This post documents some of my research in creating a trading strategy centered around shorting leveraged exchange-traded funds (ETFs). I present the following thought experiment to motivate readers:

- Suppose an underlying instrument increases by 25% on day 1 and decreases by 20% on day 2. The return of the underlying instrument is (1 + 0.25) * (1 – 0.20) – 1 = 0%.
- Now suppose I construct a leveraged ETF designed to track 3x the daily return of the underlying instrument. The return of the leveraged ETF is (1 + 0.75) * (1 – 0.60) – 1 = -30%.

The intuition here is that in flat but volatile markets, leveraged ETFs exhibit price decay due to the effect that volatility has on cumulative returns.

Below I present a real example of this price decay by plotting SPY and SPXL. SPY is an ETF that tracks the S&P 500, and SPXL is a leveraged ETF that tracks 3x the daily return of the S&P 500. These two securities are analogous to the two securities in the thought experiment.

SPY, the underlying security, has remained fairly unchanged but with moderate volatility over this time period. Overall return is approximately -1%. SPXL, the 3x leveraged ETF, has returned almost -8% over the same time period. A market-neutral portfolio of going long 3x of SPY and going short 1x of SPXL would result in a small profit over this time period.

The price decay observed in leveraged ETFs also exists in inverse leveraged ETFs. For every long 3x ETF out there, there often exists a short 3x ETF. What happens when you construct a portfolio that is comprised of going short equal amounts of both the long 3x ETF and the short 3x ETF? Intuitively, one would expect that the two securities would be mirror images of each other and that the sum of the cumulative returns for both securities would be 0%.

But both the long 3x ETF and the short 3x ETF have decreased in value over this time period and going short equal amounts of both would have resulted in an annualized return of around 12%. In addition, this trading strategy is exposed to low risk because shorting this pair of securities is market neutral. The chart above presents the motivation behind this trading strategy, and when I first saw it, it seemed like a very profitable arbitrage opportunity.

The remainder of this post is organized as follows: Section 1 presents background on ETFs and leveraged ETFs for uninitiated readers. Section 2 examines the source of alpha in shorting leveraged ETFs. Section 3 describes exactly how to execute this trading strategy. Section 4 recommends specific leveraged ETF pairs. Section 5 describes the risks to this strategy. Section 6 contains links to further resources.

**1. Introduction to ETFs and Leveraged ETFs**

An exchange-traded fund an investment fund traded on a stock exchange that owns assets such as stocks, commodities, and bonds and divides ownership of these assets into shares. ETFs are attractive investments because they provide easy diversification, low costs, tax efficiency, while retaining all the features of ordinary stock, including short selling and options. As of December 2015, there are over 1,800 ETFs that cover almost every asset class, sector, and trading strategy.

ETFs track the price of its holdings by trading extremely close to the net asset value of its holdings throughout the trading day. The price of a share of the ETF and the value of its holding are kept close because authorized participants (usually large financial institutions) are allowed to buy or sell shares from the ETF fund manager by giving or receiving the underlying basket of securities. When the price difference between the net asset value of an ETF share and the underlying basket of securities gets too large, authorized participants can either purchase or redeem shares. In addition, an ETFs holdings are publicized and investors on the secondary market can also engage in arbitrage by buying or selling the ETF and the underlying basket of securities.

Leveraged exchange-traded funds are a special type of ETFs that are designed to be more sensitive to daily market movements than non-leveraged ETFs. Leveraged ETFs can either be long or short the underlying basket of securities and can be designed to return 2x or 3x the daily return for long ETFs or 2x or 3x the inverse of the daily return for short ETFs.

**2. Source of Alpha in Shorting Leveraged ETFs**

The hedge fund I previously worked at could be described as a fundamental global macro fund. It was fundamental in the sense that we believed that there were timeless and universal cause-and-effect linkages that drive financial markets. In other words, we used a first principles approach by identifying certain unconditional propositions or assumptions that couldn’t be deduced from any other propositions and then reasoned upward from there. When designing any trading strategy, it’s important that any sources of alpha have strong support from first principles.

**Understanding Impact of Volatility on Cumulative Returns**

Let’s return to a hypothetical example to fully understand how volatility affects cumulative returns. Suppose there is a leveraged ETF with initial price $100, and it will increase or decrease by 10% a day with equal probability. Also suppose that this leveraged ETF will trade for two days. What are the four potential outcomes for this leveraged ETF?

- $100 * 1.10 * 1.10 = $121 with 25% probability
- $100 * 1.10 * 0.90 = $99 with 25% probability
- $100 * 0.90 * 1.10 = $99 with 25% probability
- $100 * 0.90 * 0.90 = $81 with 25% probability

It is important to note that the expected value for this leveraged ETF is still $100 since the daily expected return is 0%. But even with an expected value that is unchanged, the price has declined below the initial price of $100 in 75% of the outcomes. The problem with volatility is that you lose more when you’re up and you win less when you’re down — both are bad. That’s why the most common outcome (with 50% probability) is that the ending price is $99. When you move beyond a two-period world, more and more of the outcomes will be drawn towards $0 with a few lucky outcomes with very large prices. Below I plot a histogram that displays the ending price of 10,000 simulated leveraged ETFs identical to the hypothetical example except that they trade for a period of 1,000 days instead of 2.

Of the 10,000 simulated leveraged ETFs, 95% of them ended up with an ending price of less than $100 (which was the initial price). Of these 95%, the majority of them ended up being very close to $0. But there is an important caveat — 5% of the simulated leveraged ETFs exceeded their initial price, and some exceeded it by a very large amount, and **therefore these simulations were not plotted in the histogram.** The simulation that got the luckiest ended up with an ending price of $91,087. These extremely lucky simulation outcomes are necessary because the expected mean ending price of all 10,000 simulations is still $100.

