Across a variety of sources, I often see the following argument (paraphrased):
Leveraged ETFs are a bad investment, because if the stock goes up x%, then down x%, an ETF leveraged n-times has a value of (1-nx)(1+nx) = 1-n^2x^2. So, increased leverage makes you hurt more from an (up,down) or (down,up) move.
While this argument (or something similar) is often given, it strikes me as incorrect, or at least improperly defended. Sure, Leveraged ETFs do worse when the market makes two moves in opposite directions, but it does better when the market makes two moves in the same direction. I.e. (1-nx)(1-nx) > (1-x)(1-x) and (1+nx)(1+nx) > (1+x)(1+x). In fact, the four cases (UP, UP), (UP, DOWN), (DOWN,UP), (DOWN,DOWN), when summed together, mutually cancel, so that leverage doesn't have an effect on the expected value. (**EDIT: I've now explained this at the bottom of the post, in a section labeled (EDIT))
But, stocks aren't symmetric and tend to increase over time, so the leverage actually works in your favor.
Running an analysis of the buy-and-hold strategy everyday from 2010 to now, TQQQ almost always outperforms the QQQ over long time horizons.
With all of this in mind, I wonder what real arguments can be given against long holding leveraged ETFs. I'm especially interested in arguments that would apply to a risk neutral investor (obviously to a risk-averse investor that -81% as the worst return is very significant).
I'm by no means an experienced or knowledgeable trader, so let me know if I'm missing something obvious and significant in my highly simplified model.
(EDIT)
To explain this in more detail, assume we model the market in the following way.
- 50% chance the market goes up by 1%
- 50% chance the market goes down by 1%
Start with $100, and hold for two days. Then, the expected return is
- 25% chance of (UP,UP) = (1.01)^2 return = 1.0201
- 25% chance of (DOWN,UP) = (.99)(1.01) return = 0.9999
- 25% chance of (UP,DOWN) = (1.01)(.99) return = 0.9999
- 25% chance of (DOWN,DOWN) = (.99)(.99) = return = 0.9801
Each of these has a 1/4 chance of occuring, so add all these numbers together and then dividing by 4 gives 1. So, if we start with $100, we should expect to end with $100.
Now, let us generalize. Assume the market is symmetric, so something like this
- 1/8 chance for 10% return
- 1/8 chance for 2% return
- 1/4 chance for 1% return
- 1/4 chance for -1% return
- 1/8 chance for -2% return
- 1/8 chance for -10% return
Or even
- 1/8 chance for 100% return
- 1/8 chance for 10% return
- 1/4 chance for 1% return
- 1/2 chance for -28% return
Anything where the expected value for a single day is zero. Then the expected value over n periods is is also zero (irrespective of leverage). If the expected value over a single day is postive, then the expected value of multiple periods is also postive (and increases exponentially with leverage).
For instance, here is the expected value over n days for the following market
- 50% chance the market goes up by x%
- 50% chance the market goes down by x%
Then the expected return over n time periods is
Comments on D Stanley's answer
Can you expand a bit more on what your view of risk is (especially, what does it mean to risk 3X the amount?). I'm not sure I see exactly why you are viewing the risk as, for lack of a better term, 'annualized'.
As you can see in the data, over a 1 yr time horizon, the annualized average returns are almost exactly 3X. Over longer time horizon, you are right that the annualized returns are less than 3X, I hadn't thought about looking at the annualized returns benchmark. Here is the data on that
However, I think thats not the right way to look at risk. Let me take an example. Let's take my baseline as investing $100 in QQQ. If I decide to invest 3x that money (i.e. $300) in QQQ, then I'd say my risk is 3x as much. All losses are multiplied by a factor of 3. In order to make this increased investment worth it, I should expect 3x as much returns. This is not the same as expecting 3x annualized returns. If I want to get 3x the return over 10 years (i.e. if were to make $20, then I want to make $60 instead), I need much less than a 3x annualized return.
For instance, over a 10 year time horizon, the average annualized returns of TQQQ are only about 2.5x QQQ. But, that corresponds to a ~10x return for TQQQ over QQQ in the 10 year period.
This is not to say I don't believe your statement that one is risking more than they expect to gain is ultimately true, but rather I don't see how your example of the annualized returns being less than 3x actually implies that the risk is 3x and the returns are less than 3x.