Long-Term Investing in Leveraged ETFs
Julius van der Zee1,AARTICLE INFO ABSTRACT
Available: 8 June 2017 JEL classifications: G1 G11 G17 Keywords: Exchange-traded fund Leveraged ETFs Long-term investing
Leveraged ETFs are designed to deliver a positive or negative multiplier return to a specific benchmark. They are promoted as daily investment instruments instead of a long-term investment instruments. This research paper focus on the long-term (one year) relation between leveraged ETFs and their three different underlying indices; the S&P 500, gold price and crude oil. This paper shows, contrary to existing literature, that some leveraged ETFs deliver their promised exposure even in the long-term. However, when buying a leveraged ETF investors should still take into consideration that leveraged ETFs perform differently in each market segment and are highly trend sensitive. Investors also need to be aware that leveraged ETFs suffer from the constant leverage trap, compounding problem, high expense ratios and certain risks.
1 Email: juliusvdzee@gmail.com. Student Number: s2379783.
A Corresponding author at: Faculty of Economics and Business, Study Program: MSc Finance, University of Groningen, The
1. Introduction
Deville (2008), Aggarwal and Schofield (2014), and Charupat and Miu (2011) argue that Exchange-traded funds (ETFs) are one of the most successful and innovative exchange listed products of the past decades. ETFs have grown tremendously in number of issues, in value and in complexity. ETFs have evolved from simple index trackers to sophisticated custom made ETFs. These more complex ETFs were first introduced in the United States (US) in 2006 and use leverage and/or derivatives. These ETFs are introduced with the goal to generate high daily returns for active investors rather than long-term (buy and hold) returns. Leveraged ETFs seek to deliver returns that are a positive or negative multiple of an underlying index (benchmark), for example, they aim to deliver 2x or 3x long exposure. In the market, these ETFs are called leveraged, ultra or bull ETFs. Another example of leveraged ETFs are inverse ETFs. Inverse ETFs aim to deliver -1x, -2x or -3x short exposure to the underlying index, for example the inverse gold ETF would gain 1% for every 1% drop in the price of gold. These ETFs are often called bear, short or ultrashort ETFs. Plain-vanilla ETFs have exposures of 1x the underlying index. For simplicity in this research paper, the terminology leveraged ETF is used for any leveraged, ultra, bull, inverse, bear, short and ultrashort ETF and the term plain-vanilla ETF is used for any traditional type of ETF introduced since the 90’s.
Leveraged ETFs are constructed and managed differently than plain-vanilla ETFs. To achieve the above described daily returns, leverage needs to be used intensely. Leverage is created by borrowing to pay for short-duration (custom) derivatives like forwards, futures options and/or swaps (e.g. vanilla, total return and default swaps). The counterparties of these contracts promise to give the ETF issuer (daily) returns based on a specified (custom) underlying index in exchange for fees and expenses. Hands-on portfolio rebalancing, exposure sizing and risk management is required as the leveraged ETF’s exposure and its instruments needs to be reviewed, adjusted and rebalanced daily to maintain the promised index multiple and leverage ratio. This process is significantly different and more intensive than a buy and hold index copy-cat ETF, in which case no exposure adjustments beyond index and divided payments adjustments are made (see, e.g., Charupat and Miu, 2011; Kosev and Williams, 2011).
Charupat and Miu (2011) argue that leveraged ETFs became one of the fastest-growing
segments of the ETF market in terms of assets under management (AUM) and trading activity. Leveraged ETFs grew from a few listed in 2006 to 108 leveraged ETFs in 2009 till 201 listed
leveraged ETFs in the US by the end of May 20172. The AUM of leveraged ETFs in the US
increased from US$31.0 billion in 2009 till US$41.9 billion by the end of May 2017, according to the database of IHS Markit3. The AUM represents 5.35% of the total US ETF market, which is relative small. However, leveraged ETFs account for approximately 40% of the total trading volume of ETFs in the US in 2009, which indicates very frequent (daily) trading. In 2015, the top 10 leveraged ETFs shares were traded over 90 million daily on NYSE ARCA, which is around 9.0% given NYSE’s daily trading volume of about 1,000 million4.
Rompotis (2014) explains that plain-vanilla and leveraged ETFs are interesting financial instruments for investors. Firstly, they offer flexible trading throughout the entire day. Secondly, Rompotis argues that the all-in costs of ETFs are much lower than creating the same exposure yourself as the costs are spread over larger AUM. Thirdly, these new ETFs also offer investors exposure to various markets, either small-, mid- or large cap and domestic or foreign. They also offer exposure to several asset classes and underlying indices like equities, currencies, commodities, precious metals, currency markets, fixed-income instruments, real estate and bonds which otherwise might be difficult to access. Indices could also be designed for a particular issuer and/or investor. Thus, ETFs made it convenient for investors to tailor their financial portfolio based on their financial objectives and expand investors’ allocation opportunities by providing exposure to alternative asset-classed, investment structures and durations.
Rompotis (2014) also explains certain advantages offered to investors by leveraged ETFs. Firstly, leveraged ETFs are interesting for short-term investors, because they could provide high returns in a very short time period. Secondly, ETFs are a simple way for investors to obtain leverage without needing to invest directly in derivatives or execute multiple costly trades. Additionally, avoiding the use of derivatives by investors themselves means that they do not need a margin account. Consequently, investors do not need to refinance their positions when the accumulated losses from their investments in derivatives have decreased their margin amount below the required level. Another advantage is that leveraged ETFs can be used to lower the risk of investors’ portfolio. To summarize, leveraged ETFs can be traded (brought or sold) simply, fast, at every moment through a standard trading account and at standard trading fees. Therefore, ETFs are much simpler and easier than using derivatives and trading in margin by oneself.
Most literature and two well-known and major issuers of leveraged ETFs, ProShares5
3 https://ihsmarkit.com/
and Direxion6, advise to use leveraged ETFs in the short-term and mention they are not suitable for long-term buy and hold investing. In this paper, long-term buy and hold investing in leveraged ETFs is defined as a period of one year and beyond.
Lu, Wang and Zhang (2009) investigated the relation between the long-term performance of leveraged ETFs with equity markets as underlying index. They conclude that the relations between leveraged ETFs and the underlying indices do not necessarily hold. Their results indicate that investors can assume that leveraged ETFs will deliver their promised returns over holding periods less than one month. However, as the holding period gets longer, investors need to be cautious about the long-term relation. This conclusion is verified for Canadian equity leveraged ETFs by Shum (2011). He argues that Canadian equity leveraged ETFs abstain from their promised exposures for holding periods exceeding one month.
Murphy and Wright (2010) analysed the ability of 12 commodity-based leveraged ETFs.
They conclude that commodity-based leveraged ETFs are an effective way to gain the promised exposure to the corresponding underlying indices on a daily basis. However, over the entire life, commodity-based leveraged ETFs struggle to deliver their promised exposures. Rompotis (2014) explains that leveraged ETFs cannot deliver their promised exposure due to the constant leverage trap and the nature of continuously compounding.
However, Bansal and Marshall (2015), disagree with these conclusions. They argue that the studies examine a period with extraordinary market volatility attributable to the 2008-2009 financial crisis and that this higher volatility leads to higher tracking errors as is well documented in literature. The tracking error is the divergence between the returns of the specific ETF and its underlying index. Bansal and Marshall research focusses on a less volatile period and they conclude that leveraged ETFs could be used by long-term investors looking to leverage up a market view. Also, Hill and Foster (2009) show that leveraged ETFs can be successfully used in long-term strategies. They argue that the impact of compounding over multiday periods is not material and therefore the probability of approximating the one-day target for beyond one-day periods is high.
