Leverage can be a double-edged sword. Just ask Bill Hwang. After 20x'ing his investment over 10 years using 5:1 leverage on total return swaps, he is now back to working at McDank's after his portfolio went tits up.

Same goes for the absolute apes out there holding 3x leveraged products like TQQQ and UPRO without a offsetting, negatively correlated hedge like TMF (a 3x leveraged 20yr Treasury ETF).

So, how much can you be "jacked to the tits", and how long can you do it for?

The math suggest it's around 2x and around a decade. And no, its not cuz of "volatility drag" or "beta slippage", so fuck off with that shit.

Let's get the basics down first. A leveraged ETF promises returns of a multiple of some benchmark return on a *daily* basis where that multiple is specified in the prospectus.

For 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 should 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 - *x*^{2}

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%.

You might be wondering: "what the fuck?" 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%.

This drop always occurs because *x*^{2} 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 *x*^{2} 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. That's not true. Volatility drag kills ETF's where the underlying does not trend upwards consistently over time - think leveraged commodity, precious metals, or inverse ETF's. For bullish ETF's that track an upward trending broad market index, the volatility drag can actually be positive and result in compounding well beyond the slated return multiplier.

Regardless, 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?It turns out that according to the Kelly Criterion (Google this shit, I don't have time to walk you through the math), the optimal leverage throughout 1979 - 2009 for the S&P 500 and Nasdaq 100 was historically 2x.

2x leverage, with daily resetting, coupled with the circuit breakers in various indexes should prevent the massive drawdowns we could theoretically see with 3x leveraged ETF's. I would argue it is safe to hold these products long term, as long as you're aware of the loss from the high management expense ratio (usually 1%). If you're a perma-bull with a degenerate appetite for risk (like me), these can be an excellent way to eat the market.