Understanding Returns Of Leveraged And Inverse Funds

August 25, 2009


Realized Beta Results For Funds That Track Higher Volatility Indexes

As of mid-2009, more than half of leveraged and inverse fund assets were in ETFs based on the broad-based equity or fixed-income categories. However, many investors also use leveraged and inverse funds tracking U.S. sector indexes with higher return volatility. To evaluate the realized betas for funds with greater historical risk-reward profiles, we calculate realized leverage ratios over a long-term history for two-, seven- and 30-day holding periods for hypothetical funds with daily targets of 2x and -2x three other indexes: the NASDAQ-100 Index, the Dow Jones U.S. Financials Index and the Dow Jones U.S. Oil & Gas Index. Figures 9-11 show realized leverage ratios for hypothetical 2x and -2x funds based on these indexes. These returns do not illustrate the performance of an actual investment.


The history of daily NASDAQ-100 Index returns begins in 1985, with the index having a return volatility of 28.6 percent over the 1985-2008 period. This is significantly higher than the return volatility of 18.3 percent for the S&P 500 over the same period. The frequencies we observe of realized betas for a hypothetical 2x and -2x NASDAQ-100 fund held for 30 days across all beta ranges are somewhat lower than the S&P 500 due to the higher volatility of the index, but still above 80 percent. (The only exception is the -1.75 to -2.25 range for the -2x funds.) For example, for a hypothetical -2x NASDAQ-100 fund held 30 days, the -1.50 to -2.50 realized beta range frequency was 74.1 percent, compared with 85.3 percent for the S&P 500 leveraged strategy.


The Dow Jones U.S. Financials and Dow Jones U.S. Oil & Gas Index data are available back to 1992, thus providing 17 years of return experience. The annualized return volatilities based on daily data for each index were 24.85 percent and 24.80 percent, respectively; a bit lower than that of the NASDAQ-100 Index, but higher than the S&P 500. The realized betas for these hypothetical funds are also a bit higher than for the NASDAQ-100 Index, which is precisely as we’d expect given the slightly lower return volatilities of the underlying indexes. Therefore, the analysis of higher volatility indexes further supports the connection between volatility and holding period risk for holders of leveraged and inverse funds with daily target multiples.


To summarize these findings, there is a high probability of approximating the one-day target for investment horizons longer than one day. The shorter the period and the lower the index volatility, the higher the probability. For longer time periods and more volatile benchmarks, we observed lower probabilities.


For Longer-Term Holding Periods And More Volatile Funds, Rebalancing Helps Close The Gap

For investors whose goal is to approximate the one-day target over time, rebalancing can be an effective strategy. Investors should routinely monitor the return of the index relative to the performance of the fund and rebalance holdings when they move out of line. The process is analogous to that used by investors rebalancing asset-mix weights versus asset-class policy targets in more conventional investment situations.


It bears repeating that the impact of rebalancing on returns of leveraged and inverse fund strategies is directly related to the effect of compounding. While rebalancing may be helpful if investors seek to match their long-term returns to the one-day target over time, the returns from such a rebalancing strategy can theoretically be lower than those of an un-rebalanced strategy in a trending market or low volatility market environment. Rebalancing has the effect of removing both the negative and potential positive effects of compounding.

Monitor And Rebalance The Fund Position: Mind The Gap

The rebalancing process for leveraged and inverse fund positions is straightforward: Watch the gap between the index return and fund return, and rebalance holdings either when this gap moves beyond a specified trigger or at a fixed calendar-based interval. Figure 12 shows the investor decreasing fund exposure if the index return is less than the fund return, and increasing fund exposure if the index return is greater than the fund return.

The size of the rebalance trade for any period can be calculated as the starting fund value x (index return - fund return). Figure 13 demonstrates an extreme case of large daily index returns and the rebalancing trades that could be implemented by an investor who wants to keep positions in line with the daily leverage target. Since inverse funds are designed to move in the opposite direction of their underlying indexes, they typically will require a greater frequency and/or degree of rebalancing.

An investor applying the same rebalancing trigger percentage to low- and high-volatility index ETFs with leverage is likely to find that larger-size rebalancing trades may be required, as the potential for larger performance gaps and less proximate realized multiples is otherwise increased. Alternatively, an investor can set an appropriate trigger for rebalancing by taking into account the volatility of the index and the target rebalancing frequency. For example, to rebalance weekly, the investor could base a trigger on the weekly volatility of the index for the fund. In conclusion, compared with returns from an un-rebalanced fund, rebalancing fund position(s) reduces the size of the gap such that the investor’s realized return from the fund position over multiday periods is closer to the daily multiple of the index.



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