Most studies indicate that leveraged ETFs are short-term investment instruments for active investors. Leveraged ETFs could deliver multiple returns in comparison to the underlying indices and are easy to trade, so potentially attractive additional investment instruments. However, the long-term performance of leveraged ETFs as part of a buy and hold investment strategy remains a topic of discussion.
In this paper existing literature is complemented with a long-term (one year) comparison between leveraged ETFs and plain-vanilla ETFs with three different underlying indices. The underlying indices used are the Standard and Poor’s 500 index (S&P 500), the gold price and the Bloomberg crude oil WTI index. This paper begins by analysing the long-term relations of ETFs with their underlying indices over a holding period of 5, 21, 63 and 252 trading days with the same research methods as used by Lu et al. (2009). The first method used, is to study the long-term amplification ability of leveraged ETFs. This is done by using overlapping data returns and the CAPM. In addition, the stationary bootstrap method is deployed to generate more random samples and to better understand the range of long-term performance relations of the leveraged ETFs with their underlying indices. The daily changes in Net Asset Value (NAV) of ETFs listed in the US are used and compared with the daily changes in the underlying indices. The period analysed is from the launch date of the different ETFs until the end of December 2016. The research question can be stated as follows; “are leveraged ETFs suitable for long-term investing?”.
The aim of this paper is to extend the discussion of the long-term performance of leveraged ETFs as substitute instruments for index investing. In addition, this paper aims to grant a recommendation for investors to distribute investment capital effectively by choosing the right financial instruments. Finally, this study aims to shed light if investors could benefit from selecting leveraged ETFs instead of plain-vanilla ETFs.
This paper confirms that S&P 500 ETFs deviate from their promised exposure for every holding period. Crude oil ETFs only deviate from their promised exposure in the long-term. However, this paper finds contrary to recommendations of existing literature that gold ETFs’ relations with their underlying index remains equal to their promised exposures even in the long-term. Although, even when this relation holds, investors still need to manage their portfolio actively. They also need to have enough market knowledge and investment skills. Further, investors should take into consideration the disadvantages of investing in leveraged ETFs. These disadvantages consist of the additional risks associated with the use of derivatives in leveraged ETFs, the higher expense ratios of leveraged ETFs, the constant leverage trap and compounding problem. These last two are the most important factors to take into account by investors when considering investing in leveraged ETFs.
performance of the S&P 500 ETFs, gold ETFs and crude oil ETFs respectively. Finally, section 7 conclude the paper.
2. Literature review
This literature review consists of six parts. The first part discusses the evolution of ETFs. The second part discusses the management of ETFs and their expenses ratio. The third part explains the risks associated with leveraged ETFs. The fourth part summarizes past research in the long-term relations of leveraged ETFs and their underlying indices. The fifth part discusses the constant leverage trap and compounding problem of leveraged ETFs. The sixth part describes the equation used for measuring the promised exposure of the ETFs.
2.1. The evolution of ETFs
According to Aggarwal and Schofield (2014) the first ETF (TIPs35, tracking TSE-35 index) was introduced in Canada on the Toronto stock exchange in 1990. The first ETF introduced in the US on the American stock exchange was the “SPDR”. The SPDR, or “Spider” tracks the S&P 500. Deville (2008) describes that the ETF marketplace experienced its effective boom in March 1999. In that year the Nasdaq-100 Index tracking stock was launched, popularly known as ‘Cubes’ or ‘Qubes’. In the second year of trading, a daily average of 70 million shares of Cubes were being traded, which is around 4% of the Nasdaq trading volume. The spotlight on Cubes increased market awareness of other ETFs and the total assets under management (AUM) more than doubled to US$70.0 billion by the end of December 2000. Since then, ETFs kept on growing extensively. By the end of May 2017 there were 5,4477 different kinds of ETFs globally with an AUM of US$3,841.0 billion7. AUM is the total market value of assets that the ETF issuing companies (financial institutions) manages on behalf of investors (Aggarwal and Schofield, 2014).
Statista8 tracks, reports and details the number of ETFs and AUM in billions of US$ of ETFs globally. Graph 2.1 and table 2.1, on the next page, demonstrate the growth in numbers of ETFs and AUM from 2003 until 2017 globally. This table indicates a yearly growth in ETFs of around 50% per year in 2006 and 2007. However, nowadays the growth of ETFs has dropped to around 10% annually. Although this is still very significant, it shows signs of a more mature
7 https://ihsmarkit.com/
market. The data also clearly demonstrates the AUM growth outstrips the number of issued ETFs in recent years, meaning that ETFs grow in average size.
Graph 2.1
This graph publishes the number of ETFs listed globally (N of ETFs) and the assets under management in billion US$ of all ETFs globally (AUM bn US$) from 2003 until the end of May 2017.
Table 2.1
This table reports the number of ETFs per year globally (N of ETFs), AUM in billion US$ per year globally (AUM) and growth
in percentage per year. Numbers with * represent the number of ETFs and AUM globally on the 31st of May 2017.
03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 N of ETFs 276 330 441 713 1181 1591 1950 2448 2995 3313 3551 3942 4399 4779 5447* Growth 17.9% 29.0% 48.0% 50.5% 29.8% 20.3% 22.7% 20.2% 10.1% 6.9% 10.4% 11.0% 8.3% 13.1% AUM 204.3 283.2 396.5 565.9 794.2 710.7 1042.5 1311.6 1353.7 1756.2 2253.2 2647.1 2911.3 3422.2 3841.3* Growth 32.7% 33.7% 35.6% 33.9% -11.1% 38.3% 23.0% 3.2% 26.0% 24.9% 16.1% 9.5% 16.2% 11.6%
Aggarwal and Schofield (2014), Deville (2008), and Kosev and Williams (2011) argue that the initial ETFs were an alternative to traditional non-traded mutual funds, including index trackers and bond futures. They argue that these ETFs have similar underlying assets as mutual funds. They both provide exposure to (diversified) baskets of securities typically tracking a specific equity section, commodity benchmark, fixed income benchmark or trend. Moreover, the simplicity of ETFs, the low-cost diversification benefits and some tax advances attract attention from investors. ETFs especially attract the attention of investors, because of their smaller nominal value, liquidity and intraday trade. The latter is a major difference compared to mutual funds. ETFs are listed on an exchange and can be traded throughout the day at standard trading cost, similar to stocks. Investors can buy, sell and short ETFs, write options on them, and set market, limit or stop-loss orders. ETFs are often traded at market prices close to their Net Asset Value (NAV), rather than at discounts or premiums often applicable to mutual
0 1000 2000 3000 4000 5000 6000 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 N o f ET F s o r A UM (b n US$ ) Year
Number of ETFs and AUM per year globally
funds. ETFs also have lower expense ratios and certain (capital gains) tax efficiencies compared to traditional mutual funds. Most ETFs provide a high degree of transparency and publish all or substantially all of their holdings frequently. So investors can easily understand the underlying assets in which they invest.
As explained in the introduction, in 2006 the first leveraged ETFs were introduced in the US. Leveraged ETFs are introduced with the goal to generate daily returns that are a positive or negative multiple of the daily returns of their underlying index. These leveraged ETFs borrow money to buy derivatives to maintain their desired exposure (see, e.g., Deville, 2008; Aggarwal and Schofield, 2014; Charupat and Miu, 2011).
