Exchange traded funds (hereafter ETFs) have become increasing popular in recent years. Since the first ETF, SPR, lauched in 1993, the number of ETF’s has exploded to more than 700 today. ETFs, such as FAS, BGZ, BGU, EDC, EZA, etc are often the most actively traded stocks on US exchanges. As an investment vehicle, ETFs offer a cost efficient way of diversification and are a powerful tool in risk and tax management. Portfolio managers often incorporate them in their tactical asset allocations, market neutral strategies and sector/style rotations. As an integral part of many portfolios, ETFs give means to effectively improve meanvariance efficiency, achieving higher average returns for a given level of risk, or lower risk for a given average return. As a hybrid of an openended mutual fund and a stock, ETFs trade continuously throughout the day and investors can buy and sell options on them. This trading flexibility often makes ETFs more popular than their counterpart Indexes.
An increasingly popular subgroup of ETF, leveraged ETFs (hereafter LETFs), comes with a unique set of problems. Investors/ traders often have little understanding of the risks associated with trading LETFs. Leveraged ETFs promise double or triple daily returns of underlying indexes by leveraging double or triple index exposure. However, they also come with double or triple the risks. The volatility of daily returns erodes the value of LETFs. The longer the holding time and the higher daily volatility, the faster the decay. The tracking errors between LETFs and the indexes they track can be significant over a long period of time. As a pathdependent security, the return of a LETFs from the time period t to t+1 depends on not only the leveraged percentage change of index from t to t+1, but also how the values of index evolve from t to t+1.
Derivative Security
To achieve the targeted daily index exposure, the managers of LETFs invest all or a portion of their net assets in derivatives, mostly index futures, equity swaps and index options. Table 1 below shows the source of daily returns from 3X bull or 3X bear ETFs by Direxions. Since most, if not all, of exposure of LETFs comes from derivatives, LETFs are essentially a “derivative security”. This embedded pathdependent option can be viewed as a source of nonlinear return payoffs in table 2 below, taking from the prospectus by Direxions.
Table 1
Strategy 
Equities

Derivatives 
Bull Funds (3X) 
80100% 
200220% 
Bear Funds (Inverse) (3X) 
0% 
300% 
Furthermore, to maintain a constant leverage ratio requires the managers to constantly buy and sell derivatives, often at the exact wrong time. as Cheng and Madhavan (2009) of Barclays wrote in “The Dynamics of Leveraged and Inverse ExchangeTraded Funds”:
“Whether the ETFs are leveraged, inverse or leveraged inverse, their rebalancing activity is always in the same direction as the underlying index's daily performance: When the underlying index is up, the additional exposure of total return swaps needs to be added; when the underlying index is down, the exposure of total return swaps needs to be reduced.”
In essence, the managers have to “buy high and sell low" to achieve their targeted daily exposure. As depicted in the flow diagram below, rebalancing in adverse market conditions leaves the funds with a smaller asset base, which requires a larger return to get back to their original levels. In addition, the needs of rebalancing at the end of trading days often draw predatory trading practices, such as frontrunning and gaming.
Graph1
Volatility
We can use the approximation formulas between the compounding (geometric) return and the arithmetic return to illustrate this negative impact. Since leveraged ETFs are high Beta stocks by design, the return on LETFs are sensitive to volatility. Since the holding period return of an LETF is a compound return of leveraged daily percentage changes over the holding period, volatility will always have negative impact on the holding period returns.
R t, LETF ~~ L* Rt,Index  0.5 * L 2 * σ t, index 2
Where L is leverage. If the underlying index is flat during the year and the market volatility is at 25%, the 3X/3X ETFs can be expected to lose approximately 28% of their value. That is, the volatility decay on 1year return is 28%.The table 2 below from the prospectus of Direxions shows that 1year returns of 3X Bull ETF’s with 25% market volatility lose 17% of their value in a flat market, an 3XBear ETFs lose 31% under the same circumstances. (Yellow highlighted cells).
Table 2
(Source: Direxions total market 3X /3X prospectus)
As the graphs below show, the higher the volatility the more volatility drag it exerts on the LETF returns. 3X Bear ETFs are more susceptible to the Volatility drag than 3X bull ETFs. As in the table2 in the blue highlighted cells, if volatility is high enough, both long and short ETFs can lose almost all their value regardless of the market direction.
Graph 2
Graph 3
Trading Volatility
One of the riskfree market neutral (β=0) trading strategies in 2009 was to short both leveraged long and inverse ETFs, provided you could find the shares to short. This strategy will work well when the market experiences high volatility.
This doubleshort strategy has a high probability of relatively small gains and a small probability of a very large loss. Under certain market conditions, such as strong directional movement (index return>20%, or index return<20%) and low volatility (as in 10%), you could get cobbled by implementing this doubleshorting strategy, as in the cells in table 2 highlighted in green.
Conclusion
Like any other asset classes, the risk/reward profile of an ETF dictates the types of trading strategies that need to be implemented. Leverage, volatility and nonlinearity can be a source of alpha. Graph 2 and 3 show that the return of LETFs has a convex return profile, which can be useful in portfolio construction and risk management.
In addition, a doubleshort market neutral strategy is applicable for high volatility LETFs, such as emerging market, commodity and etc. In practice, this strategy might be difficult to implement since you often can’t find the shares to short. On the other hand, for low volatility ETFs, such as treasury bills, a double long strategy will be more appropriate if the underlying index experiences strong directional trends.
Disclosure: Long UYG, TZA, FXP, ERY