Seeking Alpha had a short article on the mathematics of leveraged ETFs. It has a demonstration of the
classic upside/downside dichotomy (i.e. it takes 100% gain to overcome a
50% decline). It also mentions, without going into detail, the effect
of constant rebalancing to maintain the advertised leverage position.
What is not is that these two mechanisms conspire to frustrate the use of leveraged ETFs as a long term position. the daily re leveraging of the portfolio exacerbates the tyranny of the upside/downside dichotomy.
The portfolio sheds leverage after a decline in order to maintain its
ratio, just when that leverage would work in the investor's favor in any
reversion to the mean. On the other side, while the portfolio
naturally de-levers on an upside move, daily rebalancing
adds leverage, to the portfolio's detriment when the markets
mean-revert. Thus, the observation that over a long term holding
period, a leveraged ETF will tend to underperform the the underlying asset simply multiplied.
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