### Equity Volatility Indices: VIX, VXN, VXD, RVX

The present research will go through the most popular equity volatility indices proposed by the CBOE. The aim of the research is to identify how they fluctuate and to quantify the magnitude of their movements. The actual study will be followed by a second one entirely focused on commodity volatilities and the examined asset classes will be Gold and WTI Crude Oil (the **HyperVolatility Forecast Service** provides market projections for the VIX, Gold, WTI crude oil and many other asset classes. Send an email to **info@hypervolatility.com** and get a free 14 days trial). The great attention towards volatility indices and the remarkable popularity gained by VIX futures are surely undeniable but what is the risk involved in these markets? What is the volatility index that best fits your trading style and portfolio needs? Do you know how the VIX performs compared to other volatility indices? The **HyperVolatility**** **team trades and analyzes volatility movements on a daily basis on different asset classes and the present study is a summary of some of our findings. The examined data sample goes from January 2011 until April 2013 and the present research will examine 4 equity volatility indices: the VXN (Nasdaq 100), the VXD (Dow Jones), the RVX (Russell Index) and the VIX (S&P500). The first chart displays the distribution ranking of each index and it is a good approximation of how volatile the aforementioned indices can be:

The graph clearly indicates that, on average, almost all indices move within the 18% – 22% interval (the RVX is the only one above this range as its median is 23.43%). The lowest fluctuations, for all indices, are concentrated within the 9% – 12% range (the VXD is the only index showing a figure lower than 10%) while the wildest volatility explosions tend to group around the 45% – 48% area (the RVX again is the only outsider with a 58.84% peak). Statistically speaking, the most important intervals to consider are the 25%, the median and the 75% ones because they represent the most common spectrum of oscillation. Consequently, in case of low volatility most of the indices will tend to move within the 15% – 18% range (the RVX does not go below 20% though) while in high volatility environments equity volatility indices will tend to oscillate between 20% and 24% (the RVX is again the only outsider with 28.1%). The RVX is definitely the index showing the highest figures, which is normal given the fact that it tracks the volatility of less liquid stocks, but is it really the most volatile one? The answer is no because the fact that the RVX has an average value of 23.43% does not mean that it experiences the highest degree of fluctuations; it simply implies that the RVX is constantly higher than the others. In order to clarify this issue it is necessary to quantify the magnitude of the equity volatility indices’ movements. The next chart displays the volatility of the volatility indices. This time, however, the oscillations are expressed in monthly volatility because the CBOE indices are already annualized:

The chart evidently shows that the most volatile equity index, amongst those proposed by the CBOE since 2011 so far, is the VIX and not the RVX. The second most volatile is the VXD and the least volatile is the RVX. How is this possible? Wasn’t the RVX the index showing the highest values? The explanation is simple. The VIX and VXD indices have a higher variability rate because a fairly good amount of moves tend to be large, fast and powerful. On the other hand, the RVX has a lower variability because it tends to fluctuate more often around its mean value and consequently the dispersion is lower. The next graph, which plots the ranking of the dispersion rate for the volatility of CBOE equity volatility indices, will help to expand more this concept:

The graph confirms what previously stated: the VIX and the VXD are, on average, the most volatile indices. The 3^{rd} index is the VXN while the RVX is the one that experiences the lowest degree of diffusion. The dispersion of the VIX and VXD is the largest even for small and large moves indicating that these 2 volatility indices move a lot more quickly than the others. Almost all indices do not go over the 30% threshold but when large market moves happen the monthly volatilities reach 50% and in some cases, like the VIX, 60%. To sum up, the VIX and VXD are the most volatile indices while the VXN and RVX ranked 3^{rd} and 4^{th} respectively (it is worth reminding that the sample analyzed goes from January 2011 until April 2013). Financial markets have different risk dimensions and equity volatility indices make no exception. The next table tries to provide empirical evidence to quantify 1 of those dimensions: the intraday risk

Before getting started it is important to point out that the numbers reported in the table are volatility points. The intraday risk, on average, is around 1.35% for all equity volatility indices but the RVX reaches 1.5%. On the other hand, the table suggests that very large market moves can push equity volatility indices up or down by 13%, 14% or 15% in one single day.

However, one question, given the above mentioned results, would be particularly appropriate: wasn’t the RVX the least volatile index? If that is true, how come the intraday risk is higher?

The RVX index is more “dangerous” than other volatility indices as far as intraday risk is concerned. Nevertheless, even if the RVX fluctuates more wildly during trading hours its mean reverting pressure is higher in the medium term. In other words, the RVX is fairly volatile on a daily basis but it tends to mean revert towards its mean much more quickly than other indices. Furthermore, violent volatility bursts or aggressive drops tend to counterbalance themselves more effectively and in the medium term they result in a lower dispersion of the RVX with respect to its mean. The aforementioned phenomena explain why the RVX has a higher value in terms of volatility points but it is generally less volatile than the VIX or the VXD.

**Conclusions**

1) On average all indices tend to oscillate within the 18% – 22% interval

2) In case of low volatility, indices will tend to move within the 15% – 18% range while in high volatility environments the equity volatility indices will likely oscillate between 20% and 24%

3) The RVX is definitely the index showing the highest value in terms of volatility points but it is the less volatile because the mean reverting pressure is higher in the medium term

4) The most volatile equity indices, amongst those proposed by the CBOE, are the VIX and the VXD

5) The dispersion rate for the VIX and VXD indices is the largest even for small and large moves which means that they oscillate more quickly and frequently than others

6) Intraday risk is around 1.35% for all equity volatility indices but the RVX reaches 1.5%

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