I got curious about leveraged ETFs and decided to create a simulation. The results are interesting.
LETFs have always intuitively seemed mathematically sound, but brokerages warning from holding these for extended periods of time has put me off. So I skimmed a few papers and decided to build a simulation to test it out myself.
It's really quite simple, it gets daily data of SP500 from 1927-12-30. Shuffles it, runs the shuffled random selection for 20 years, rinse-and-repeat 10 000 times, both for lump-sum and DCA. The resulting histogram was non-informative, but taking a logarithm of all the values resulted in a beautiful normal distribution.
I used geometric mean because for exponential data, geometric mean and geometric standard deviation (GSD) are much more meaningful for an average investor as the geometric mean gives a more likely result. In a dataset with a few really large values, the arithmetic mean gets skewed in an unrealistic direction in our case, as the few small outliers that cause it happened due to incredibly lucky runs consisting of almost only days with positive percentage change which hasn't happened in stock market history.
Here's what I found for 20 years:
| | 3x leverage | 2x leverage | 1x leverage |
|:--------:|:--------:|:--------:|:--------:|
| Lump-sum geometric mean | 3.9 | 5.1 | 3.4 |
| Lump-sum GSD | 9.8 | 4.5 | 2.1 |
| DCA geometric mean | 3.2 | 3.0 | 2.0 |
| DCA GSD | 4.7 | 2.9 | 1.7 |
What was really interesting was that the lump-sum 2x leverage geometric mean was bigger than lump-sum 3x leverage geometric mean, but for DCA it was reversed. I am thinking that it might be a bug, but for the life of me I cannot find it. If anyone has any idea why for DCA the results are like this, please let me know. And constructive criticisim of course is always welcome.
The code in question: https://github.com/Tormihunt/2x-leverage-testing