July 26, 2010 | By Adam Warner

\Just when you thought we had enough ways to bet on volatility without actually buying an option, along comes another one!

Yes, recently Barclay’s “miracled” us with XXV. What is XXV, you ask?

Inverse S&P 500 VIX Short-Term Futures ETN (NYSE: XXV) is the inverse VIX.

Well, more specifically, it’s inverse iPath S&P 500 VIX Short Term Futures ETN (NYSE: VXX). (See the prospectus here.)

At first glance, I figured XXV had the same tragic flaw of compounding math that makes all other contrived ETNs and ETFs perfectly fine to trade, but bad long-term investments.

**But that’s not really the case. XXV uses the original offering price as a basis rather than the day-over-day change.**

**The implication of this is very interesting. XXV will not gradually drift lower like similar products, but it might abruptly crash.**However, it also may prove to be a decent holding over time. Let me explain.

Here’s how they calculate the value of this exchange-traded note each day:

“The closing indicative note value for each ETN on any calendar day will equal (a) the principal amount per ETN plus (b) the inverse index performance amount on such calendar day plus (c) the accrued interest on such calendar day minus (d) the accrued fees on such calendar day; provided that if such calculation results in a negative value, the closing indicative note value will be $0.”

For the purposes of our analysis, we’re going to disregard (c) and (d). The principal amount was $20, so that’s (a). And, for (b), they give us this definition:

“On the initial valuation date, the inverse index performance amount for each ETN will equal $0. On any subsequent calendar day, the inverse index performance amount for each ETN will equal the product of (a) negative one times (b) the principal amount per ETN times (c) the index performance percentage on such calendar day.”

So the index performance is equal to (-1) x (20) x (index performance percentage).

They define index performance percentage as follow: “On the initial valuation date will equal 0%.

**On any subsequent calendar day, the index performance percentage will equal (a) (i) the closing level of the Index on such calendar day (or, if such a day is not an index business day, the closing level of the Index on the immediately preceding index business day) divided by (ii) the closing level of the Index on the initial valuation date minus (b) 100%.”**

So here’s the formula to calculate XXV on any given day (the “20″ in the formula is the principal amount of XXV; the “27″ is the (approximate) price of VXX on the day of the offering): It’s (20 + (-1 x 20 x ((VXX/27)-1)).

Now, let’s say on day one VXX lifts 10%. That produces a closing price of $18 for XXV. Pretty straightforward. On day two, VXX lifts another 10%, for a net rally of 21%. Throw that in the formula, and XXV is now worth $15.8. That’s down 12.2% for the day, a day in which VXX lifted 10%. So, as you can see, XXV will get disproportionately ugly in a VXX rally.

If on day three, VXX goes back to $27 where it started, that’s a 17.3% one-day drop. In response, XXV does actually bounce back right to $20. That’s a rally of 26.5% in response to a 17.3% drop in VXX. Get the picture?

The implications I see are as follows:

**There’s no compounding math problem here, i.e., XXV will not drift over time, per se. It might crash, though, because as you can see, it will have exponentially uglier reactions to VXX rallies when XXV is below $20.**If VXX roughly doubles from where it was when they set the XXV principal amount, then XXV goes to $0. I say “roughly,” because I didn’t account for accrued interest or expenses in this example.

But here’s the good news: It’s very tough to envision a scenario where VXX doubles. On a day-to day basis, it has to overcome the contango issue we’ve gone over. In a VIX explosion, that contango issue will evaporate as the term structure inverts. But that’s because VIX futures will not lift as much as the VIX, which is actually a worse situation for VXX.

I’m loathe to make judgments on a product a few days into its life, so take this with a grain of salt, but I believe you can hold this pup if you’re so inclined to bet against VXX. Just keep the dangers in mind, i.e., the potential for a compounded reaction to a VXX lift.

Follow Adam Warner on Twitter @agwarner.

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