A reader asked: “You have had multiple blog entries regarding the erosion of price in leveraged funds due to re-balancing costs. Why are there long periods during which this erosion appears not to occur? I have been short both Ultra S&P500 ProShares (SSO) and UltraShort S&P500 ProShares (SDS) since June 1, 2009 and am losing money. Thoughts?”
Leveraged Exchange-Traded Fund (ETF) managers typically achieve leverage via positions in options related to the underlying index. The price of an option has three main components: (1) price or level of the underlying; (2) time value; and, (3) implied volatility. The leveraged fund manager:
Wants and depends on component (1).
Does not want component (2) but can manage it to some degree by rolling positions to maintain approximately constant time to expiration.
Does not want component (3) and can do little to manage it.
Substantial daily changes in implied volatilities of the options in the ETF portfolio may cause the portfolio value to deviate (above or below) its leverage target relative to the underlying index. A trend in implied volatility over many days may cause a persistent, cumulatively growing deviation. Whether this tracking error is positive or negative depends on the specific types of options positions in the ETF portfolio. In other words, the grind of rebalancing costs may not always be the dominant source of leveraged ETF tracking error.
Since 6/1/09, the implied volatility of the S&P 500 Index (indicated by VIX) has generally trended down (by about 20%). That trend may be the source of your surprise.
Reader Christophe Gauthron commented:
I would like to submit a simpler explanation which is rooted in the mathematics of leveraged ETF compounding.
Leveraged ETF price models explain the value erosion effect. See “The Dynamics of Leveraged and Inverse-Exchange Traded Funds” and “Path-Dependence of Leveraged ETF Returns” These models also explain that in periods of extreme market returns and lower volatility (as has been the case for the second half of 2009), the effect of compounded daily returns dominates the effect of value erosion: for example, a 2x ETF may return more than 2x. Furthermore, the asymmetric nature of the compounded positive and negative returns may result in a positive gain for a matched pair of leveraged ETFs (2x and -2x).
Unfortunately, many investors have been lured into the idea that shorting a pair of leveraged ETFs is a sure gain. Indeed, it is easy to build a calculator based on the above studies that shows the expected outcome of holding a pair of leveraged ETFs. Results match well the empirical data.