2.2. Management of ETFs and ETF’s expense ratios
ETFs can be passively or actively managed. An active managed ETF aims to generate a
positive alpha. Alpha is the generated excess returns, above a pre-selected benchmark without additional risks. If active managed ETFs have positive generated alphas, the fund managers could have skills or just luck (Fama and French, 2010). Existing literature of generated alpha performance of plain-vanilla ETFs argues that passive managed plain-vanilla ETFs cannot outperform the market return (Pace, Hili and Grima, 2016). Rompotis (2011) explains that passive managed ETFs just invest in all the components of the underlying index at the same weights so they cannot outperform their underlying indices. In car terms, a car purely following the lead car doesn’t overtake or take shortcuts so the follower will always finish after the lead car. In ETF terms, the index is the lead car and the plain-vanilla tracking ETF the follower, the following distance is caused by the expenses. Because, leveraged ETFs are known as passively managed ETFs which just follow their underlying indices, in a positive or negative multiple, they are expected to have zero alpha.
The ETF issuer/manager deducts their pre-agreed management fee and the incurred transaction costs from the performance of the ETF. According to Charupat and Miu (2011) this fee consists of two major categories. The first one is management fees; this is the cost of operating the fund, which is different for each fund and/or company. Secondly, the investors are charged with the cost of execution, leverage/borrowing and hedging. The fee will logically be higher for leveraged ETFs than for plain-vanilla ETFs, because leveraged ETFs need to pay significant interest rate costs for creating the leverage used and transaction costs for buying and selling the required derivatives.
investing. Nowadays, Vanguard desires to be the lowest cost provider in the industry. Their strategy to introduce low cost passive index tracking ETFs created a huge cash inflow into those low costs ETFs as US wealth managers targeted the lowest (operating) cost for the same risk-reward. (Vanguard’s ETF tracking the S&P 500, “VOO”, and Blackrock ETF tracking the S&P 500 “IVV” have an AUM of US$67.5 billion and US$110.9 billion respectively ultimo May 20179). Based on this success and the very large AUMs of these ETFs, Vanguard lowered their investments costs further to 10 basis points (bps) or less10, “VOO” has an expense ratio of 5 bps. BlackRock expense ratios are slightly above the expenses ratios of Vanguard for similar ETFs11.
The expense ratios of leveraged ETFs are much higher than the expense ratios of plain-vanilla ETFs. For example, ProShares, who only issues and manages leveraged ETFs, has fixed expense ratios between 89 and 95 basis points12. This is about 10 times the charge by Vanguard for their plain-vanilla ETFs. Thus when investing in leveraged ETFs, the ETFs need to generate sufficient gains to overcome the higher expense ratios.
2.3. Risks associated with investing in leveraged ETFs
Aggarwal and Schofield (2014) discusses that leveraged ETFs come with additional risk. First, market volatility is the most important risk for leveraged ETFs. This risk relates to the impact of market volatility on the performance of leveraged ETFs to deliver their promised exposure. High volatile markets can lead to big losses in leveraged ETFs (which cannot be recuperated easily) and to imperfections in delivering the promised exposure. Also, liquidity risk is a concern when investing in leveraged ETFs. Liquidity risk is the risk stemming from the lack of marketability of an investment which cannot be bought or sold quickly enough to prevent or minimize a loss. Counterparty risk is especially an issue for leveraged ETFs, because these ETFs use swaps and over-the-counter (OTC) derivatives. Counterparty risk is the risk that the counterparty of a contract will not live up to its contractual obligations. A good example of counterparty risk is given by Acharya and Richardson (2009), they conclude that credit default swaps kick-started the latest credit crisis when Lehman Brothers could no longer honour their commitments; Bear Sterns caused similar issues later on.
Kosev and Williams (2011) describe the lack of transparency of leveraged ETFs as a
risk concern. Transparency of financial products is the degree of how exact investors understand
9 https://ihsmarkit.com/
10 https://investor.vanguard.com/etf/list
the underlying assets, their inherent risks and the liabilities imbedded in the product. The more complex leveraged ETFs have highly complicated structures using a multiplicity of derivatives to create the desired exposure for anticipated returns.
The last kind of risk relates to the variance in the market prices of leveraged ETFs. Rompotis (2014) argues that the shares of leveraged ETFs are traded on the secondary market and their market price could fluctuate to a change in the NAV but are also affected by supply and demand. Thus, it is not easy to predict if an ETF will trade at a premium or discount to its NAV.
Thus, the more complex ETFs can vary considerably in both structures and the risk they present. Leveraged ETF’s risks are very important for the financial market and need to be taken in consideration by investors. However, risks are not discussed in this research.
2.4. Past research in the long-term relation of leveraged ETFs
Lu, et al. (2009) examined the long-term performance of US equity markets leveraged
ETFs meeting their promised exposure for different holding periods. They conclude that when holding a leveraged ETF shorter than one month, investors can assume that leveraged ETFs deliver their promised multiple returns to their underlying indices. They also conclude that when the holding period gets longer, investors need to be very cautious about the long-term performance. Their results also show that when holding a leveraged ETF with -2x exposure longer than 3 months, the relation between the leveraged ETF and its benchmark breaks down. The relation between a leveraged ETF with 2x exposure and its benchmark breaks after a one-year holding period. However, their research was limited to equity markets as underlying indices and in a period with high volatility, namely during the recent financial crisis. Shum (2011) also argues that Canadian equity markets leveraged ETFs performances abstain from their promised exposures for holding periods which exceed one month.
Murphy and Wright (2010) extended the research of Lu et al. (2009) by investigating
Mackintosh (2008) shows that the long-term performances of leveraged ETFs are not linear related to the return of indices. Mackintosh’s research furthermore indicates that there is a direct relation between the level of tracking error and market volatility; indicating that the more volatile the market, the higher the tracking error, and the higher the difference between the long-term returns of leveraged ETFs and their promised exposure.
Charupat and Miu (2011), analysed the price deviations of leveraged ETFs compared
with their underlying indices. They argue that large premiums or discounts are prone to occur due to valuations of the underlying derivatives. They conclude that there are some significant differences between long exposure leveraged ETFs and short exposure leveraged ETFs. On average, short exposure leveraged ETFs trade at a larger premium while long exposure leveraged ETFs trade at a discount or a slight premium to their NAV. Additionally, they argue that discounts happen more often than premiums for all long exposure leveraged ETFs. Furthermore, long exposure leveraged ETFs are negatively correlated with the returns of their underlying indices and vice versa, short exposure leveraged ETFs are positively correlated with the returns of their underlying indices. The final remark of Charupat and Miu is that leveraged ETFs are successful in delivering the promised returns over holding periods of up to a week.
Contrary to existing literature, Bansal and Marshall (2015) find that tracking errors of ETFs can be favourable to long-horizon investors. They argue that long-term investors looking to leverage up their market views, should not be persuaded that leveraged ETFs are a poor vehicle to achieve these returns. Also, leveraged ETFs could be used in aggressive portfolios. However, they warn that it doesn’t mean that all leveraged ETFs are suitable for all equity investors, with greater leverage comes greater risks. Also, Hill and Foster (2009) demonstrate that leveraged ETFs can be successfully used in long-term investing strategies. They argue that the impact of compounding on these ETFs over multiday periods is not material. Therefore, the probability of approaching the one-day target for beyond one-day periods is high, albeit the market volatility needs to be low.
2.5. The constant leverage trap and compounding problem
the 2x leveraged ETF return should be 𝑟𝑡𝐷 = 2 ∗ 𝑟
𝑡𝐵 and the 3x leveraged ETF return should be 𝑟𝑡𝑇 = 3 ∗ 𝑟
𝑡𝐵. This relation is checked with simple mathematical simulations in table 2.2 below and in table A.1 until table A.3 in appendix A.
