Over the past year I have read many articles on Seeking Alpha, such as this, "Playing Inverse Volatility for Easy Gains," advocating why right now may be a good time to buy the XIV instead of shorting the VXX. I am here to dispute this claim and prove to you why if you had the choice of shorting the VXX or buy the XIV,** you would want to short the VXX.** Forgetting all of the "headline" risk and European sensationalism that seems to dominate our day-to-day lives, let's get to the math.

Firstly, my initial projection is that the Spot VIX will eventually revert to its mean (historically about 20.2-20.8) and drag down the VXX with it. When the spot VIX reached over $35, my initial reaction was to buy the XIV but after some careful analysis I didn't and this is why.

If the VXX drops from 41 to 21 in one day that is a 50% drop and correspondingly the XIV would rise from 6(1.5) = 9. However, it all depends on *how* the XIV gets there and this is based on daily re-balancing. If the VXX drops one dollar every day then the % rises in the XIV will be higher thus putting it close to $12. This is where it gets tricky, due to daily re-balancing the XIV actually gets pounded in times of high volatility. Below is a simulation of what would happen to the XIV were it to cross VXX at $36 three times.

VXX | % VXX | XIV |
---|---|---|

36 | $6.48 | |

48 | -33.33% | $4.32 |

44 | 8.33% | $4.68 |

43 | 2.27% | $4.79 |

40 | 6.98% | $5.12 |

38 | 5.00% | $5.38 |

37 | 2.63% | $5.52 |

36 | 2.70% | $5.67 |

34 | 5.56% | $5.98 |

33 | 2.94% | $6.16 |

40 | -21.21% | $4.85 |

38 | 5.00% | $5.10 |

37 | 2.63% | $5.23 |

35 | 5.41% | $5.51 |

As you can see in a simulation of the VXX crossing 36, three times, the XIV is still lower. This is due to extended amounts of backwardation that will crush the XIV.

Here are the descriptive statistics I ran through MegaStat over a time-series period of 11/30/10 - 11/2/11; this is what I found:

- The correlation matrix = -.954 almost perfect negative correlation.
- r^2 = .910 Almost a perfect "goodness of fit."
- Durbin-Watson Test = .13 --> almost perfect negative autocorrelation.
- Kurtosis for XIV -1.0480 and VXX is -0.7184. Higher values indicate a higher, sharper peak; lower values indicate a lower, less distinct peak.
**This is where the XIV Fails to follow the VXX as it displays a higher sharper peak.** - Mean for XIV is 12.80 and VXX is 32.59
- Sample standard deviation for XIV is 4 and for VXX is 8.6. This tells me a one standard move (68% of all values) is way too HIGH for XIV.
- XIV +or minus 1std.dev = 8.8<=12.80<=16.80
- VXX +or minus 1std.dev = 24<=32.59<=41.19

**Now over a one-year period why is the XIV down 40% and VXX barely down on a percentage basis?** The answer to that question is the daily rebalancing (plus some XIV black-box formula not disclosed in their prospectus) and this is why there is an almost perfect negative correlation and goodness of fit on a daily basis. Despite all the volatility we have recently had, over a longer period of time, the VXX (blue) is a better short than a Long XIV (red) over a longer-period of time, and here is a chart to back it up.

**11/7/11 VXX (blue) vs. XIV (red)**

**One-year chart - VXX (blue) vs. XIV (red)**

In this case it's a no-brainer to short the VXX over going long the XIV. I am fully aware of the risks of shorting the VXX and its "unlimited risk." However, the VXX will erode over time due to negative decay roll, and the XIV will erode itself in times of high volatility and be unable to recover its highs. The high of the VXX when it opened was $400 and if you had shorted even in the $100s, it is safe to say you're short is still profitable. Although a 100% gain from the year-low in August of $20 to year-high of $55 looks to be an extreme rise (150%+). Over the long run, your VXX short will far out-perform an XIV long, which is down over the same time period from $19 to $6.

- The VIX futures roll yield probably costs 8% per month due to constant contango
- Contango exists in the futures market much more often than not. According to Chad Gray the VIX has an upward sloping curve about 75% of the time.

And since many of us don't have the time to read the prospectus, here it is directly from the horse's (XIV's) mouth:

Daily rebalancing will impair the performance of the ETNs (NASDAQ:XIV) if the underlying index experiences volatility.

You may lose all or a significant part of your investment in the ETNs if the index increases or does not decrease by an amount sufficient to offset the applicable fees and charges.

**Disclosure: **I am short VXX.