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This Week's Strategy Lesson: The Ins and Outs of Leveraged ETFs (Part 1)

Leverage is a very powerful thing. The Greek mathematician Archimedes is famous for saying: “Give me a place to stand and a lever long enough and I will move the world.” While there are some differences between leverage in physics and leverage in financial markets, they can be equally astounding and dramatic. In this series, we are going to look at several aspects of leveraged ETFs and the different things that can affect their performance.

One of the things you might frequently hear is that you shouldn’t hold leveraged ETFs long-term because of decay. While this certainly is the case in many instances, it is not always true and it doesn’t affect all instruments the same. It’s important to know why this is the case and what causes these divergences.

Mathematics, Plain but Not Always Simple

There are different factors that can cause “decay” in leveraged instruments, but we are going to start with one of the main causes which has been labeled by some as “beta slippage”.

Most leverage ETFs try to match some multiple of the daily returns of the underlying instrument they track. Beta slippage is a result of some of the quirks of how percentages and compounding multiple periods works.

For example, if stock A is initially valued at $100 and then goes up 10% in the first quarter and then up another 10% in the second quarter, we can’t simply add the two 10%’s to arrive at a 20% total return. The actual return is 21%.

The math works like this…

The first quarter’s 10% gain grows $100 to $110. Therefore, second quarter started from a bigger base. The 10% return in the second quarter is 10% on $110 not $100. 10% on $110 is $11. We started with $100 which grew to $110 at the end of quarter 1 and then to $121 at the end of quarter 2. The total return was 21%.

We have a similar quirk when compounding two periods where one of them was negative. If stock A starts at $100 and drops 20% to $80, we will need a greater than 20% increase to get back to break even. Here we need to make back $20 to get back to $100, but $20 is 25% of our $80. So we need a 25% increase to get back to the original starting $100.

The chart above shows the different values you need to get back to even (vertical axis) based on the how much the original decline was (horizontal axis). You can see as the decline gets larger, the percentage amount needed to get back to even gets larger at an increasing rate. While you only needed 11.1% after a 10% decline, you need 900% after a 90% decline.

It might not be immediately apparent, but we have just stumbled on one of our potential sources of decay (I say “potential” here because not all return scenarios decay, this can also work in your favor to amplify your returns!).

It might be easiest to demonstrate with an example…

If we set up a scenario where a stock valued at $1,000 goes down -1% on the first day and then goes up +1.01% the second day, after the two days, we are back to our starting value. If this sequence of returns repeated itself 10 times, after the 20 days, we would still just end up with a stock worth the same as we started with, $1,000. We deliberately chose values so that the starting and ending value were the same.

Now let’s add some leverage…

If we applied 3x daily leverage, we would just multiply the up and down percentages by 3. So, on a down day, it would go down -3.00% and on an up day, it would go up +3.03%. With 5x, that would be -5.00% and +5.05%.

However, if something goes down -3.00%, it actually needs to go up +3.093% to get back to even, not just +3.03%. Likewise, for the -5.00% decline, it has to go up +5.263% to get back to break even, not just 5.05%.

If we run these three scenarios through 10 cycles, we will see that the no leverage scenario ends at its break-even value while the 3x leverage loses some value over time and ends the 21 days down -0.6% and the 5x leverage ends down -2.0%.

As we add more periods or leverage, this decay trend continues. After 2270 days of this pattern (or almost 9 years of trading), the 3x leverage scenario is down 50% and the 5x leverage scenario is down 90%, all while the no leverage scenario is still flat.

The decay here is caused by the loss/recover percentage relationship. We have covered two of the factors determining the rate of decay: the amount of leverage and the number of periods. In part 2, we are going to add in volatility as the third major contributor. We will also see how this daily leverage in positive trending instruments can amplify the gains, completely flipping the decay pattern.