Table 2.2 starts with the underlying index (S&P 500) at 100 points. Two different leveraged ETFs are introduced, a 2x S&P 500 ETF and a 3x S&P 500 ETF both starting at 100 points. The S&P 500 is simulated for 7-days and the performance of the two different ETFs are calculated and analysed. Table 2.2 indicates that when the S&P 500 returns to its original level at day 6, the 2x S&P 500 ETF loses 7 points and the 3x S&P 500 ETF even loses 19 points. At day 7 the overall market return is positive, however the ETFs are still negative compared to their starting point. In this mathematical example the market betas are equal to their promised exposure, namely 2.0 for the 2x S&P 500 leveraged ETF and 3.0 for the 3x S&P 500 ETF. The market betas measure the exposure of ETF’s return with regard to the underlying index daily. However, the overall return multipliers as indicated by the number between parentheses in table 2.2 are not in line with their respective promised exposure. This deviation occurs because of the constant leverage trap and compounding problem.
Table 2.2
This table simulates the performance of the S&P 500 leveraged ETFs with 2x and 3x exposure for 7-days versus the S&P 500. The daily returns of the three different investment options are calculated as well as the overall returns are calculated. The number in parentheses is the overall return multiplier for the 7-day return of the two different ETFs. The overall return multiplier is calculated by dividing the overall return of the specific ETF though the overall return of the S&P 500.
Day S&P 500 Change (%)
S&P 500 2x S&P 500 ETF Change (%) 2x S&P 500 3x S&P 500 ETF Change (%) 3x S&P 500 1 100 100 100 2 90 -10% 80 -20% 70 -30% 3 108 20% 112 40% 112 60% 4 96 -11% 87 -22% 75 -33% 5 90 -6% 76 -13% 61 -19% 6 100 11% 93 22% 81 33% 7 103 3% 99 6% 88 9%
Overall return (multiplier) 3.00% -1.25% (-0.42) -11.83% (-3.94)
125-days and the NAV of the 2x and 3x S&P 500 ETF converge to very low values. After the initial 125-days, the market rebounds and returns to its initial level at day 252. However, the returns of the 2x and 3x S&P 500 ETFs are lower than the return of the S&P 500. The overall return multipliers are even negative, which is addressed by Carver (2009). He explains that a leveraged ETF’s NAV can converge to a very low value, when the NAV becomes too low it has difficulty to recuperate and outperform the underlying benchmark going forward. Surprisingly, the daily market betas of all three simulations are equal to their promised exposures.
The important conclusion from these simulations is that the markets betas are equal to their promised exposures. However, the overall return multipliers are not equal to their promised returns. This occurs because of the constant leverage trap and compounding problem. Furthermore, if the underlying indices enjoy positive trends, leveraged ETFs outperform the underlying indices with more than their promised exposures. Although, when the underlying indices go down initially, investors will lose money with leveraged ETFs even when the underlying indices return back to their original levels. Important element to notice when investing in leveraged ETFs is the critical impact of the trend of the underlying market. Actually, leveraged ETFs are highly path-dependent (Rompotis, 2014).
2.6. Measurement method
As explained, the constant leverage trap could lead to lower levels of exposure than promised by the specific ETFs. To measure if the levels of exposure are equal to their promised levels the Capital Asset Pricing Model (CAPM) is applied. This well-known equitation calculates the market beta (β) as measure of the exposure of the ETF’s return in regard to its underlying index. Leveraged ETFs are expected to have market betas equal to their promised exposure to the underlying indices. For example, a -2x leveraged ETF is expected to have a market beta of -2.0.
2.6.1. Capital Asset Pricing Model
𝐸(𝑅𝑝) = 𝑅𝑓+ 𝛽[𝐸(𝑅𝑚) − 𝑅𝑓] (Eq. 1)
In equitation 1 𝐸(𝑅𝑝) represents the individual’s ETF expected return. 𝑅𝑓 incorporates the return on risk-free securities. [𝐸(𝑅𝑚) − 𝑅𝑓] represents the excess return of the ETF over and above the risk-free rate. β is the coefficient that represents the strength of the relationship between the investor’s ETF and the underlying index. An important concept of the CAPM is that investors are compensated for systematic risk, because systematic risk cannot be diversified away (Pace et al., 2016).
3. Data and methodology
This section describes the methodology used and the different ETFs analysed in this research paper. Thereafter, the regression model used for calculating the promised exposure is described.
3.1. Methodology
In section 2 different (negative) aspects of leveraged ETFs are discussed. The delivering of the promised exposure of the selected ETFs in the long-term will be analysed in detail in section 4, 5 and 6. Section 4 analyses the promised exposure of ETFs with the S&P 500 as underlying index for different holding periods. This is performed by using overlapping data returns and analyse this returns with the CAPM. The holding period periods analysed are 5, 21, 63 and 252 trading days. Also, the tracking error for each ETF with regards to volatility is examined. Thereafter, the stationary bootstrap method is used to generate more samples of the data and to better understand the range of the long-term performance relations of ETFs with their underlying indices. The initial analysis applied is similar to the methods used by Lu et al. (2009). In section 5 and 6 ETFs benchmarked to the gold price and crude oil will be analysed respectively in the same way as the S&P 500 ETFs are analysed.
3.2. Sample description
Bloomberg WTI crude oil sub index in US$ (in this research simple called crude oil ETFs). The Bloomberg index is intended to reflect the performance of crude oil as measured by the price of futures contracts of West Texas Intermediate sweet, light crude oil in US$. It is a "rolling index", which means that it does not take physical possession of any commodities. The roll occurs over a period of five business days in certain months according to a pre-determined schedule, generally beginning on the fifth business day of the month and ending on the ninth business day13.
All the ETFs are listed on the NYSE Arca stock Exchange in New York, the United
States. The period analysed is from the first introduction/launch day of each ETF until the end of December 2016. From the database of IHS Markit14 the daily NAVs of each ETF are downloaded. An ETF’s NAV is the sum of all its assets (the value of its holdings in cash, shares, bonds, financial derivatives and other securities) less any liabilities, divided by the number of shares outstanding. With the NAVs the realized daily returns for each ETF are calculated. The studied plain-vanilla S&P 500 (SPDR) and gold ETFs are issued by the State Street Global Advisors15 and the studied leveraged ETFs are issued by ProShares16. From both their websites the published ETF characteristics and information like the expense ratios, levels of exposure and launch dates are downloaded.
First, the ETFs with the S&P 500 as underlying index are analysed. The S&P 500 is the most frequently used US benchmark and commonly regarded as a proxy of the United States equity market performance. The daily closing price of the S&P 500 are downloaded from the website of Yahoo17. Based on these closing prices the daily realized returns are calculated. The S&P 500 ETFs with exposure of 3x, 2x, 1x (plain-vanilla), -1x, -2x, -3x are chosen and described in detail in table 3.1.
Table 3.1
This table reports the names of the six different ETFs with the S&P 500 as underlying index and publishes the levels of exposure, launch dates and expense ratios of the specific ETFs.
ETF name Exposure Launch date Underlying index Expense ratio
ProShares ultrapro S&P 500 3x 6/23/2009 S&P 500 0.94%
ProShares ultra S&P 500 2x 6/19/2006 S&P 500 0.89%
SPDR S&P 500 1x 1/22/1993 S&P 500 0.094%
ProShares short S&P 500 -1x 6/19/2006 S&P 500 0.89%
ProShares ultrashort S&P 500 -2x 7/11/2006 S&P 500 0.90%
ProShares ultrapro short S&P 500 -3x 6/23/2009 S&P 500 0.90%
Secondly, the gold ETFs are analysed with 2x, 1x and -2x exposure. The specific details of the gold ETFs are given in table 3.2. The daily price of the LBMA Gold Price is the US$ price of gold bullion P.M. and is downloaded from the website of London Bullion Market Association18. The ProShares gold ETFs are benchmarked at the 15:00 P.M. gold price19.Based on the daily gold prices, the daily realized returns of the gold price are calculated.
