Are leveraged and inverse exchange-traded products (ETPs) effective investment management tools? Leveraged funds are designed to produce a fund performance that is a multiple of the underlying index. A 2x fund should increase twice as much as the index. Inverse funds are designed to move in the opposite direction of the benchmark, and they can also be leveraged.

The authors analyzed the expected fund performance in a perfect world of zero operating costs and management expenses. In other words, they looked at the benchmark indexes and levered or inverse versions of those indexes. The specific benchmarks were the S&P 500 Index, the Russell 2000 Index, and an index that mimicked the ICE U.S. Treasury 20+ Year Bond Index, as well as futures indexes for crude oil, natural gas, and volatility (VIX).

The method they used was to test whether funds could be expected to work even under perfect conditions or their design doomed them to failure. To test the idea, the authors conducted a Monte Carlo analysis over a sample period of 5,040 days (20 years) and used six levels of leverage ranging in integers from –3 to +3, with 1 meaning no leverage. The number of Monte Carlo simulation runs for each was 10,000. A fund was considered dead (i.e., its life cycle was over) when the fund’s value fell below 5% of its starting value.

The authors also looked at the performance of 35 actual ETPs. That included seeing how closely they tracked the indexes they were trying to mimic. This “tracking error” was calculated for each of the real funds.

“Given the expected return–risk characteristics of the underlying benchmark indexes, fund collapses were predictable from the get-go,” the authors state.

Stocks and bonds include a risk premium, which means investors get rewarded for taking long positions in the market rather than short ones. This factor showed up in the results: Being short increased the risk of those funds collapsing. Each of the unlevered theoretical funds had single-digit positive compound annual growth rate (CAGR). The median life of funds with either no leverage or positive leverage was identical to the 5,040-day (20-year) test period. The stock ETPs (S&P and Russell) that had two and three times inverse leverage all had a more than 90% chance of failing within 20 years. For the bond ETP simulation, the two and three times inverse funds had an 85.8% and a 98.7% chance of failing, respectively.

There is no risk premium when investing in commodities or volatility futures, and simulations based on futures indexes showed a broadly opposite result. The expected CAGR for each fund is negative, meaning long positions are a losing proposition. The results showed that the crude oil, natural gas, and VIX funds that were leveraged 3x had a 100% chance of failing within the 20-year period. For the 2x leveraged ETPs, the gas and VIX funds also had a 100% failure rate, but the oil fund did slightly better, with a 98.7% failure rate.

The authors found that the real-world experience showed parallels to the theoretical for stock and bond ETPs. “Again, the results are consistent with the prediction that if the benchmark return is expected to be positive, funds with negative leverage ratios will fail,” the authors state.

The results for the levered gas, oil, and VIX funds were dire. “In a noncarry [i.e., futures] market in which the expected benchmark return is negative, both levered short and levered long funds will eventually fail,” the authors conclude [their emphasis]. “Our prediction of failure was, sadly, accurate.”

Investors should avoid using levered and inverse ETPs as investment instruments. The authors state that “levered and inverse ETPs are not effective hedging instruments for any holding period greater than one day.” These instruments are unstable, and even under perfect theoretical conditions, the demise of such funds is predictable.