Using Inverse ETFs (SQQQ, QID, SPXU, etc.) is a very effective alternative to initiating a short position when we aim to make our portfolio neutral as a downturn approaches. However, these ETFs have garnered a negative reputation, often described as melting cash even faster than Floyd Mayweather—a clear misunderstanding, in my opinion. Therefore, I thought that dedicating a post to this topic could help provide a more accurate picture of these instruments and how they can be used for hedging.

It would be challenging to delve deeply into hedging with an inverse ETF without first understanding how these leveraged ETFs operate. So, in this first part of 'Hedging with Leveraged ETFs 101,' I will focus on the infamous decay of Leveraged ETFs. I have read countless articles about it, and it is often misunderstood. Some people claim it is a myth, while others advise never staying in them overnight. So, where lies the truth?

But before we explore this topic, here's a small disclaimer: Leveraged ETFs are complex instruments that can be difficult to explain simply. I'm not entirely convinced that I can make it easy to understand and entertaining at the same time. If you find yourself feeling depressed while reading this post, I sincerely apologize. Looking at some __awkward family pictures__ should restore your joy. Go ahead and view a couple, then skip to the last section of this post, which highlights the key points to remember.

#### First source of decay : Beta slippage/Path dependence

The main reason usually cited for explaining the decay of Leveraged ETFs relative to the performance of the underlying asset is the path-dependent nature of their returns. What do I mean by that?

Leveraged ETFs are designed to provide an amplified return by a factor of Beta over the underlying asset on a daily basis. This means that if the Nasdaq 100 (QQQ) goes up by 2% during a day, TQQQ (a 3X amplified version of it) should go up by 6%. However, nothing guarantees that over a long period of time, TQQQ's overall return will be 3X that of QQQ. In fact, once you take a position in a leveraged ETF, the compounding effect will start on day two, creating its own unique path that will decouple from that of the underlying asset due to compounding. Let’s take a simple example:

You have a $100 position in TQQQ.

**Day 1: **Nasdaq goes up 5%; then TQQQ goes up 15%, leaving you with $115.

**Day 2: **Nasdaq goes up again by 5%; TQQQ goes up 15% again, now you have $132.25.

If you had taken a position in QQQ, you would have $110.25, for a return of 10.25%. But your position in TQQQ gives you a return of 32.25%, i.e., 3.14X the return of holding QQQ instead of 3X. If this bull trend continues, compounding will increasingly inflate the difference in return between the leveraged ETF and Beta times the underlying ETF. During great bull trends like in 2017, while QQQ had a remarkable 32.70% run, TQQQ outperformed significantly, giving a 118.65% return (around 3.63X instead of 3X).

Why then is this associated with decay? This path dependence tends to amplify the return during great bull runs, but the opposite is true in the other direction. The worst case occurs during a highly volatile sideways market. To better understand this, here is another simple example:

Let’s compare a $100 investment in TQQQ and QQQ.

**Day 1:** Nasdaq goes down 8%, leaving QQQ at $92 and TQQQ now worth $76.

**Day 2:** Market rebounds by 8.7%, QQQ returns to the initial value of $100, but TQQQ is still at a loss, only bouncing back to $95.83.

Although this example might sound unrealistic, this effect is real and just typically happens over a longer time frame during downturns. In a volatile year like 2020, QQQ gave a 48.60% annual return, while TQQQ provided only a 2.26X amplified return (109.85%). It’s not bad at all, but this illustrates the fact that the amplified return of these leveraged ETFs is only valid on a daily basis and that the long-term return will follow its own path depending on market volatility (and this can lead to some decay). The market has been predominantly in a bull market since the inception of most leveraged ETFs (around 2008-2010), allowing Bull ETFs like TQQQ to benefit from this path dependence/compounding effect, while bear positions like SQQQ have experienced nearly continuous decay. However, these same leveraged ETFs would probably not have performed as well if they had existed during the 1972-1982 big sideway period. As proof of this, consider the damage caused to leveraged ETFs by the 2022 bear market: While QQQ reclaimed its all-time high (ATH) in December 2023, as of October 1st, 2024, TQQQ has yet to reclaim its previous ATH set in December 2021. But there is more to this story of decay than path dependency alone.

