Get your tin foil hats back out! Zero Hedge can’t seem to keep their manipulation theories under control (I addressed one here in one of TGR’s most popular posts) and today’s example is to egregious to pass up.
In this post, Zero Hedge reviews ground breaking “research” from Innovative Quant Solutions “on the very relevant topic of whether the VIX has any predictive power left at all, and just how gamed of an indicator has it lately become.” The brief is titled “Is the VIX Too Low?” and consists of six graphs, or appendices.
The VIX is a “volatility index;” its value corresponds to the annual volatility implied by options on the S&P 500 index. Without going into the details of its construction, its number should be interpreted as the mairket expectation of volatility over the next 30 days. Today, for example, the VIX moved back above 32, indicating that the expected annual volatility of the S&P 500 index over the next month is currently 32%. I should stress that the IQS analysis was performed on the 500 individual stocks which comprise the S&P 500, rather than the index itself.
Ultimately, for those who choose not to read ahead, I’ll demonstrate that IQS’s conclusions are based on flawed comparisons of a short term forward looking measure (VIX) and a long term historical reading (S&P annual realized vol), using merely graphs (no statistics) that have two axes (thereby preventing comparisons).
Here we go: Appendices A-C show the historical realized return and volatility of the S&P 500 components, and are of little analytical interest. Appendix D, however, is where the fun begins. Appendix D states:
We overlay S&P 500 of Equal-Weighted Returns (A) with the VIX. The pattern is consistent with intuition. Higher volatility of returns for higher VIX. The VIX has been declining while volatility of returns remains high. Is the VIX high enough for the latest data point?
Their question (“is the VIX high enough?”) is very difficult to answer by looking at the accompanying chart because it overlays returns and volatility on two axes. The relationship between returns and volatility is that between draws from a distribution and the distribution’s second moment; though there is a clear mathematical relationship, it is not one that can be inferred from a graph. Most obviously, returns can be negative and the VIX is always positive. Moreover, they are plotted on two axes! Adding a second axis is the easiest way to distort a chart – for example, the majority of the VIX points are plotted “below” the returns. That’s a choice of IQS, perhaps to enhance their argument that the VIX is too low. Either way, with two axes you can not make “too high” or “too low” observations because the height on the chart is arbitrary depending on the chosen scale.
Appendix E states:
We overlay S&P 500 Cross Sectional Volatility of Monthly Returns (B) with the VIX. Again, the pattern is consistent with intuition. The two lines seem to track each other quite well.
This chart has major problems as well. Specifically, it still has two axes and their very-different scales mean that the time series aren’t tracking at all. Yes, they are correlated, but if the VIX were really a volatility index, wouldn’t you expect it to at least have the same values as the volatility itself? For example, the last VIX point is about 29; the last standard deviation observation is about 12. The fact that they overlay is encouraging but hardly conclusive.
And now Appendix F, the prime evidence for the paper’s claim:
We overlay S&P 500 Volatility of Time-Series of Monthly Returns (C) with the VIX. The lines have tracked reasonably well over time. However, the latest data points suggest that either the VIX is too low or that recent realized volatility in returns will dampen sharply.
This chart shows incomparable time series. Specifically, it lines up the implied vol over the next 30 days with the realized vol over the last 12 months, a ridiculous pairing. Also, their two axes are coming back to haunt them: the last VIX observation is about 29; the last realized observation is about 36. If you just look at the graph, however, you might think the difference was much greater. This is a perfect example of why having two axes is extremely misleading.
So, what can we conclude from these junk charts? Nothing. Any message is lost in poor presentation and unclear comparisons. In reality, the VIX tracks 30-day vol quite well (if slightly overstating it); this is a well-known result. In “normal” times, the VIX even has some predictive power for S&P vol. In abnormal times, like 2008, the VIX only rises in lockstep with backward looking vol (no predictive power).
I have such a bad taste in my mouth from plodding through “research” like this. Tin foil hats may be removed.
is the expected return, 
is a benchmark hurdle, and 
is the standard deviation of the returns. If you buy into a Gaussian mean/variance paradigm, then the Sharpe ratio tells you how many units of excess return you receive per unit of risk you take.
is the downside deviation, or the standard deviation of returns below the benchmark. The intuition of using this statistic is that people do not penalize investments for positive volatility (i.e. unpredictable but beneficial returns); they only care about negative volatility.