Table 3.2
This table reports the names of the three different ETFs with the London Bullion Market Association Gold Price in US$ as underlying index and publishes the levels of exposure, launch dates and expense ratios of the specific ETFs.
ETF name Exposure Launch date Underlying index Expense ratio
ProShares ultra gold 2x 12/1/2008 LMBA gold price 0.95%
SPDR gold shares 1x 11/18/2004 LMBA gold price 0.40%
ProShares ultrashort gold -2x 12/1/2008 LMBA gold price 0.95%
Finally, the crude oil ETFs are analysed with exposure of 2x and -2x. There are also
crude oil ETFs with a multiple of 3x, however these were recently introduced into the market, so there is not enough historical data for proper analysis. There exists no plain-vanilla crude oil ETF on this specific underlying index. The historical data for the crude oil price is downloaded from the website of the Financial Times20 and used to calculate the daily realized returns of the crude oil in US$. The specific details of the crude oil ETFs are given in table 3.3.
Table 3.3
This table reports the names of the two different ETFs with the Bloomberg WTI crude oil sub index as underlying index in US$ and publishes the levels of exposure, launch dates and expense ratios of the specific ETFs.
ETF Name Exposure Launch date Underlying index Expense ratio
ProShares ultra Bloomberg crude oil 2x 11/24/2008 Bloomberg crude oil 0.95% ProShares ultrashort Bloomberg crude oil -2x 11/24/2008 Bloomberg crude oil 0.95%
The 3-month US$ Treasury bill is generally used as the risk-free rate, and likewise chosen here as a proxy. More specifically the 3-month US$ treasury bill monthly ask yield is selected, because it reflects the actual return for investors. The risk-free rate plays an important role in asset pricing models, since investors are merely concerned with excess return. Excess return is the return over and above the risk-free rate. The 3-month US$ treasury bill monthly ask yield is downloaded from Yahoo Finance21.
18 http://www.lbma.org.uk/pricing-and-statistics 19 http://www.proshares.com/
3.3. Regression for analysing the market betas
As explained before the long-term relation of ETFs with their underlying indices are analysed. This is done by comparing the market betas with the promised exposure of the different ETFs. The market betas are calculated with the earlier described CAPM. The CAPM is described in detail in equation 2 and table 3.4 explains the variables used in equitation 2.
𝐿𝑛∆𝑅𝐸𝑇𝐹𝑖,𝑡 − 𝐿𝑛∆𝑅𝑓,𝑡 = ∝𝑖+ 𝛽𝑖(𝐿𝑛∆𝑅𝑚𝑖,𝑡− 𝐿𝑛∆𝑅𝑓,𝑡 ) + 𝜀𝑖,𝑡 (Eq. 2)
Table 3.4
This table explains the variables used in equitation 2 at time t.
Variable Explanation
𝐿𝑛∆𝑅𝐸𝑇𝐹𝑖,𝑡 Daily change in the ETF
𝐿𝑛∆𝑅𝑓,𝑡 Daily change in the risk-free rate
𝐿𝑛∆𝑅𝐸𝑇𝐹𝑖,𝑡− 𝐿𝑛∆𝑅𝑓,𝑡 Excess return of the ETF
∝𝑖 Generate alpha for the ETF
𝛽𝑖 Measure the sensitivity of the ETF’s excess return to the underlying index
𝐿𝑛∆𝑅𝑚𝑖,𝑡 Daily change in the underlying index
𝐿𝑛∆𝑅𝑚𝑖,𝑡− 𝐿𝑛∆𝑅𝑓,𝑡 Excess market return
𝜀𝑖,𝑡 Is the error term
4. Analysis of long-term performance of S&P 500 ETFs
In this section the long-term performance of the different S&P 500 ETFs are reviewed and analysed with descriptive statistics, scatters, regressions and the stationary bootstrap method.
4.1. Analysis of S&P 500 ETFs
Table 4.1
This table provides a summary of the descriptive statistics of the underlying index (S&P 500) and the descriptive statistics of the S&P 500 ETFs with different levels of exposure with regard to the underlying index. The tracking error is
the divergence between the return of the specific ETF and the underlying index. The period analysed is from the 23rd of June
2009 until the end of December 2016.
-3x ETF -2x ETF -1x ETF S&P 500 1x ETF 2x ETF 3x ETF
Mean -0.187% -0.126% -0.064% 0.062% 0.053% 0.115% 0.177% Median -0.207% -0.134% -0.079% 0.090% 0.056% 0.137% 0.208% Maximum 19.870% 13.280% 6.616% 4.970% 4.726% 9.433% 14.187% Minimum -14.240% -9.490% -4.738% -6.970% -6.627% -13.281% -19.904% Standard deviation 2.960% 1.975% 0.987% 1.015% 0.987% 1.973% 2.963% Tracking error 3.975% 2.988% 2.000% - 0.110% 0.966% 1.953% Start date 6/23/2009 6/23/2009 6/23/2009 6/23/2009 6/23/2009 6/23/2009 6/23/2009 Observations 1884 1888 1885 1888 1888 1892 1884
Since all the ETFs and the S&P 500 have the same measuring date, they can be fitted into graphs. The graphs represent a long buy and hold investment positon in the different S&P 500 ETFs and the S&P 500 brought on the 23rd of June 2009 and held until the end of December 2016. In graph 4.1 the 1x, 2x and 3x S&P 500 ETFs are published against the S&P 500. Some interesting observations can be extracted. Firstly, the 3x S&P 500 ETF provides a much higher return during this period than any other S&P 500 ETF or just investing in the S&P 500. Secondly, in periods with high volatility, like June 2015, the high exposure S&P 500 ETFs suffer big losses compared to the lower exposure ETFs and the S&P 500.
Graph 4.1
This graph publishes a long buy and hold investment position in; the S&P 500, the S&P 500 plain-vanilla ETF and S&P 500
leveraged ETFs with different levels of positive exposures held from the 23rd of June 2009 until the end of December 2016.
0 100 200 300 400 500 600 700
23-jun-09 23-jun-10 23-jun-11 23-jun-12 23-jun-13 23-jun-14 23-jun-15 23-jun-16
Positive S&P 500 leveraged ETFs versus S&P 500
A similar graph (4.2) is constructed with the S&P 500 leveraged ETFs with negative exposure. All negative leveraged ETFs end with almost the same very low value. In table 4.2 the long-term returns, market betas and corresponding overall return multipliers for the S&P 500 ETFs are reported of a long buy and hold investment position for 1, 3, 5 and 7 years started on the 23rd of June 2009. It is interesting to note that the overall return multipliers of the S&P 500 ETFs in the different holding periods are nowhere equal to their promised exposure. However, the market betas of the S&P 500 ETFs are almost equal to their promised exposure. The difference between the market betas and the overall return multipliers can be explained by the constant leverage trap and compounding problem.
Graph 4.2
This graph publishes a long buy and hold investment position in; the S&P 500, and the S&P 500 leveraged ETFs with different
levels of negative exposures held from the 23rd of June 2009 until the end of December 2016.
Table 4.2
This table reports the long-term returns, market betas and overall return multipliers of a long buy and hold investment position
of 1, 3, 5 or 7 years in the different S&P 500 ETFs started on the 23rd of June 2009. The (overall return) multipliers are
calculated by dividing the n-year return of the ETF though the n-year return of the underlying index (S&P 500).
