A prime example of the evils of leveraged ETFs is the cumulative performance of the ProShares SKF fund, which tracks double the inverse returns of the Dow Jones U.S. Financials Index. Through July 2nd, the cumulative performance of the SKF since its inception in February 2007 is -33%, despite the underlying index, tracked by the IYF, being down by -63%. This sort of example has lead many to scream that leveraged ETFs "don't work."

While these results aren't intuitive, *this is more-or-less a caveat emptor situation, and there is a rebalancing strategy that will keep the cumulative performance of the SKF near -2x that of the IYF.*

First, the divergence is not principally caused by the daily returns of the SKF straying from -2x those of the IYF. Error in daily return replication is not the main issue. The answer is more basic. If you start with $100, make 10% and then lose 10%, you are left with $99. If you make 20% and then lose 19% you are left with than $97.20 even though the sum of your returns was positive. The more volatile the returns are, the more likely it is that you will have a situation where the sum of daily returns is positive but your cumulative return is negative. Higher leverage multipliers will also aggravate this effect.

Fortunately, this "volatility premium" problem is avoided by periodically rebalancing the position.

*The necessary adjustment is found by multiplying the original position size by the underlying IYF NAV ratio, divided by the SKF price.* The "NAV ratio" is the current IYF price divided by its adjusted price when the trade was initiated. Assuming no daily tracking error, if you initiate a $10000 position in SKF when IYF is at 100 and IYF immediately falls to 90, your 100 share position will be worth $12000. In order to maintain the -2x cumulative return ratio, you now only want 75 shares, or 10000 * (90/100) / 120.

If instead, IYF immediately went to $110, your position would be worth $8000 and the new target would be 138 shares, or 10000 * (110/100) / 80. Below is the result of such daily rebalancing before transaction fees.

The SKF now "works" and its cumulative return remains reasonably close to -2x that of IYF. The returns are a bit worse than ideal as there is some tracking error in the daily returns of SKF, and this error may be more or less pronounced in other ETFs.

Transaction fees are of course crucial and such trading will eat away at an account. Academic papers and exhortations to trade that ignore ignore fees are a pet peeve of mine. But you don't need to rebalance every day to approximate the effect. Rebalancing once a week does most of the work, shown here, assuming $8 in commissions per trade:

You could also try something like only rebalancing when the (IYF price / initial IYF price / SKF price) ratio changes by a certain threshold percentage since the last rebalance. With a 10% threshold, this method only required 20 new trades since the SKF inception in February 2007.

Below we see the results of an initial $10000 position which such sporadic end-of-day rebalancing, including fees. There will also be bid/ask slippage, but you get the idea.

This says nothing about money management stops and is not a recomendation of any particular position, strategy or parameter, but only a general framework for expressing longer-term views through leveraged ETFs. The system described might also involve margin calls.

CME has offered an inverse explanation of leveraged ETFs, noting the "negative gamma" exposure of ETF managers. The paper concludes, "there is a perfectly simple way of avoiding such gamma losses – using index futures." I have offered another approach here which essentially takes the other side of the ETF manager's daily hedging.

In fact, insofar as ETF manager hedging amplifies daily momentum into the close, one wonders if the above performance could be improved by rebalancing with limit instead of market orders.

**Disclosure: None**