Volatility Drag and ETFs, from Mr. Isomorphisms
0.95 is lower than 1 /1.05. For this reason a 5% increase followed by a 5% decrease (or vice versa) results in a net decrease. *
In researching volatility drag, with respect to daily vs monthly ETF's (and levered vs unlevered ETF's) I am drawing near to the conclusion that the famous drag phenomenon might be due to a flaw in design rather than in execution. If you design a product to match *percentage* moves, you will induce drag.
The discussions I've read of this phenomenon all go too deep (AM-GM inequality, Jensen's inequality, geometric averaging, lognormal returns, ….) into maths to pick up what I think might be the root flaw of some of these 3rd-gen / 4th-gen ETP's.
* .95 and 1.05 aren't the best numbers to see the mismatch. 1 / 0.5 = 2, not 1.5.
Comments
Jim on October 3, 2015 12:09 am
This piece should be required reading for traders of leveraged ETFs: http://www.math.nyu.edu/faculty/avellane/thesis_Zhang.pdf
The key insight is that the loss due to path-dependency is proportional to:
(k - k^2) / 2 * int(v^2 dt,0,t)
Where k is the leverage ratio, v is volatility, and t is time.
Example:
Double long (k=2): (2 - 2^2) / 2 = -1
Double short (k=-2): (-2)^2 - (-2) / 2 = -3