I had earlier written an article titled Where Do Volatility ETPs Go From Here? to present my predictions for the values of the various volatility ETPs, VXX, UVXY, SVXY, and XIV, for September expiration. I had presented the output of my model, which showed the following end values for these ETPs, depending on the end value of VIX.

VIX | VXX | UVXY | SVXY | XIV |

$ 12.0 | $ 11.9 | $ 23.2 | $ 133.2 | $ 33.9 |

$ 12.5 | $ 12.4 | $ 25.2 | $ 128.0 | $ 32.5 |

$ 13.0 | $ 12.9 | $ 27.3 | $ 123.1 | $ 31.3 |

$ 13.5 | $ 13.4 | $ 29.4 | $ 118.6 | $ 30.2 |

$ 14.0 | $ 13.9 | $ 31.7 | $ 114.4 | $ 29.1 |

$ 14.5 | $ 14.4 | $ 34.0 | $ 110.5 | $ 28.1 |

$ 15.0 | $ 14.9 | $ 36.4 | $ 106.8 | $ 27.2 |

$ 15.5 | $ 15.4 | $ 38.8 | $ 103.4 | $ 26.3 |

$ 16.0 | $ 15.9 | $ 41.4 | $ 100.1 | $ 25.5 |

$ 16.5 | $ 16.4 | $ 44.0 | $ 97.1 | $ 24.7 |

$ 17.0 | $ 16.9 | $ 46.7 | $ 94.2 | $ 23.9 |

$ 17.5 | $ 17.4 | $ 49.4 | $ 91.5 | $ 23.3 |

$ 18.0 | $ 17.9 | $ 52.3 | $ 88.9 | $ 22.6 |

$ 18.5 | $ 18.4 | $ 55.2 | $ 86.4 | $ 22.0 |

$ 19.0 | $ 18.9 | $ 58.2 | $ 84.1 | $ 21.4 |

$ 19.5 | $ 19.4 | $ 61.2 | $ 81.9 | $ 20.8 |

$ 20.0 | $ 19.9 | $ 64.4 | $ 79.8 | $ 20.3 |

The key determinant, of course, is the ending value of VIX. In this article, I present three approaches to predict where VIX will be by September expiration.

First, I used my own volatility prediction model, the logic of which was earlier presented in an article titled Is VIX Too Low? And Where Do Volatility ETPs Go From Here?

I will not repeat the logic of that model, and would instead request interested readers to look up the model by reading the earlier article. This model is predicting that there is 50% chance that VIX will be at or below 12.3%, 84% chance (1-sigma) that VIX will be at or below 14.0%, and 97.5% chance (2-sigma) that VIX will be at or below 15.7%.

Next, I used an EGARCH volatility prediction model, which is pretty much industry standard. This is a variant of ARCH time series analysis models. From Wikipedia

In econometrics,

AutoRegressive Conditional Heteroskedasticity(ARCH) models are used to characterize and model observed time series. They are used whenever there is reason to believe that, at any point in a series, the terms will have a characteristic size, or variance. In particular ARCH models assume the variance of the current error term or innovation to be a function of the actual sizes of the previous time periods' error terms: often the variance is related to the squares of the previous innovations.Such models are often called

ARCHmodels (Engle, 1982), although a variety of other acronyms are applied to particular structures of model which have a similar basis. ARCH models are employed commonly in modeling financial time series that exhibit time-varying volatility clustering, i.e. periods of swings followed by periods of relative calm.

I will not go into the details of ARCH, GARCH, and EGARCH, which is quite technical and dry, but interested readers can look it up. In layperson's terms, these models when used for forecasting volatility recognize that volatility patterns have clusters in them. Low volatility periods are followed by more low volatility periods, and high volatility periods, in turn, are followed by more high volatility periods. Hence, to forecast the future, these clusters need to be taken into account in addition to other inputs like historical volatility. The EGARCH model predicts a VIX of ~14.4% by September expiration, which is in between my 1- and 2-sigma predictions (14.0% and 15.7% respectively).

Finally, I tried to look back in history and see if I could predict VIX spikes from historical S&P and VIX changes. To analyze that, I first looked at the largest dips in S&P 500 in the last 4 years. Since S&P has already dipped by ~3.9% from its all-time high, I only looked at dips that were 3.9% or more. This is the result.

