Hack the market

This weekend I read Jason Zweig’s “Will leveraged ETFs Put Cracks in Market Close?” which references a paper by Minder Cheng and Ananth Madhaven at Barclay’s.   I tried, but couldn’t find their original paper over the weekend.  As luck would have it from across the internets Paul Kedrosky came to the rescue with a post referencing that paper, “The Dynamics of Leveraged and Inverse Exchange-Traded Funds“.

If you have any interest in ETFs, then you should read this paper carefully as it provides a very nice and accessible mathematical treatment of leveraged and inverse ETFs.

I’ve had success using ETFs in portfolio-oriented strategies to conveniently provide specific exposures, eg, to emerging markets.  I’ve also explored strategies that pit ETFs against futures and similar arbs that take advantage of contract rolls or other anomalous behaviors across the markets.  But I’ve never looked at ETFs the way they really should be understood: as structured products that should have well-defined (if not necessarily obvious) properties.

Like many structured products, some of these characteristics are not obvious and may be quite unintuitive but are always important to understand.  For instance, the hedging required to implement these funds is both non-linear and asymmetric.

Specifically, leveraged ETFs must re-balance their exposures on a daily basis to produce the promised leveraged returns. What may seem counterintuitive is that irrespective of whether the ETFs are leveraged, inverse or leveraged inverse, their re-balancing activity is always in the same direction as the underlying index’s daily performance. The hedging flows from equivalent long and short leveraged ETFs thus do not “offset” each other. [...]

The impact is particularly significant for inverse ETFs. For example, a double-inverse ETF promising -2X the index return requires a hedge equal to 6X the day’s change in the fund’s Net Asset Value (NAV), whereas a double-leveraged ETF requires only 2X the day’s change. This daily re-leveraging has profound microstructure effects, exacerbating the volatility of the underlying index and the securities comprising the index.

Hence Mr Zweig’s concern that these ETFs feed the volatility we’ve seen for the last 8 months or so near the market close.  If the day has been up then both “bull” and “bear” levered ETFs will need to buy in order to stay hedged – reinforcing the trend and effectively supporting serial correlation of returns.

Another important property of levered and inverse ETFs is that they are designed to track the daily returns of their underlying index which does not mean that over the long term they will faithfully track the returns of their index.  Cheng and Madhaven illustrate that this can be viewed as an embedded path-dependent option within the product.  This is graphically illustrated with two charts of DIG and DUG over a shorter and longer period.  Over a short period, they track each other admirably, mirror-like, as one would expect.  But over a longer period they diverge quite spectacularly.  In fact, in the example below, one would have lost money betting on either over the same period!

"Heads I win, tails you lose" - ProShares

Another interesting result of Cheng & Madhaven’s research is that the “[hedging] demand as a fraction of closing volume is a non-linear function of return…”.  Thus, the greater the move in the underlying index, the hedging activities of these ETFs will have a (non-linearly!) greater market impact on the close.

There are other gems in here as well including hints at pricing options on these ETFs, and techniques for quantifying the market impact of hedging activities.  But don’t take my word for it.  Go read the original!