-3x ETF -2x ETF -1x ETF S&P 500 1x ETF 2x ETF 3x ETF
1-year return -58.3% -42.4% -23.1% 26.3% 22.0% 46.1% 70.5%
1-year market beta -2.94 -1.96 -0.98 0.98 1.97 2.95
1-year multiplier -2.22 -1.61 -0.88 0.84 1.75 2.68
3-year return -87.4% -71.7% -44.4% 61.5% 48.0% 108.5% 164.2%
3-year market beta -2.90 -1.93 -0.96 0.96 1.93 2.90
3-year multiplier -1.42 -1.17 -0.72 0.78 1.76 2.67
5-year return -97.1% -89.1% -65.3% 145.6% 118.6% 365.2% 757.0%
5-year market beta -2.89 1.93 -0.96 0.96 1.93 2.90
5-year multiplier -0.67 -0.61 -0.45 0.81 2.51 5.20
7-year return -98.2% -91.9% -69.7% 155.0% 127.1% 403.1% 766.6%
7-year market beta -2.91 1.94 -0.97 0.97 1.94 2.91
7-year multiplier -0.63 -0.59 -0.45 0.82 2.60 4.95 0 20 40 60 80 100 120 140 160
23-jun-09 23-jun-10 23-jun-11 23-jun-12 23-jun-13 23-jun-14 23-jun-15 23-jun-16
Negative S&P 500 leveraged ETFs versus S&P 500
To calculate the long-term amplification capability of S&P 500 ETFs, overlapping data is used to calculate the long-term returns. For example, when the performance of 21 trading day returns are analysed, first the 21 trading day returns of the S&P 500 and S&P 500 ETFs are calculated from the beginning of the period. This is the first observation, one-day later, another 21-day return is calculated and this is the second observation. This process continues till the whole period is covered. In this manner the long-term performance of the returns of 5, 21, 63 and 252 trading days are studied. These periods correspond to the holding period of a week, month, quarter and one year. With the overlapping data returns, scatters are constructed which plot the n-holding period returns of the S&P 500 ETFs versus the n-holding period returns of the S&P 500. These scatters should indicate whether the promised leveraged ETF’s exposure remains constant or deviates when the holding period increases. These scatters are plotted in appendix B and there could be expected that when the holding period increases the ETFs deviate from their promised exposure.
the volatility multipliers show the same pattern as the market betas for all the different S&P 500 ETFs analysed.
As explained, the higher the market volatility, the higher the tracking error becomes. To test this relation scatters are constructed for the S&P 500 ETFs which publish the n-day tracking error versus the n-day realized standard deviation (volatility) over the same holding period. These scatters are given in appendix D and indicate that the tracking error increases as the standard deviation (volatility) increases.
The fact that overlapping returns are used to investigate the relation between the long-term performance of leveraged ETFs and their underlying index could lead to some bias. To further investigate the relation between the promised exposures and the underlying index, the bootstrapping method is used. This method is widely used in finance as it is a powerful tool to resample the distribution of the actual data and makes it easier to understand the range of long-term performance relation of the leveraged ETFs with their underlying index (Lu et al., 2010). In this paper the data is resampled for holding periods of 5, 21, 63 and 252 trading days. Each time a sample of daily returns is created of the benchmark and the corresponding ETFs. Then, the market betas and volatility multipliers are re-calculated in the same way as before for each holding period. For every S&P 500 ETF a simulation of 700 samples with 1260 trading days (5-years) is executed.
Table 4.3
This table reports the mean and 95 percentile confidence interval of the 700 market betas simulated with 1260 trading days and calculated for holding periods of 5, 21, 63 and 252 trading days for each S&P 500 ETF.
Period 5 21 63 252
S&P
500 2.5 per. Mean 97.5
per. 2.5 per. Mean 97.5
per. 2.5 per. Mean 97.5
per. 2.5 per. Mean 97.5 per. -3x ETF -2.933 -2.905 -2.874 -2.961 -2.905 -2.848 -3.005 -2.905 -2.803 -3.129 -2.907 -2.679 -2x ETF -1.957 -1.939 1.921 -1.978 -1.939 -1.900 1.999 -1.939 -1.872 -2.098 -1.938 -1.779 -1x ETF -0.977 -0.968 -0.959 -0.988 -0.968 -0.948 -1.003 -0.968 -0.935 -1.003 -0.968 -0.935 1x ETF 0.958 0.967 0.979 0.947 0.968 0.990 0.934 0.973 1.012 0.883 0.973 1.068 2x ETF 1.918 1.939 1.957 1.901 1.940 1.977 1.878 1.942 2.013 1.787 1.945 2.091 3x ETF 2.877 2.907 2.935 2.852 2.906 2.964 2.812 2.908 3.009 2.693 2.906 3.103 Table 4.4
This table reports the mean and 95 percentile confidence interval of the 700 volatility multipliers simulated with 1260 trading days and calculated for holding periods of 5, 21, 63 and 252 trading days for each S&P 500 ETF.
Period 5 21 63 252
S&P
500 2.5 per. Mean 97.5
per. 2.5 per. Mean 97.5
per. 2.5 per. Mean 97.5
per. 2.5 per. Mean 97.5 per. -3x ETF 2.887 2.917 2.944 2.861 2.917 2.973 2.819 2.918 3.022 2.703 2.921 3.142 -2x ETF 1.929 1.947 1.964 1.908 1.947 1.986 1.881 1.947 2.009 1.791 1.947 2.112 -1x ETF 0.962 0.972 0.981 0.953 0.972 0.993 0.940 0.972 1.006 0.900 0.973 1.058 1x ETF 0.963 0.973 0.984 0.952 0.973 0.996 0.934 0.968 1.012 0.883 0.973 1.068 2x ETF 1.925 1.946 1.964 1.909 1.947 1.984 1.887 1.949 2.021 1.801 1.954 2.102 3x ETF 2.888 2.917 2.946 2.862 2.918 2.974 2.821 2.917 3.018 2.711 2.918 3.116
4.2. Summary of observations on S&P 500 ETFs
From graph 4.1 could be expected that leveraged S&P 500 ETFs with positive exposure could have been a great investment for investors over the analysed period. However, this paper shows that the relation between the S&P 500 ETFs and the underlying index does not hold significantly for every period as indicated in appendix C. The market betas also deviate as the holding period increases and the volatility multipliers show the same effect. Furthermore, table 4.3 and table 4.4 indicate that the relation between the S&P 500 and their underlying index deviates as the holding period gets longer. These results show that investors cannot assume that a leveraged S&P 500 ETF mirrors the index perfectly. Thus, there can be concluded that the relation of the leveraged S&P 500 ETFs with regard to the underlying index does not hold enough to be long-term substitutes.
5. Analysis of long-term performance of gold ETFs
periods of high volatility and these ETFs are only benchmarked once a day at 15:00 p.m. The gold ETFs seem to have not been analysed in this way before.
5.1. Analysis of gold price leveraged ETFs
The descriptive statistics of the three different gold ETFs and of the underlying index (gold price) are captured in table 5.1. The data in the table is from the 30th of January 2009 until the end of December 2016. The 30th of January 2009 is chosen as this is the first measuring day of the ETFs in the database of IHS Markit. Table 5.1 indicates that the means of the ETFs are almost perfect to their promised exposure to the underlying index. Furthermore, the standard deviations and tracking errors increase as the levels of exposure increases of the different ETFs. The maximums and minimums are almost exact the opposite of their equivalents.