Start | End | Start S&P | End S&P | Start VIX | End VIX | ΔS&P | ΔVIX |

4/29/2011 | 10/3/2011 | 1363.6 | 1099.2 | 14.8 | 45.5 | -19.4% | 208.1% |

4/23/2010 | 7/2/2010 | 1217.3 | 1022.6 | 16.6 | 30.1 | -16.0% | 81.2% |

4/2/2012 | 6/1/2012 | 1419.0 | 1278.0 | 15.6 | 26.7 | -9.9% | 70.5% |

1/19/2010 | 2/8/2010 | 1150.2 | 1056.7 | 17.6 | 26.5 | -8.1% | 50.8% |

9/14/2012 | 11/15/2012 | 1465.8 | 1353.3 | 14.5 | 18.0 | -7.7% | 24.0% |

2/18/2011 | 3/16/2011 | 1343.0 | 1256.9 | 16.4 | 29.4 | -6.4% | 78.9% |

5/21/2013 | 6/24/2013 | 1669.2 | 1573.1 | 13.4 | 20.1 | -5.8% | 50.4% |

10/19/2009 | 10/30/2009 | 1097.9 | 1036.2 | 21.5 | 30.7 | -5.6% | 42.8% |

9/22/2009 | 10/2/2009 | 1071.7 | 1025.2 | 23.1 | 28.7 | -4.3% | 24.3% |

11/5/2010 | 11/16/2010 | 1225.9 | 1178.3 | 18.3 | 22.6 | -3.9% | 23.7% |

There have been only 10 instances in the past 4 years where S&P fell by more than 3.9%. The average drop for these 10 instances is 8.7%, and the average spike in VIX is 65.5%. However, I believe that it makes no sense to consider the 2011 instance, as that dealt with the 2011 debt ceiling crisis and the resulting downgrade of US debt by the S&P. That will come, I am sure, in October-November timeframe. But for usual market volatility from QE tapering, I would consider the bottom 9 of the instances. These have an average S&P drop of 7.5%, and a VIX spike of 49.6%.

Here's the chart.

As you can see, the R^{2} is very healthy at ~75%, which is about as good as it gets for real life data. A lot of people are calling for a 5-10% drop in the S&P 500 from the tapering, which matches the average 7.5% drop in the historical period. Plugging that into the equation, we get a VIX spike of ~55% from the day the S&P 500 hit its all-time high. That day (August 2nd) VIX was at ~12. So, it is possible that if we get a 7.5% drop, VIX will spike to ~18.5.

However, I remain skeptical about a 7.5% drop. In May and June when taper madness was in full swing, we only got a ~6% drop in S&P. Since then, we have had a good earnings season. My S&P model indicates that even adjusting for taper, S&P is actually undervalued, as noted in an article titled The S&P 500 Is Undervalued, Not In A Bubble. Hence, I would be surprised if we get more than a 5% drop in the S&P 500 from tapering alone (debt crisis is another story), which means a VIX spike to 15.75 per the above equation. Of course, a lot will depend on the September employment numbers.

So, to summarize, these are the 3 techniques I tried.

1. My own VIX prediction model is indicating 14-15.7 for end value of VIX by September expiration

2. EGARCH is indicating 14.4

3. Historical analysis is indicating 15.75, assuming no more than a 5% drop in S&P 500 from all-time high

With that, I am therefore going to predict (famous last words!) that VIX will be in the 14-16 range by September expiration. This means per my volatility ETP model, VXX will be in the 14-16 range, UVXY in the 32-41 range, SVXY in the 100-114 range, and XIV in the 25-29 range. However, my models underestimate VXX and UVXY drops, and SVXY and XIV gains. Adjusting for that, VXX will be 13.5-15.5, UVXY 29-38, SVXY 103-117, XIV 26-30.

That's my prediction, and I am sticking to it. September will be rather volatile, so I am not putting in too much money behind these predictions; however. I will write a follow-up article on trading strategies to benefit from this modeling exercise.

**Disclosure: **I am long XIV, SVXY, and I hold puts and calls on VXX and UVXY. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.