The myth is:

Leveraged ETFs are not suitable for long term buy and hold

myth is expressed in various ways. Some quotes from the internet about leveraged ETFs:

“unsuitable for buy-and-hold investing,” “leveraged ETFs are bound to deteriorate,” “over time the compounding will kill,” “leveraged ETFs verge on insanity,” “levered ETFs are toxic,” “levered ETFs [are] a horrible idea,” “…practically guarantees losses,” “in the long run [investors] are almost sure to lose money,” “anyone holding these funds for the long term is an uneducated lame-brain.” “Warning: Leveraged and Inverse ETFs Kill Portfolios.”

A leveraged ETF is defined for our purposes to be any ETF that promises returns of a multiple of some benchmark return on a daily basis where that multiple is specified in the prospectus.

example if an ETF promises a return of 2 times the S&P 500 index then if the S&P 500 index goes up 1.2% in one day the ETF will go up 2 x 1.2% = 2.4%.

The salient point about this definition is that the multiple may be any number such as -3 or 2.5 and includes the multiple 1, and that the return is marked to the benchmark daily, not annually. This is true even if the return is measured annually. Including the multiple 1 is done for mathematical convenience – most people would not call such an ETF leveraged but technically it is an ETF with leverage 1

Daily volatility hurts the returns of leveraged ETFs (including those with leverage 1). This is due to the equality

(1 - x)(1 + x) = 1 - x2

Suppose the market goes down by x and then the next day it goes up by x. For example if x = 0.05 then the market goes up by 5% then down by 5%. Then the net result is that the market has gone to (1-0.05) times (1+0.05) = 0.9975 which is a drop of 0.0025 or 0.25%.

That’s not fair! The market has gone down by 5% then up by 5% but our ETF that has a leverage of 1 has gone down by 0.25%. Doggone it!

This drop always occurs because x2 is always positive and the sign in front is negative. So whenever the market has volatility we lose money. We call this volatility drag.

The larger x is the larger x2 is so the larger the volatility drag. For a leveraged ETF the leverage multiplies x and so multiplies the volatility drag. Even an ETF with a leverage of 1 has volatility drag.

The myth has resulted from the belief that volatility drag will drag any leveraged ETF down to zero given enough time

we know that leverage of 1 (i.e. no leverage) is safe to hold forever even though leverage 1 still has volatility drag

If 1 times leverage is safe then is 1.01 times leverage safe? Is 1.1 times safe? What’s so special about 2 times? Where are you going to draw the line between safe and unsafe?

Maybe 2 times is safe. Why shouldn’t an ETF with leverage 2 still be suitable for holding forever?

It turns out that there may be a reason but it’s not volatility drag.

The formula for the long term compound annual growth rate of a leveraged ETF cannot be written in terms of just the benchmark return and volatility

involves terms containing the skewness and kurtosis of the benchmark

does not assume that benchmark returns are Gaussian or that returns are continuous as do formulae derived using Ito’s lemma.

for the world’s stock markets and for low levels of leverage (up to about 3) the formula can be approximated by this formula:

R = kμ - ½k2σ2/(1 + kμ)                                           

where R is the compound daily growth rate of the ETF, k is the ETF leverage, μ is the mean daily return of the benchmark, and σ is the daily volatility (i.e. standard deviation) of the daily return of the benchmark.

Plotting some of these markets (and leaving others out for clarity) on our contour chart shows how R varies according to leverage and allows us to see all the markets at once.

The pattern is quite clear. Over various markets over various time periods (mostly the last 2 or so decades) except for the Nikkei 225 the optimal leverage is about 2

Unfortunately there may be a reason not to hold leveraged ETFs for the long term but it has nothing to do with volatility drag. It is because of fees.

Most leveraged ETFs where the leverage is greater than one charge an annual fee of about one percent. This imposes a “fee drag” on the ETF.

Also leveraged ETFs suffer from tracking error. They do not exactly hit their target return for the day every day.

Leveraged ETFs can be held long term provided the market has enough return to overcome volatility drag. It usually does. For most markets in recent times the optimal leverage is about 2. But some markets and time frames will reward a leverage of up to 3. No markets will reward a leverage of 4.