Table 5.1
This table provides a summary of the descriptive statistics of the underlying index (gold price) and the descriptive statistics of the gold ETFs with different levels of exposure with regard to the underlying index. The tracking error is
the divergence between the return of the specific ETF and the underlying index. The period analysed is from the 30th of January
2009 until the end of December 2016.
-2x ETF Gold price 1x ETF 2x ETF
Mean -0.043% 0.022% 0.020% 0.041% Median -0.064% 0.021% 0.019% 0.039% Maximum 18.291% 7.081% 7.084% 14.178% Minimum -14.090% -9.150% -9.150% -18.312% Standard deviation 2.285% 1.148% 1.148% 2.282% Tracking error 3.316% - 0.022% 1.145% Start date 1/30/2009 1/30/2009 1/30/2009 1/30/2009 Observations 1915 1922 1922 1917
Table 5.2 reports the long-term returns, market betas and corresponding overall return multipliers for a long buy and hold investment positon for 1, 3, 5 and 7 years from 30th of January 2009 in the different gold ETFs. In table 5.2 the long-term returns, market betas and corresponding overall return multipliers for gold ETFs are reported. It is interesting to notice from the table that the overall return multipliers are nowhere equal to their promised exposure for every ETF in the different holding periods. However, the daily market betas for the ETFs are almost equal to their promised exposures, which can be explained by the constant leverage trap and compounding problem.
Graph 5.1
This graph publishes a long buy and hold investment position in the gold price, the gold plain-vanilla ETF and the gold ETFs
with -2x and 2x exposure held from the 30th of January 2009 until the end of December 2016.
Table 5.2
This table reports the long-term returns, market betas and overall return multipliers of a long buy and hold investment position
of 1, 3, 5 or 7 years in the different gold ETFs started on the 30th of January 2009. The (overall return) multipliers are calculated
by dividing the n-year return of the ETF though the n-year return of the underlying index (gold price).
-2x ETF Gold price 1x ETF 2x ETF
1-year return 37.2% 16.3% 15.8% 23.9%
1-year market beta -1.998 1.000 1.995
1-year multiplier 2.28 0.97 1.46
3-year return -79.6% 79.2% 77.0% 153.5%
3-year market beta -1.998 1.000 1.994
3-year multiplier -1.01 0.97 1.94
5-year return -74.3% 41.3% 38.4% 39.4%
5-year market beta -1.999 1.000 1.996
5-year multiplier -1.80 0.93 0.95
7-year return -76.3% 35.7% 31.8% 18.5%
7-year market beta -2.000 1.000 1.997
7-year multiplier -2.14 0.89 0.52 0 20 40 60 80 100 120 140 160 180 200
30-jan-09 30-jan-10 30-jan-11 30-jan-12 30-jan-13 30-jan-14 30-jan-15 30-jan-16
Gold ETFs versus gold price
To analyse the long-term amplification capability of gold ETFs, again overlapping data returns are used. This is done in the same way as explained for the S&P 500 ETFs. With these data some scatters are plotted in appendix E. These scatters publish the n-day holding period returns of the gold ETFs versus the n-day holding period returns of the gold price. These scatters indicate that the promised leveraged ETF’s exposure remains constant and do not deviate when the holding period increases.
To study the promised exposure with regard to their underlying index the n-day holding period returns of the gold ETFs are regressed against the n-day holding period returns of the gold price with use of CAPM (Eq. 2). The regression is adjusted for autocorrelation with an autoregressive (AR) model and executed without a constant, as leveraged ETFs generated zero alpha. The volatility multipliers are also calculated for the gold ETFs. The results of the market betas, T-statistics, VOLMs and R-squared are reported in the tables in appendix F. These tables demonstrate that all market betas are equal to their promised exposure for the different holding periods. The market betas do not extremely deviate from their promised exposure even as the holding period increases. For example, the market beta for the 2x gold ETF with a 5-days holding period is 1.999, which is almost the same as the 1.988 market beta for the 2x gold ETF with a 252-days holding period. Also, the volatility multipliers are almost equal to the promised exposure, which means that investing in the gold ETFs almost exactly deliver the promised exposure in the short and long-term.
For the gold ETFs scatters are plotted for the n-day tracking error against the n-days realized standard deviation (volatility) for the same holding period. These scatterplots are given in appendix F and indicate that a higher realized standard deviation (volatility) comes with a higher tracking error.
as the holding period increases, however the market betas are almost equal to their promised exposure.
Table 5.3
This table reports the mean and 95 percentile confidence interval of the 700 market betas simulated with 1260 trading days and calculated for holding periods of 5, 21, 63 and 252 trading days for each S&P 500 ETF.
Period 5 21 63 252
Gold 2.5 per. Mean 97.5 per. 2.5 per. Mean 97.5 per. 2.5 per. Mean 97.5 per. 2.5 per. Mean 97.5 per. -2x ETF -2.004 -2.000 -1.996 -2.008 -2.000 -1.992 -2.014 -2.000 -1.987 -2.033 -1.990 -1.967 1x ETF 0.998 1.000 1.002 0.995 1.000 1.004 0.991 1.000 1.008 0.980 1.000 1.020 2x ETF 1.990 1.997 2.004 1.980 1.997 2.013 1.972 1.997 2.021 1.937 1.998 2.066
Table 5.4
This table reports the mean and 95 percentile confidence interval of the 700 volatility multiplier simulated with 1260 trading days and calculated for holding periods of 5, 21, 63 and 252 trading days for each S&P 500 ETF.
Period 5 21 63 252
Gold 2.5 per. Mean 97.5 per. 2.5 per. Mean 97.5 per. 2.5 per. Mean 97.5 per. 2.5 per. Mean 97.5 per. -2x ETF 1.996 2.000 2.005 1.993 2.000 2.008 1.987 2.000 2.014 1.967 2.000 2.034 1x ETF 0.998 1.000 1.002 0.995 1.000 1.004 0.992 1.000 1.009 0.981 1.000 1.020 2x ETF 1.991 1.998 2.004 1.980 1.997 2.012 1.974 1.998 2.023 1.938 1.999 2.066
5.2. Summary of observations on gold ETFs
Contrary to the S&P 500 ETFs, the relation between the gold ETFs and their underlying index is almost equal to their promised exposure in every holding period. The levels of exposure do not significantly deviate from their promised exposure if the holding period increases. Also, table 5.3 and 5.4 indicate that when the bootstrapping method is used the long-term relation does not extremely deviate from their promised exposure contrary to the S&P 500 ETFs. This means that investing in gold ETFs provides almost exactly the promised levels of exposure to the gold price. Therefore, gold ETFs could be attractive substitute investment instruments for investing in gold for short and long-term. The tradability of the gold ETFs can make them attractive alternatives to buying gold outright.
6. Analysis of long-term performance of crude oil ETFs
high volatility. The benchmark has no correlation with equity indices or gold and seems to have never been analysed in this way before.
6.1. Analysis of crude oil ETFs
The descriptive statistics of the two crude oil ETFs and the underlying index (crude oil) are reported in table 6.1. The data in this table is from the first of July 2009 until the end of December 2016. The first of July 2009 is chosen as this is the most historical date in the database of crude oil. The table indicates that the means are almost perfect their equivalents. In addition, the maximum and minimum of the 2x and -2x crude oil ETF are almost their equivalents. However, the maximums and minimums of the ETFs are not in line with the maximum and minimum of the underlying index.
Table 6.1
This table provides a summary of the descriptive statistics of the underlying index (crude oil) and the descriptive statistics of the crude oil ETFs with different levels of exposure with regard to the underlying index. The tracking error is the divergence between the returns of the specific ETF and the underlying index. The period analysed is from the 1st of July 2009 date until the end of December 2016.
