Case solved: no arbitrage

Apology to the readers - I got too excited and did not read prospectus carefully enough. The fair value of XXV should be calculated as $20 * (1-return on VXX). I used Aug 4, 2010 as a reference price, since it is the first trading day for XXV, however prospectus says that the reference price should be the one from "inception date" of July 16th. On that date VXX closed at 109.48 (adjusted for split) , creating the following formula:

simulated XXV = $20 * (1 - (VXX-109.48)/109.48 )

which results in values that are fairly close to actual XXV values. See prospectus on page PS-7 for the proper formula.


For more exact calculation I reverse-engineered a better reference price of 108.03, which is probably close to the VWAP price of VXX on that day, making the formula

simulated XXV = $20 * (1 - (VXX-108.03)/108.03 )

This answered my previous question of why XXV return was lower than VXX - it was not, I just was using the wrong reference price. The second question was regarding volatility - XXV has about half of daily volatility of VXX. Here again the explanation is fairly simple - as VXX goes lower its dollar volatility decreases, and dollar volatility of XXV decreases, but in % terms XXV volatility decreases because XXV is now at a higher price.

In fact I can make a prediction that at some point as VXX goes lower, XXV will approach its maximum value of $40 slowly, penny by penny.

I want to thank all the readers who emailed me with their comments, especially William W. for his helpful explanations!