.nyu.edu/analysis/VOL.SPX:IND-R.EGARCH) provides updated values from several GARCH models.  The first chart in this post shows these numbers in graph form from one of the models.  The latest value is 15.68%.  One should then compare this number to the At-The-Money (ATM) implied volatility level of July/August S&P500 Index option, depending on days to go before expiration.  July ATM implied volatility is around 14% while August ATM implied volatility is around 15%.

Based on realized (future estimate) volatility analysis, I would say that current implied volatility levels are low or undervalued.  Usually, volatility values from various GARCH models are lower than ATM implied volatility values.  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 at an average14.5% implied volatility level and dynamically scalp deltas at 15.68% volatility level for a theoretical profit.  Of course, commissions, slippage, and other costs would come into play, but these costs are very low for market makers.  To them, the current situation would be like owning free options, and free options are always good...should the EGARCH model estimate prove to be accurate.

Second, I have calculated the median values of VIX dependent on where the SPY ETF price is relative to its various moving averages since 1994.  As shown in the second chart (in black & grey), the median value (50/50 probability) for VIX when SPY is above its moving averages is around 18%, while it ranges from 22-26% depending on whether SPY has fallen below its corresponding moving averages.  I would say the 20-day, 50-day, & 200-day moving averages are most widely used.  I have also included two other "distinct" periods when VIX remained high or low for an extended period of time.  Between 2003-2007, VIX remained very low, with median VIX levels around 13.6% during SPY rising trend and 16.4-24.4% during SPY falling trend (shown in blue & cyan).  On the other hand, between 2008-2011, VIX remained very high with corresponding median VIX levels of 20.5% and 26-31% (shown in red & orange).  I believe the long-term median values in black & grey are more befitting to the current market environment in 2012.  Based on probability analysis, current VIX value of 16.6 is low compared to 18% median value.

Finally, the third chart above shows graph of VIX relative to FVE.  As described in the previous post, FVE takes in to calculation realized volatility and characteristic movement of SPY, as well as other factors.  According to FVE, VIX is clearly undervalued.

However, an investor must always consider that models, even the best ones, do not predict outcomes, but only try to calculate expected or more likely outcomes.  As in Texas Holdem, even with a 90% probability of winning the hand, one could lose everything especially if one bet all-in.  Calculating appropriate VIX levels in the methodology described above is still much more of a challenge.

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