-2x ETF Crude oil 2x ETF
Mean 0.072% -0.037% -0.077% Median 0.064% -0.043% -0.069% Maximum 20.477% 10.158% 43.699% Minimum -37.211% -10.231% -20.471% Standard deviation 4.169% 2.066% 4.200% Tracking error 6.219% - 3.746% Start date 9/1/2009 9/1/2009 9/1/2009 Observations 1874 1874 1874
Graph 6.1
This graph publishes a long buy and hold investment position in the crude oil ETFs and the crude oil price held from the 1st of
July 2009 until the end of December 2016.
Table 6.2
This table reports the long-term returns, market betas and overall return multipliers of a long buy and hold investment position
of 1, 3, 5 or 7 years in the different crude oil ETFs started on the 1st of July 2009. The (overall return) multipliers are calculated
by dividing the n-year return of the ETF though the n-year return of the underlying index (crude oil).
-2x ETF Crude oil 2x ETF
1-year return -3.7% -12.9% -32.2% 1-year beta -2.001 2.000 1-year multiplier 0.29 2.50 3-year return -42.7% -14.7% -47.0% 3-year beta -2.000 2.000 3-year multiplier 2.90 3.19 5-year return -69.0% 2.8% -29.9% 5-year beta -2.000 2.000 5-year multiplier -24.7 -10.7 7-year return 3.0% -69.0% -95.8% 7-year beta -1.996 2.007 7-year multiplier -0.04 1.39
Again, overlapping data returns are used to calculate the 5, 21, 63 and 252 trading day returns. With these overlapping data returns scatters are constructed for the different holding periods. In appendix H scatters are plotted of the n-day holding period returns of the crude oil ETFs versus the n-day holding period returns of the crude oil. These scatters indicate that the relation between the ETFs and the underlying index is expected to be almost perfect, but some outliers occur.
Next, the n-day holding period returns of the crude oil ETFs are regressed versus n-day holding period returns of the underlying index (crude oil) with the CAPM (Eq. 2). The regression is adjusted for autocorrelation with an autoregressive (AR) model and performed without a constant. In the tables in appendix I the market betas, T-statistics, volatility multipliers
0 20 40 60 80 100 120 140 160 180 200
30-jan-09 30-jan-10 30-jan-11 30-jan-12 30-jan-13 30-jan-14 30-jan-15 30-jan-16
Gold ETFs versus gold price
and adjusted R-squared are reported. These tables demonstrate that the market betas do not significantly deviate from their promised exposure in a holding period of 5, 21 or 63 trading days. However, for a holding period of 252 trading days, the market beta is significantly not equal to its promised exposure. The volatility multipliers show the same pattern as the market betas.
For these ETFs the n-day tracking error versus the n-day realized standard deviation (volatility) is regressed for the same holding period. These scatters are given in appendix J and these scatters indicate that the tracking error increases as the standard deviation (volatility) increases.
Again, the fact that overlapping data returns are used, the results could be biased. Thus, for the crude oil ETFs the stationary bootstrap method is applied with a simulation of 700 samples with 1260 days (5-years). Table 6.3 reports the 95 percentile confidence interval results of the market betas and table 6.4 reports the 95 percentile confidence interval results of the volatility multipliers. Table 6.3 indicates that the market betas over a holding period of 5 trading days have a smaller 95 percentile confidence interval than a holding period of 21, 63 or 252 days. For example, the 95 percentile for the 2x crude oil ETF with a holding period of 5-days is between 1.930 and 2.110 and the 95 percentile for the 2x crude oil ETF with a holding period of 252-days is between 1.686 and 2.407. Thus the relation of the ETFs deviates as the holding period increases. The relations also deviate for the volatility multipliers when the holding period increases as indicated in table 6.4.
Table 6.3
This table reports the mean and 95 percentile confidence interval of the 700 market betas simulated with 1260 trading days and calculated for holding periods of 5, 21, 63 and 252 trading days for each S&P 500 ETF.
Period 5 21 63 252
Crude oil 2.5 per. Mean 97.5 per. 2.5 per. Mean 97.5 per. 2.5 per. Mean 97.5 per. 2.5 per. Mean 97.5 per. -2x ETF -2.081 -1.997 -1.927 -2.100 -1.997 -1.903 -2.142 -1.998 -1.863 -2.276 -1.998 -1.733 2x ETF 1.930 2.005 2.110 1.911 2.005 2.153 1.859 2.006 2.214 1.686 2.012 2.407
Table 6.4
This table reports the mean and 95 percentile confidence interval of the 700 volatility multiplier simulated with 1260 trading days and calculated for holding periods of 5, 21, 63 and 252 trading days for each S&P 500 ETF.
Period 5 21 63 252
6.2. Summary of observations on crude oil ETFs
The crude oil ETFs deliver their promised exposure for holding periods of 5, 21 and 63 trading days. However, as the holding period increase to 252 trading days the market betas significantly deviate from their promised exposure. In addition, the market betas between the crude oil ETFs and their underlying index increase as the holding periods increase. The CAPM and the stationary bootstrap method show that in the long-term (one year) the relation between the crude oil ETF and their underlying index is significantly different and the relation expands when the holding period increases. Therefore, crude oil ETFs do not perfectly mirror their underlying index and are not suitable for long-term index tracking investing. Hence, crude oil ETFs can be considered as substitute investment instruments for short-term investing in crude oil only. The tradability of crude oil ETFs allows investors to unwind when their vision changes.
7. Conclusion
In this paper, the long-term performance of plain-vanilla and leveraged ETFs versus their underlying indices are studied. In particular leveraged ETFs are studied with three different underlying indices, namely the S&P 500, gold price and crude oil. Overlapping data returns are analysed with the use of CAPM to analyse the long-term performances. In addition, the stationary bootstrapping method is used to generate more samples and to better understand the parameter range.
The S&P 500 ETFs analysis indicates that the relation between the S&P 500 and the leveraged ETFs does not hold for the different holding periods. In addition, the 95 confidence interval of the market betas and volatility multipliers expands as the holding period increases. Thus, leveraged S&P 500 ETFs do not mirror the performance of the S&P 500 and are not suitable as long-term index tracking investment instruments. This is in line with the findings of Lu et al. (2009).
(2015) and Hill and Foster (2009) that ETFs could be used for long-term investing and could be used in aggressive portfolios.
However, investors investing in any leveraged ETF should take into consideration the constant leverage trap and compounding problem that lead to overall returns which are not equal to their promised exposure. Investors should also be aware of the higher expense ratios and risks associated with investing in leveraged ETFs. Furthermore, investors should have enough market knowledge and should understand the characteristics of the underlying indices, because the performance of leveraged ETFs depend fully on the performance of their underlying indices as leveraged ETFs are path-dependent.
Leveraged ETFs are expected to become more popular and used in the future. PWC rapports expect that the growth of ETFs will continue over the next five years, with more than 41% of the participants predicting that global ETFs’ AUM will reach at least US$7.0 trillion by 202122 versus US$3.9 trillion now. Therefore, leveraged ETFs are a fertile area for future research. The long-term performance of leveraged ETFs will remain under discussion in the future. Our recommendation for further research is to analyse the long-term performance of other leveraged ETFs with different underlying indices. Additionally, the influence of the constant leverage trap, compounding problem and path-dependency of leveraged ETFs seem a fertile area for future research. Further analysis about the positive and/or negative side of these influences using Monte Carlo simulations with different scenarios of a random underlying index is also recommended.
A limitation of this research could be that only three underlying indices were studied, thus the conclusions on long-term performance are only considered for these three underlying indices.
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