VXX Calculations, VIX Futures and Time Decay

As I type this, the VIX is up about 6.5% for the day and VXX is only up about 2.0%.

While it looks like today is a good day to be long volatility, getting 4/13 of the move in the VIX with a VIX ETN does not look like an efficient way to play the volatility trade. In fact, I have discussed the issue of what I call the VXX juice factor on a number of occasions and have concluded that on average, anyone owning VXX should not expect to capture more than 50% of the move in the VIX, at least based on data since the January 30^th launch of VXX. Going forward, however, 40% might be a more realistic target.

A reader asked about the extent to which VXX returns may be adversely impacted by time decay, rolling and other issues.

When it comes to VXX price erosion, there are two primary factors to consider. The first is the mean-reverting tendency of the VIX and VIX futures. The second factor is the daily rebalancing of the two VIX futures that are utilized to calculate the value of VXX.

The VXX calculation is derived from the two nearest months of VIX futures. At the moment, this means the May futures and the June futures. For the sake of simplicity, I will refer to these as the front month and second month futures. I’ll explain the calculation with an example.

VIX options expire on Wednesday, May 20^th this month (see 2009 expiration calendar), which means that at the close of business on the day before expiration, May 19^th, VXX will hold exclusively the June VIX futures (VX-M9). As each calendar day passes, VXX will sell 1/23 (there are 23 trading days in the current VIX options expiration cycle) of the June VIX futures position and buy an identical amount of the July VIX futures, so that the percentage holdings of the front month and second month futures always create a synthetic blend of a basket of VIX futures with a constant maturity of 30 days. [Note that this is different from the calculations of the cash VIX, where the front month and second month options roll forward one month 8 days before VIX options expiration.]

As long as the near month and second month futures are similar in price, the daily rebalancing has little effect on the price of VXX. When the term structure has a steep slope and there is a substantial difference in price between the front month and the second month (as was the case with SPX options on 11/20/08), the daily rebalancing can generate its own profit and loss. As the graphic below shows, there was a 0.75 difference between the May and June futures settlement prices yesterday. Calculating 1/23 * 0.75, yesterday’s daily rebalancing probably resulted in a 0.03 change in price.

In terms of pricing implications, when VIX futures are in contango (upward sloping over time, second month more expensive than front month), there will be a daily loss of value due to rebalancing. On the other hand, when VIX futures are in backwardation (downward sloping over time), the daily rebalancing process will generate a gain.

Following the launch of VXX on January 30^th, VIX futures were consistently in backwardation until the beginning of April, at which point the term structure flattened out. At present, there is some slight contango that could adversely impact VXX prices going forward. Technically, this rebalancing is called "roll yield" and when the roll yield becomes negative, VXX prices will suffer daily losses as a result.

For more on this subject I recommend Standard & Poor’s white paper on VXX returns: Directional Exposure to Volatility Via Listed Futures

For more details on VXX, iPath has two documents worth checking out:

• Prospectus
• Information Sheet

[graphics: FutureSource]

Disclosure: Long VIX and VXX at time of writing.