### Should Leveraged ETFs Be Held for Long Horizons?

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There are numerous misconceptions and emotions surrounding the use of leveraged ETFs (LETFs). This article provides a simple and clear explanation of how these instruments can be used to enhance portfolio returns over longer term investment horizons. We show that commonly used 2x ETFs have delivered the expected return over multi-year time horizons.

### Regulators and myths

Regulators, compliance departments and many others, driven by a desire to set what they consider realistic investor expectations, have taken an extreme and unrealistic view. They have been focused on the issue that 2x products may not deliver exactly 2x over holding periods longer than a day. In this argument, they often use a theoretical expected return of 0%. If you think expected returns are going to be zero, then there is no reason to take on volatility drag and fees imposed by products like LETFs over a longer time horizon.

But the stock market does not have an expected return of 0%. Returns have been closer to 9% over the last 145 years and 11% since 1951.

Paradoxically, we readily accept leverage in margin accounts, which are highly regulated and scrutinized by the most sophisticated risk management groups. Numerous financial products use leverage in the form of options, futures and swaps. There is the emotional argument that somehow all leverage is bad, which is not based on sound logic but rather on the cumulative impact of powerful anecdotal stories. Yet we are all happy to use high levels of debt (a.k.a. leverage) throughout our lives for home ownership, vehicle purchases and education.

### LETF basics

It is well known that compound return is less than the corresponding average return due to volatility. This is known as “volatility drag,” which decreases returns. For example, the average annual U.S. stock market return from 1951 through 2014 was 12.4% while the compound return was 10.9%. The 150 basis point difference was due to volatility drag, the result of a non-levered 17.5% standard deviation in annual returns.

When using leverage, the volatility drag is amplified exponentially and has a much greater effect on overall returns as a result of an increased standard deviation. Volatility drag over longer time periods causes a greater degree of tracking error than the return times the leverage multiple over the same time period. The LETF return is given by the following equation:

LETF Return = (Average Return * Leverage) – (Volatility Drag + Fees)

As this equation shows, it only makes sense to use leverage over a long time horizon in cases where the expected market return is positive and the leverage multiplied by the returns exceeds the volatility drag and fees.

The most important determinant of whether leverage will increase compound returns is the level of expected returns. For a 2x U.S. equity LETF, the critical value is 6% expected return based on a 17.5% standard deviation. That is, if the expected market return is higher than 6%, then on average a 2x LETF generates higher compound returns and increased long horizon wealth, as compared to a non-levered 1x holding.

As an example, continuously holding a daily 2x leveraged U.S. stock market position from 1951-2014 would have generated an annual compound return that was 1.87 times the annual unlevered compound return. If a 1% per year management fee was included, you would end up with 1.76x returns. This shows that despite the impact of volatility and fees over a 65-year period, which included a number of dramatic market declines, outsized returns close to 2x were achieved.

In a comprehensive study, Hill and Foster (2009) used an extended time series of U.S. stock market returns. They found that, during most time periods, the longer term 2x compound returns are very close to two times the unlevered compound returns. They went on to show that if volatility is high during a period, returns are less than 2x and if volatility is low, returns are greater than 2x, but most of the time they are very close to double the unlevered returns. Thus, the actual returns experienced in the stock market are sufficient to produce much larger levered returns (versus an unlevered position), as the increased volatility drag does not destroy the additional returns resulting from the use of leverage.