Are Leveraged ETFs Leaky or is that a Myth?

I've recently been reading and hearing that it’s a myth that leveraged ETFs are leaky.  The truth is that this depends on how one defines “leaky.”  There was an interesting episode of the Rational Reminder podcast where Marco Sammon and Chris Murray explained the nature of leveraged ETFs.  They went far deeper into mathematical details than I will here.  I will look at a simple example and then bring what we learn back to leveraged ETFs to help you decide whether you think the leaks are real or imagined.

With any investment, all dollars go somewhere.  There is no leak in the sense that no dollars are ever destroyed.  However, we can have a leak of utility, as I’ll show in the following example.

Example

Suppose you are offered an investment where your money either doubles or drops 80% on each of 20 flips of a fair coin.  We assume that you’ll let your money ride for the full 20 flips.

In one view, your expected return is (+100% - 80%)/2 = 10% per flip.  After 20 flips, you expect a $100,000 investment to increase by a factor of (1.1)^(20) to about $670,000.

In another view, you expect the coin flip to go your way 10 times and against you 10 times.  In this case, you expect a $100,000 investment to be multiplied by (2 x 0.2)^(10) to finish at about $10.

It seems like one of these views has to be completely wrong, but that’s not the case.  Let’s look at the possible outcomes.  If a million people each invest $100,000, we expect one very lucky person to win all 20 coin flips and end up with about $100 billion!  Several others will lose only one coin flip and end up with about $10 billion.  

As we keep adding one more lost coin flip, the ending value drops by a factor of 10: $1 billion, $100 million, …, $1000, $100, $10, $1, … down to fractions of a penny.  Your share of all this money is about $670,000, but most of it will probably go to someone else.

Which view is correct?

Both views are correct, but the one that is more useful depends on the question you’re trying to answer.  The first view is the arithmetic average return.  The second view has many names: compound average return, log return, median return, and mean utility (for a log utility function).

If you put your entire portfolio into this investment, you should focus on the median view that says you'll probably lose almost all your money.  You might make billions, but you're far more likely to end up with cents on the dollar.  Any reasonable level of risk aversion should keep you from plowing everything you have into this investment.

If you put one dollar into this investment, it becomes similar to a lottery ticket, but with better odds.  The top prize is a million dollars, a few tickets will make $100,000, a few more $10,000, and so on.  The fact that your ticket has an arithmetic expectation of about $6.70 is more important than the fact that you’ll probably lose your dollar.

This investment doesn’t leak dollars; it leaks utility.  If a million investors were to each grow their $100,000 to $670,000, they would all derive benefits that we call utility.  However, when we concentrate the winnings among a few newly-minted billionaires, and leave most people with cents on the dollar, we collectively lose utility.  The lives of the few millionaires and billionaires don’t improve enough to compensate for what most investors lose in their lives.

Back to Leveraged ETFs

Getting back to leveraged ETFs, the question of whether they are leaky depends on whether we look at arithmetic returns or compound returns.  With arithmetic averages, we see that no dollars are lost.  Using leverage with daily rebalancing doesn’t cause any dollars to disappear; it just changes the return characteristics.  

It’s the compound average return view that shows leaks.  But remember that any average calculation covers up a range of possibilities.  The leak in compound average returns may be bigger or smaller than the average expectation.  Sometimes leveraged ETFs have big leaks, and sometimes they have no leaks at all.

If you’re considering using a leveraged ETF for a small fraction of your net worth, then it’s the arithmetic average return that matters.  You should consider what level of exposure to the underlying asset you want, and you should look into the fees and implicit borrowing costs, but leaks that come from daily rebalancing should not be a concern.  

However, if you’re considering putting a large fraction of your net worth into an ETF leveraged 2X or higher, then the leakiness we see with the compound average return is important.  The small possibility of a big return does not compensate for the risks.

Considering leveraged ETFs for my portfolio

I’ve never owned leveraged ETFs.  I find the combination of investment fees and implicit borrowing costs to be too high to consider them.  If a 1.2X leveraged ETF with very low fees and borrowing costs had existed before I retired, I might have invested in it.  I would never have considered 2X or higher.  

Now that I’m retired, I’ve chosen to include bonds in my portfolio.  My current asset allocation is about 70% stocks.  This is like using a 0.7X leveraged ETF.  At this level of exposure to stocks, I have no reason to consider a leveraged ETF at 1.2X or higher.