#### Source of decay no.2 : Borrowing cost, management fee and interest

In the above section, we assumed that the daily return of a given leveraged ETF perfectly follows Beta times the variation of the underlying asset. In reality, the design of these ETFs does not lead to perfect daily amplification. Jian Zhang of New York University wrote a very interesting PhD thesis aimed at developing a mathematical model that tracks the return of leveraged ETFs. In his work, the author shows that the daily return of a leveraged ETF can be very well approximated by the following equation:

This equation is only applicable to leveraged ETFs. The formula for inverse leveraged ETFs includes an additional term related to the cost of borrowing (shorting) the components of the underlying index or purchasing derivatives, i.e.:

So in summary, on a daily basis, a leveraged ETF should provide an amplified beta daily return minus some fees. These fees will usually be relatively small if interest rates are low and if the manager is not too greedy. Thus, usually, the daily amplification factor is very close to the advertised Beta. We can also note that, by design, the extra cost of borrowing the underlying asset **in an inverse ETF will always involve more fees and thus more decay**. This is also usually very negligible when the underlying asset is readily available for shorting, but it can become a non-negligible issue during major drawdowns like in 2008 or 2022.

During these drawdowns, often the components of the ETF become very expensive to borrow, and thus inverse leveraged ETFs can deviate considerably from the expected return (decay). To illustrate that, let’s look at the data presented by Jiang during the last leg of the great financial crisis (January 2nd, 2009, to March 20th, 2009). If we consider QLD a 2X ETF that track the Nasdaq, the average daily tracking error over this period was an incredibly low 0.04% (which, by the way, placed it at the first rank in terms of efficiency of all the 53 leveraged ETFs studied by the author). Its inverse counterpart (QID, -2X QQQ), due to the borrowing costs, had a 0.22% daily tracking error. A number still very small, but five times more than QLD. But the mathematics of inverse ETFs already told us that inverse ETFs will always experience more decay. However, the real issue arises when the underlying stock becomes really hard to borrow for the ETF manager. 2008-09 was a crisis primarily in the world of banking, so let’s look at leveraged ETFs in that field. IYF is an ETF that tracks that sector. During that period, a bullish 2X leveraged ETF (UYG) gave a daily tracking error of 0.22% over the amplified IYF. But its bearish 2X counterpart (SKF) had a horrendous tracking error of 3.3% (and with a standard deviation even worse). This considerable error is associated with the fact that the underlying stocks of this ETF were extremely hard to borrow during that period.

The main takeaway from this whole section is that the other source of decay, associated with all the fees related to the mechanics of a leveraged ETF, while typically negligible for a bull ETF, can become considerable during a severe drawdown for an inverse ETF when we need them the most. Since a picture is worth a thousand words, here is a graph of a 2X inverse ETF that tracks SPY and of the 2X inverse that tracks QQQ during the great financial crisis.

We see that this error increased considerably when the stock became expensive to borrow.

#### Conclusion

We saw that Leveraged ETFs have two main sources of decay. The first one is not really decay per se, but is associated with the path dependence of long-term returns, which are a function of market volatility. In an uptrend, this actually becomes compounding and inflates the return. However, during highly volatile selloffs or even during prolonged sideways movements, as we will show in part 2 of this article, this can lead to some decay.

The second type of decay is the one associate with all the fee related to the mechanics of a leverage ETF. These fee are mostly negligible for a bullish leverage ETF but can considerably affect an inverse leveraged ETF during drawdown.

In an other section of is thesis, Jiang derived the calculation of the superposition of these two sources of decay over a certain period of time. This allowed the authors to conclude that “the dependence on the realized variance is stronger on bearish leveraged ETF, which means the bearish Leveraged ETF with the same |β| as bullish Leveraged ETF suffers more from the accumulated realized variance.” This is really something that we must take in consideration when using an inverse ETF for hedging. But, that’s going to be the topic of the part 2 of this post: How to Use Inverse ETFs Without Going Broke

Vincent that is super interesting. I appreciate so much the content you provide in WU. Thanks a lot!