The prevailing wisdom on the volatility ETNs, VelocityShares Daily Inverse VIX Short-Term ETN (NASDAQ:XIV) and iPath S&P 500 VIX ST Futures ETN (NYSEARCA:VXX), is that XIV will rise over time and VXX will fall as long as the term structure is in contango more often than it's in backwardation. A recently elapsed period, slightly longer than a year, makes apparent that's not the case.

Over the period from 2-Mar-2015 to 18-Mar-2015, *both* XIV and VXX experienced substantial net losses. VXX declined -27.5%, while XIV declined -29.9% (Figures 1 and 2).

Figure 1. XIV prices |
Figure 2. VXX prices |

This loss for both ETNs over a prolonged period occurred while the term structure was in contango 73% of the time - 2.7X more often than it was in backwardation, as Figure 3 shows below. Why is that?

Figure 3. Percent Contango from 2-Mar-2015 to 18-Mar-2016

One way to answer this question is by reference to variance drain. I picked the period 2-Mar-2015 to 18-Mar-2015 for illustration purposes in this article because it happens that the average of percent daily returns over this period is very close to zero for both ETNs. You can see that in Figure 4 below, which shows running totals for the percent daily returns for the indexes of both ETNs. Running totals for each end at zero, which of course means that the average percent daily return was also zero.

Figure 4. Running total of daily percent changes.

The concept of variance drain was introduced by Tom Messmore in the context of comparing investment advisors based on average yearly percent returns. In brief, average periodic returns is a mathematically incorrect basis for comparison, since percentage gains accrue multiplicatively, not additively. This is best explained by example. Suppose you invest $100 in asset X. On Day 1, its market value falls by 25%. However, on Day 2, it rises by 25%. The average daily rate of return is (-25% + 25%)/2 = 0%. But your investment has not returned to its original value. Instead, it is now worth:

$100*(1-0.25)*(1+0.25) = $93.75

A 6.25% loss. Since multiplication is commutative, order doesn't matter. Investment Y that performs inversely to investment X, gaining 25% on Day 1, then losing 25% on Day 2 will also lose 6.25%. In general, this can be expressed as:

I_{0}*(1-α)*(1+α) = I_{0}-α^{2}, where I_{0} is the initial investment. Clearly, the larger α is, the greater the net loss.

Note that variance drain is not an actual loss. There's no counterparty to variance drain. Nor is it a frictional drag in the sense that fees or leverage cost are. Rather it's a demonstration that average periodic returns do not represent longer-term returns over multiple periods. In the case of the volatility ETNs XIV and VXX, the inverse relationship of their daily percent returns simply does not carry over to longer time periods, except by chance.

What this means is that the question of why both XIV and VXX lost value, which several readers have raised in the comment sections of recently published articles on the volatility ETNs, is only a question if one starts from an incorrect assumption - namely that XIV and VXX are inversely correlated over time periods longer than one day. Since they're not, both may lose value over time. Additionally, during time periods longer than one day when one loses as the other gains, those changes should not be expected to be equal and opposite.

It's also worth noting that excess of contango during this approximately one-year period did not result in XIV gaining value. On the contrary, it lost a substantial amount of its prior value. I'd like to encourage those who trade these ETNs to be certain the risks are well understood. Among those risks is the risk of placing too much faith in axioms and strategies that were formed during a period when the VIX was generally calm and declining. They may not apply during prolonged periods when the VIX is rising or is more frequently spiking.

**Disclosure:** I am/we are long XIV.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **I may initiate or close a long or short position in any of the volatility ETNs over the next 72 hours.