From August 2^{nd }to October 3^{rd}, 2011 Barclays’ S&P 500 VIX Short Term Futures ETN (VXX) had a great 137% runup. In that same period VelocityShares’ TVIX ETN, 2X leveraged on the same index went up an astonishing 348%, 73 percent more than its 2X leverage factor would project. How is that possible? Don’t inverse and leveraged funds always underperform the index they’re tracking?

Normal market price action is typically random, with the number of up and down days about equal. This bouncing back and forth is really bad for inverse and leveraged funds. A classic example is a two day sequence of 10% up one day followed by a 9.091% move down.

Fund | Day 1 (+10%) | Day 2 (-9.091%) | Gain / Loss (excess) |

1X (underlying) | 100 * (1+ 0.1) = 110 | 110 * (1-0.9091) = 100 | 0% |

-1X (inverse) | 100* (1-0.1) = 90 | 90*(1+.09091) = 98.18 | -1.8 % (1.8% loss) |

2X | 100 * 1+2*(0.1)) =120 | 120*(1+2*(-0.09091) = 98.18 | -1.8 % (1.8% loss) |

3X | 100 * 1+3*(0.1)) =130 | 130*(1+3*(-.09091) = 94. 55 | -5.45% (5.45% loss) |

The non-leveraged fund ends up unchanged. But all the daily rebalanced -1X, 2X and 3X leveraged funds suffer. For more on rebalancing see Under the hood of a leveraged ETF.

There wasn’t much back and forth for TVIX in the Aug/Sept 2011 timeframe.

The average daily increase in VXX was 2% —which went on for 44 trading days. Looking at just 3 days of ongoing 2% gains we get the following results:

Fund | Day 1 (+2%) | Day 2 (+2%) | Day 3 (+2%) | Gain / Loss (excess) |

1X (underlying) | 100 * (1+ 0.02) = 102 | 102 * (1+ 0.02) = 104 | 104 * (1+ 0.02) = 106.1 | 6.1% overall gain |

-1X (inverse) | 100* (1-0.02) = 98 | 98* (1-0.02) = 96.04 | 96.04* (1-0.02) = 94.12 | 5.88% loss (0.24% excess) |

2X | 100 * 1+2*(0.02)) =104 | 104 * 1+2*(0.02)) =108.16 | 108.16 * 1+2*(0.02)) =112.49 | 12.49% overall gain (0.24% excess) |

3X | 100 * 1+3*(0.02)) =106 | 130 * 1+3*(0.02)) =112.36 | 112.36 * 1+3*(0.02)) =119.1 | 19.1% overall gain (0.8% excess) |

When carried out for 44 days the projected excess gain for TVIX given a constant +2% daily change in VXX gives a theoretical excess of 288%. The actual excess gain was “only” 73% because VXX did have a few down days along the way.

During this timeframe leveraged funds had 3 things going for them:

- Volatility as measured by VIX trending higher
- Backwardation in the VIX futures was boosting VXX
- The increases in VXX were steady, without a lot of random motion—resulting in a positive compounding effect.

These three conditions are relatively rare, happening roughly once every two years.

On the other hand, these three conditions are considerably more common:

- Volatility as measured by VIX is trending down
- The VIX futures term structure is in contango
- The decrease in volatility is steady, without a lot of randomness—resulting in a positive compounding effect.

These conditions were satisfied from mid-June to mid-October this year, and the performance of inverse volatility funds was impressive. The chart below shows $1K invested in Barclays’ medium term volatility product VXZ, and ZIV, VelocityShares’ -1X daily reset medium term volatility ETN.

VXZ went down 36.4% during this 3 month period, ZIV was up 52.7%. This hat trick on inverse volatility paid off nicely.

#### Related Posts

- Backtests for Popular Long & Short Volatility Exchange Traded Products
- A 3D View of the S&P 500: Price, Time, and Markets
- The Cost of Contango—It’s not the Daily Roll
- 10 Questions about Mid-Term Volatility
- The Volatility Watcher’s Toolkit

Saturday, February 23rd, 2013 | Vance Harwood