# How to lose your money without really trying

April 27, 2009 in

I am very interested in the topic of leveraged ETFs (I wrote on it just last week) - and a key point I always come back to is that levered ETFs exhibit a negative drift over time. I illustrated this by plotting the inverse double levered financials ETF (SKF) vs its underlying index, the IYF. The IYF was down 66% and the SKF, which by design rises when the IYF falls, was down 16%.  That should be warning enough that leveraged ETFs do not move as common sense might expect.

One can go through the math and actually prove that

$r_L = (r_U)^x\exp\left(\frac{(x-x^2)\sigma^2N}{2}\right)$

where $r_L$ and $r_U$ are the respective ETF and underlier N-day returns, $x$ is the ETF leverage ratio and $\sigma$ is the N-day realized volatility. Critically, the term in the exponent must be less than one, which accounts for the negative drift. The negative drift term grows as either leverage or volatility increase, so levered ETFs are actually short volatility! As the authors of the linked piece put it:

The gross return of a leveraged or inverse ETF over a finite time period can be shown algebraically to be simply the gross return of the ETF's underlying index over the same period raised to the power of the leveraged multiple of the ETF, multiplied by a scalar that is less than one.

If not for the negative drift, a fantastic trade idea would be to buy both a highly-levered long and short ETF on the same underlier, taking full advantage of the non-recourse leverage: wait for the underlier to move far from it's current position, at which point one of the ETFs will be at zero but the other will have more than doubled, netting a profit. Unfortunately over time and without careful management such a position is a deathwish.

But C.S. Jefferson at Seeking Alpha has actually recommended that investors do just that - with the long and short triple-levered financial ETFs! He has even put on the trade himself! His reasoning shows that he has the entire concept backwards (in particular with regard to volatility):

In options trading, [the trade] would be somewhat reminiscent of trading a long “strangle” or “straddle” position by buying volatility. The fundamental difference is that in theory, unlike options facing expiration dates, you are not exposed to timing it to the moment the market makes its move...

The real potential outcome and goal is that the multiplier effect should push either side of the trade much higher with returns outpacing the downside losses. Because of these current price levels, your maximum loss on either side of the trade should be capped at approximately eight dollars or less per share if one approached zero, while the inverse correlation on the other side of the trade has unlimited upside.

The only way this trade can be profitable is in a sustained trend, where the "strangle" delta component outweighs the short volatility piece. Think of a simple example - the underlier moves up 10% and then down 10%.  Both the double levered long and short start at 100 and end at 96, a net loss of 4%. Now instead take a trend like two consecutive days +10% and you wind up making 4%.  But even trends can be treacherous:  follow that +10% trend with two days of -10% and you lose money all through the reversal.  The only circumstances under which this strategy works is if a trend starts immediately after putting it on, or if a later trend is sustained for a considerably long time.

Amazingly, Jefferson even recognizes the fact that this trade would have lost massive amounts of money in the past and views it as a "dislocation" or opportunity (I'm taking these two paragraphs out of order; emphasis is mine):

It’s bizarre, but if you had tried to apply this same strategy upon inception of the newly devised ETFs in the fall of last year, the outcome would have been brutal had you held and you would have taken a major beating on both ends of the trade. Clearly, the ineffectiveness of some of these similarly leveraged and inverse structured ETFs do not perform as promised. In fact, in hindsight, the ultimate trade on some of these newly issued ETFs may have been to short both sides of the trade from the get go. But without the luxury of hindsight, I would never have made that trade anyway.

You would have to assume that the design of both FAS and FAZ was to provide divergent instruments, both moving in opposite directions. However, due to extreme volatility and price dislocations in the markets since the fall of 2008, this financial crisis has presented opportunities that were unintentional. These ETFs were not designed to trade in tandem on a parallel course and trajectory rapidly approaching zero as they have recently. Interestingly enough, we now have a crisscross intersection of lines if you graph both positions to suggest extreme price dislocation.

In fact, if he had read the prospectus he would see that these ETFs perform exactly as promised and exactly as they were designed.  Woe be unto the trader who trades a product he does not understand.  Aside, it's unclear why he is obsessed with the fact that the ETFs traded at the same dollar price, causing their price graphs to intersect.  Clearly he subscribes to the school of investors that believe stock splits matter.  Let's be clear - the dollar value of a stock's price is irrelevant; that's doubly true for ETFs whose prices depend solely on percentage moves of their underliers.

The obvious retort to all this is to short both ETFs.  Plainly, if what I'm saying is true, both have strong downward trajectories.  And the answer, as you might expect, is maybe.  A double-short strategy would most likely play out over time (and certainly has in the past) but would be subject to extreme mark-to-market swings as short-term trends grow the value of one side of your short but not the other (ironically, the very move Seeking Alpha is looking to capture in the long run). The resulting margin calls could be disasterous; look at a backtest of Seeking Alpha's trade to see why.

As to C.S. Jefferson's other suggestion - "Back in early March, I opted to enter a trade of writing naked equity puts which initiated my first entry on the FAS ETF" - I can't even express the horror I feel from a risk management perspective.  However, because this trade worked out for him in March (as did every short), he is looking for an opportunity to put it on again.

Update 10/27: The joke is on us! In April I wrote, "The only way this trade can be profitable is in a sustained trend," and 6 months later the unprecedented equity rally resulted in this trade being very profitable indeed. Please do not make the mistake of confusing return for an absence of risk, however.

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