This histogram shows exactly why leveraged ETFs are not to be held for long periods of time — the price decay has a significant effect that pulls the most likely outcome towards zero. It shows why financial regulators are considering eliminating leveraged ETFs. It shows why things like the Kelly criterion exist. And it shows why shorting leveraged ETFs can be a profitable trading opportunity. The alpha in this trading strategy stems from the impact that volatility has on cumulative returns.

**3. How to Short Leveraged ETF Pairs**

Executing the strategy is straightforward.

- Identify a pair of leveraged ETFs, ideally from the same ETF fund manager. One of the leveraged ETFs should be the long ETF and the other should be the short ETF.
- Short the same notional amount of both ETFs. This means that if the long and short ETFs have different prices, calculate the number of shares to short of each such that you are short the same dollar amount amount of each.
- As prices change, the notional amount that you are short each ETF will begin to be unbalanced. For example, if the underlying basket of securities increases in price by a significant amount, the notional amount that you are short the long leveraged ETF will be greater than the notional amount that you are short the short leveraged ETF. For example, suppose you short $10,000 each of the long and short ETF. After some price movement, you could end up being short $13,000 of one ETF and $7,000 of the other ETF. Re-balance periodically by going short or covering the proper ETF to bring the notional amount into balance.
- Cover both shorts to exit the trade after sufficient time has passed.

Regarding re-balancing, there really aren’t any specific rules I can offer. My personal feeling is that once the notional amount begins to be unbalanced by around 20%, you should re-balance. This provides a reasonable cushion while preventing excessive transaction costs. It is important to re-balance because having an unbalanced notional amount exposes you to either a long or short bias on the underlying. This trading strategy does not have a view on the future direction of the underlying (in fact we are hoping that the underlying remains at a similar price but with high volatility around this price), so you should not be exposed to this bias.

**4. Recommended Leveraged ETF Pairs**

Selecting leveraged ETF pairs to short should be done based on three criteria: the interest rate charged on borrowed shares (the fee rate), the number of shortable shares available through your broker (usually inversely correlated with the fee rate), and the future volatility of the underlying basket of securities. The ideal leveraged ETF pair would be a pair of ETFs with a low fee rate, high number of shortable shares, and high future volatility.

I obtained lists of leveraged ETF from here and here and looked up the fee rate, shortable shares, and historical volatility in Interactive Brokers. Below is a screenshot containing some of the leveraged ETFs that I considered.

Based on the three criteria established above, I recommend the following leveraged ETF pairs:

- NUGT and DUST (Direxion Daily Gold Miners Bull and Bear 3x ETF)
- ERX and ERY (Direxion Daily Energy Bull and Bear 3x ETF)
- FAS and FAZ (Direxion Daily Financial Bull and Bear 3x ETF)
- TNA and TZA (Direxion Daily Small Cap Bull and Bear 3x ETF)
- TQQQ and SQQQ (Proshares UltraPro Long and Short QQQ ETF)

All these pairs have relatively low borrowing costs (5% or less per year), are easily shortable, and have moderate to high historical volatility.

**5. Risks to Shorting Leveraged ETFs**

**Shorting pairs of leveraged ETFs is not an arbitrage opportunity.**Despite what the initial charts suggest, there is no arbitrage opportunity. Returning to the hypothetical example in Section 2, while the most likely outcome is for leveraged ETFs to be drawn towards zero, there are outcomes in which the leveraged ETF increases significantly in price. This means that there is the risk for extreme loss. Extending the hypothetical example to being short a pair of leveraged ETFs does not eliminate this risk — sustained moves in either direction without much volatility lead to extreme loss. For example, the same SPXL and SPXS ETF pair that was plotted earlier returned about -90% during this 1.5 year time period in which the market trended in one direction:

**Returns to this strategy are asymmetrical.**The returns to this strategy are similar to several options-related strategies that are designed to generate a small positive return with high probability but a large negative return with low probability. In addition, as with any short-selling strategy, maximum losses are unbounded.**The position is not market neutral.**Although this strategy involves shorting equal notional amounts of leveraged ETF pairs with periodic re-balancing, this strategy is not truly market neutral. In between re-balancings, the notional amount of each leg will become unequal and necessarily expose you to either a long bias or short bias on the underlying.**Drawdowns can be significant.**Be prepared for the potential of large drawdowns. Since this strategy relies on going short on margin, your account must contain sufficient funds to maintain your position.**Transaction costs and costs to borrow can be significant.**This strategy relies on re-balancing periodically which incurs additional transaction fees. Costs to borrow (the fee rate) are a function of how hard it is for your broker to locate shares to short and can fluctuate over time. The fee rate may exceed 10% per year for certain leveraged ETFs.

**6. Further ****Resources**

This section contains recommended links to additional resources that contain discussion about shorting leveraged ETFs:

- Stock-Encyclopedia.com and 3x ETFs provide lists of leveraged ETFs.
- Shorting Leveraged ETF Pairs: Easier Said Than Done examines the impact of different re-balancing thresholds have on returns.
- Another Look At The NUGT-DUST Double Short examines the distribution of returns based on different start dates and with a holding period of one year.
- Darwin’s Inverse Leveraged Short ETF Strategy describes some of the risks involved with this strategy.
- Shorting Leverage plots some equity curves for common leveraged ETF pairs.

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